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K-CM application for supervised pattern recognition at Mt. Etna: an innovative tool to forecast flank eruptive activity

July 2019
Bulletin of Volcanology 81(7)

DOI:10.1007/s00445-019-1299-4

Authors:

Alfonso Brancato

Istituto Nazionale di Geofisica e Vulcanologia

Massimo Buscema

Semeion Centro Ricerche di Scienze della Comunicazione

Giulia Massini

Semeion Centro Ricerche di Scienze della Comunicazione

Stefano Gresta

University of Catania

Show all 6 authorsHide

We investigated the relationship between the temporal monitoring series routinely recorded at Mt. Etna and the flank eruptions that occurred between January 2001 and April 2005 by the K-contractive map (K-CM) method pattern classifier with supervised learning. The reference dataset includes 28 variables and 1580 records collected over 52 months for a total of 301 eruptive days. A two-step analysis was performed. In the first step analysis, we used the 28 parameters of each day to recognize anomalies heralding a flank eruption. K-CM estimated a sensitivity higher than 95% and a specificity close to 100%. In the second step analysis, we considered each record comprising the 28 variables for 6 days as an input (for a total of 180 inputs) and the outcomes of the seventh day as an output to predict eruption or rest. In this case, K-CM showed sensitivity and specificity close to 98% and 100%, respectively. Results highlight the reliability of the K-CM method to build up a prediction algorithm able to alert the volcano experts a day before the occurrence of a potential flank eruption. The robustness of the two analyses was investigated by the behavior of the receiver operating characteristic curve. The relative area under the curve showed values close to 1, thus providing a valid measure of the performance of the classifier. Finally, a complete overview of the performance levels of the method used was explored analyzing the retrieved Molchan error diagram, in both cases, trajectories very close to the theoretical minimum.

Selected time evolution of the monitoring parameters employed in the present study. For each series, data are normalized to the relative maximum value (for graphical display). Also shown (top of the panel) the eruptive activity at Mt. Etna (in terms of lava flow) which occurred

…

The semantic map of the 28 variables (for a relative legend, see Table 1) of the dataset that synthesizes their strongest similarity relationships providing important information about the relevance of the variables and how they relate to each other. It is possible to highlight a group

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Selection of the monitoring values collected during different periods (see Table 1 for relative parameters). Each period spans 30 days of Mt. Etna volcanic activity. In particular, each time series starts 20 days before the onset of the July-August 2001 (blue line), October 2002-

…

ROC curve (red solid line) for the first experiment (a) and second experiment (b), respectively. The dashed line means an AUC equals to 0.5 (i.e., TP and FP proportions are equal). Note that even for high specificity values, i.e., around zero on the x-axes, the sensitivity is very high. The value of the AUC is in fact close to 1

…

Molchan diagrams for the first (a) and the second experiment (b), respectively. The dashed line means a random guess (i.e., the curve of model equivalence; de Arcangelis et al. 2016). The red solid line shows the confidence level

…

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RESEARCH ARTICLE

K-CM application for supervised pattern recognition at Mt. Etna:

an innovative tool to forecast flank eruptive activity

Alfonso Brancato

&Paolo Massimo Buscema

2,3

&Giulia Massini

&Stefano Gresta

&Giuseppe Salerno

Francesca Della Torre

Received: 27 August 2018 / Accepted: 18 May 2019

#International Association of Volcanology & Chemistry of the Earth's Interior 2019

Abstract

We investigated the relationship between the temporal monitoring series routinely recorded at Mt. Etna and the flank eruptions

that occurred between January 2001 and April 2005 by the K-contractive map (K-CM) method pattern classifier with supervised

learning. The reference dataset includes 28 variables and 1580 records collected over 52 months for a total of 301 eruptive days.

A two-step analysis was performed. In the first step analysis, we used the 28 parameters of each day to recognize anomalies

heralding a flank eruption. K-CM estimated a sensitivity higher than 95% and a specificity close to 100%. In the second step

analysis, we considered each record comprising the 28 variables for 6 days as an input (for a total of 180 inputs) and the outcomes

of the seventh day as an output to predict eruption or rest. In this case, K-CM showed sensitivity and specificity close to 98% and

100%, respectively. Results highlight the reliability of the K-CM method to build up a prediction algorithm able to alert the

volcano experts a day before the occurrence of a potential flank eruption. The robustness of the two analyses was investigated by

the behavior of the receiver operating characteristic curve. The relative area under the curve showed values close to 1, thus

providing a valid measure of the performance of the classifier. Finally, a complete overview of the performance levels of the

method used was explored analyzing the retrieved Molchan error diagram, in both cases, trajectories very close to the theoretical

minimum.

Keywords Mt.Etna volcano .Flankeruption .Monitoringdatacomplexsystem .Neuralnetworks .Supervisedpatternrecognition

Introduction

Machine Learning (ML) is a subset of the vast world called

artificial intelligence, which is based on a natural computation

(NC) that opposes classical computation. While classical

computation entrusts the drafting of the rules of the studied

phenomenon to a group of experts, which evaluates how much

hypothesis are able to describe it (top down approach), NC lets

the rules emerge spontaneously from data. This approach is

made up of models that generate further models by adapting to

Editorial responsibility: S. Vergniolle

*Alfonso Brancato

alfonso.brancato@ingv.it

Paolo Massimo Buscema

m.buscema@semeion.it

Giulia Massini

g.massini@semeion.it

Stefano Gresta

gresta@unict.it

Giuseppe Salerno

giuseppe.salerno@ingv.it

Francesca Della Torre

f.dellatorre@semeion.it

Istituto Nazionale di Geofisica e Vulcanologia-Osservatorio Etneo,

Piazza Roma, 2 - 95123 Catania, Italy

Semeion Research Center of Sciences of Communication, Via

Sersale, 117 - 00128 Rome, Italy

Department of Mathematical and Statistical Sciences, University of

Colorado, Denver, CO, USA

Dipartimento di Scienze Biologiche, Geologiche e Ambientali,

Sezione di Scienze della Terra, Università di Catania, Corso Italia,

57 - 95129 Catania, Italy

Bulletin of Volcanology (2019) 81:40

https://doi.org/10.1007/s00445-019-1299-4

the data examined (bottom-up approach; Ballard 1999;Arbib

1995; Buscema and Tastle 2013). Recent years have seen an

exponential increase in data availability in several fields. This

has led the need to determine specific models for each of the

field considered which take into account the complexity of the

information in recorded data (McKinsey Global Institute

2011). In particular, the power of these models has offered

the opportunity to analyze and make explicit Bmany to many^

relationships, i.e., to perform a multivariate analysis of com-

plex phenomena. In this context, artificial adaptive algo-

rithms, capable of handling large and complex set of data,

have proven to be the ideal tool. Among these algorithms,

deep learning has shown to be of considerable effectiveness

(Bengio 2009). Artificial neural networks (ANNs) are one of

the most significant tools in multivariate analysis thanks to

their ability to deal with the non-linear behavior of a complex

system (Buscema et al. 2014). In this paper, we explore the

potential and emerging use of the K-Contractive Map (K-CM)

classification method (Buscema et al. 2014) in volcanic

processes.

A volcano can be considered as a complex system (Langer

et al. 2003;Brancatoetal.2016), whose structure and com-

ponents may change dynamically due to local and/or regional

geodynamical interactions, while retaining its cohesion in

space-time. Thus, through its changeable behavior, volcanoes

generate new data over time, covering from a long- to short-

temporal scale (e.g., Newhall and Hoblitt 2002;Martinetal.

2004; Brancato et al. 2011). We can thus define volcanoes as

natural adaptive systems, which means that volcanic processes

will interact spatially and temporally to produce outputs

(Smits 2015). Due to its complexity, this type of system has

a highly non-linear behavior and understanding of its dynam-

ics may be achieved by inverting and cross-correlating record-

ed multiparametric time series (Brancato et al. 2016).

Processes of unrest occurring at volcanoes and preceding

eruptions maybe considered as precursors that could be used

for forecasting (Marzocchi et al. 2004; Martin et al. 2004;

Brancato et al. 2011,2012; Selva et al. 2012; Tonini et al.

2016). Information on processes occurring in the volcanic

dynamics may be used to detect eventual changes in the vol-

cano’s state (Martin et al. 2004;Brancatoetal.2011,2012;

Tonini et al. 2016), though sub-surface processes are observ-

ably these directly (Mader 2006).

Mt. Etna is located along the Ionian coast of eastern Sicily

(Fig. 1) and has undergone both effusive and frequent explo-

sive basaltic eruptions over the last 500 ky ago (Branca et al.

2008,2011). This persistent and dynamic activity has focused

attention on the associated volcanic risk posing a challenge for

the Italian Civil Protection, stakeholders, and other decision

makers. Questions asked include BWhen and where will erup-

tions occur?^and BHow long will eruptions last?^, and there

is a pressing need to reduce uncertainty in forecasting given

the densely inhabited area around the volcano, where a million

people live in vulnerable areas (e.g., Bonaccorso et al. 2004;

Crisci et al. 2010; Barreca et al. 2012). Though summit erup-

tions (e.g., short-lived lava fountains) are the most frequent

phenomena at Mt. Etna (e.g., Andronico and Corsaro 2011;

Bonaccorso and Calvari 2013), major crises have been usually

associated with lava flows on the volcano flanks, which may

persist for weeks to years (Barberi et al. 1992; Calvari and

Pinkerton 1998; Andronico and Lodato 2005; Aloisi et al.

2009;Harrisetal.2011).

Mt. Etna is one of the best-monitored volcanoes in the

world (Bonaccorso et al. 2004;Mattiaetal.2015), and the

vast quantity of multidisciplinary recorded available offers a

good opportunity to thoroughly investigate hidden informa-

tion potentially associated with the dynamics of a volcanic

system (e.g., Patanè et al. 2013; Spampinato et al. 2015;

Corsaro et al. 2017). The objective of this work is to pinpoint

days during which flank eruptions at Mt. Etna might occur by

looking at changes in the state of the volcano. Our aim is to

define two states: Bin a flank eruption^(i.e., erupting) and

Bnot in a flank eruption^(i.e., quiescent,namelyrest).The

assumption is, if the volcano is not in a flank eruption today,

it is very likely it will not be tomorrow, and conversely, if a

flank eruption has started, it is very likely it will continue

tomorrow. Furthermore, we aim to determine if any changes

that occur before and during an eruption may be used to fore-

cast the onset and the end of a flank eruption, respectively.

The K-CM method is an application of the most general

Contractive Map (CM) technique (Buscema et al. 2018), be-

ing specifically designed to solve supervised pattern recogni-

tion (i.e., classification) problems by using the k-Nearest

Neighbor (kNN) criterion (Hastie et al. 2009). Classification

is defined as the process of assigning objects to a class. A

number of features are used to mark out these objects, and

the resulting set constitutes a vector, namely the pattern (also

known as record). According to the contractive map tech-

nique, because of its equations, K-CM determines a contrac-

tion of the input during the learning phase of the network. This

process, as better explained later in the text, determines what is

called learning that is the ability of the network to generalize

what seen in the known database, to unknown cases. K-CM

has already been successfully applied in classification tasks

(Buscema et al. 2014; Grossi et al. 2017). The philosophy

behind the K-CM classification method and technical details

is reported in Appendix 1.

K-CM classification is one of the current methodologies in

multivariate analysis that can find a mathematical model to

recognize the membership of samples to their proper class.

Here, we present the results of an application of the K-CM

pattern classifier with supervised learning at Mt. Etna. A two-

step analysis was performed on data recorded between

January 2001 and April 2005 focusing on the relationships

between geophysical (seismic, ground deformation, gravimet-

ric), geochemical (SO

and CO

fluxes), and volcanological

40 Page 2 of 19 Bull Volcanol (2019) 81:40

activity (mainly ash emission) records and the status (i.e.,

eruptive or not) of the volcano. It means that, in our modelling,

each record, i.e., each day characterized by geophysical, geo-

chemical, and volcanological parameters recorded in the same

day, must belong to one of the two classes: eruptive day or

non-eruptive day. The K-CM classifier is trained to predict

changes in volcanic activity (eruption or rest) forecasting be-

ing made 1 day in advance. Analysis was performed using the

same monitoring dataset used in Bayesian modelling for erup-

tion forecasting by Brancato et al. (2011), with the objective to

identify any discrepancies between the two methods and/or

new outcomes offered by the application of the K-CM ap-

proach. The use of a sophisticated neural network, such as

K-CM, allows the creation of a fully data-driven model with-

out the need to introduce any a priori theoretical knowledge

regarding the problem ora priori beliefs. It is alsoa completely

different strategy involving complex adaptive systems rather

than being based on the concept of event tree as in the

Bayesian Event Tree model previously used. Finally, we em-

phasize that the K-CM analysis is not focused on the likely

feedback of the pattern recognition to inform on the underly-

ing volcanic processes, meaning that scope of our study is not

to model how Mt. Etna works but to deliver a forecasting tool.

Material and methods

Monitoring dataset

Intensive monitoring at Mt. Etna, both routinely and during

dedicated campaigns (for the latter, a linear interpolation was

used to estimate the missing data), has generated time series

data of seismicity (earthquakes), ground deformation, gas

emission, microgravity, and petrology as listed in Table 1.

Fig. 1 Sketch map of Mt. Etna

volcano. Green, yellow, blue, and

red triangles indicate the

geochemical, ground

deformation, gravity, and tilt

sensor locations, respectively (as

listed in Table 1). Yellow solid

lines indicate the ground defor-

mation profiles used in this study.

The contour lines at 500 m inter-

vals and the urbanized areas are

shown. Main towns are also la-

belled (modified from Brancato

et al. 2016)

Bull Volcanol (2019) 81:40 Page 3 of 19 40

We are aware that interpolation is not appropriate for a pre-

diction tool, since it cannot be used to project into the future;

thus, we only used interpolation for short rest periods at Mt.

Etna. All 28 selected monitoring parameters (Nvariables;

Tab le 1) represent a multidisciplinary dataset intended to pro-

vide a detailed picture of the quiescent background state of Mt.

Etna. The reader has to focus that each of the 28 variables

represents an operational variable for overall pattern recognition

rather than providing individual independent field observations,

as clearly indicated by the clinometric parameters. CDV data,

recorded at CDV station (Fig. 1), perform both independently

(Clinometric measurement (CDV station) or Clinometric vari-

ation (> 0.033 μrad day

−1

; CDV station) or Clinometric varia-

tion (CDV station); CDV, tilt_var_0.033_CDV and var_CDV,

respectively; Table 1) and together with other tilt data (Variation

of the Clinometric mean (CDV=Casa Del Vescovo, MNR=

Monte Nero, MSC= Monte Scavo stations) or Clinometric

mean (CDV, MNR, MSC stations); tilt_var_3stat and

stat_mean, respectively; Table 1) to derive different variables

to describe different volcanic scenarios. The merging is useful

as the tilt network reflects the final intrusive phase by causing

changes at most stations with an amplitude related to source-

station distance (i.e., a high variation for a closer station and a

smaller one for a distal station; Ferro et al. 2011). In detail, these

phases are usually preceded by large variations (up to over

100 μrad; Gambino et al. 2014).

ThetimeseriesspansJanuary2001–April 2005 (a total

of 1580 records), during which Mt. Etna underwent the

July–August 2001, the October 2002–January 2003, and

the September 2004–March 2005 flank eruptions, with a

total of 301 eruptive days. This reference period was cho-

sen as it includes most of the flank events, which have

occurred at Mt. Etna over the last few decades. A further

flank eruption that occurred between May 2008 and

Table 1 List and relative units of the 28 variables of the dataset collected at Mt. Etna

Variable Units Abbreviation

M. Silvestri-Bocche 1792 line μstrain day

−1

SerPiz_MtStemp 0.07 1 1

Serra Pizzuta-M. Stempato line μstrain day

−1

MtSil_Bocche1792 0.07 1 1

Deformation Pernicana Fault cm day

−1

vel_def_Pern 0.07 1 1

Gravity (FM4 station) μgal day

−1

grav_FM4 0.07 1 1

Clinometric variation (MSC station) μrad day

−1

var_MSC 0.07 1 1

Variation of the Clinometric mean (CDV, MNR, MSC stations) μrad day

−1

tilt_var_3stat 0.07 1 1

Clinometric variation (CDV station) μrad day

−1

var_CDV 0.07 1 1

(P78 station) g m

−2

day

−1

_P78 0.13 1 1

Areal dilatation μstrain day

−1

ar_dil 0.14 1 1

Number of VT earthquakes (M=2+;Wsector) Eventday

−1

eqs_W_Sect 0.20 1 1

Number of VT earthquakes (D< 5 km) Event day

−1

eqs_D < 5 km 0.20 1 1

Number of VT earthquakes (M=1+) Eventday

−1

eqs_volc 0.20 1 1

Number of earthquakes (D≥200 km; M= 5+; Tyrrhenian slab) Event day

−1

eqs_slab_Tyrr 0.20 1 1

Number of VT earthquakes (M= 3+; Pernicana Fault) Event day

−1

eqs_Pern 0.20 1 1

Number of VT earthquakes (D≥20 km; M= 3+; NW sector) Event day

−1

eqs_NW_Sect 0.20 1 1

Ash emission No units ash 0.20 3 2

Clinometric variation (MNR station) μrad day

−1

var_MNR 0.25 1 1

emission t day

−1

0.25 1 1

W flank dilatation Strain day

−1

dil_W 0.73 4 6

Clinometric variation (> 0.033 μrad day

−1

; CDV station) No units tilt_var_0.033_CDV 0.73 4 6

Gravity (PL station) μgal day

−1

grav_PL 0.73 4 6

Clinometric measurement (MNR station) μrad day

−1

MNR 0.94 3 4

Clinometric mean (CDV, MNR, MSC stations) μrad day

−1

stat_mean 0.94 4 7

(P39 station) g m

−2

day

−1

_P39 1.00 4 7

Sideromelane No units sideromelane 1.04 3 5

Clinometric measurement (MSC station) μrad day

−1

MSC 1.23 4 8

Number of seismic swarms (> 30 earthquakes day

−1

) No units eqs_swarm 2.78 2 5

Clinometric measurement (CDV station) μrad day

−1

CDV 4.17 4 15

Columns 4–6 report the estimates of the Association Strength S

,theNode Centrality C

, and the Node Degree D

, respectively. The list is sorted based on

the S

column

Code given to the variable name for software purposes

40 Page 4 of 19 Bull Volcanol (2019) 81:40

July 2009 was not considered since there was a switch to

continuous acquisition starting from late 2005. This led to

a complete change in the dataset.

We point out that the analysis in Brancato et al. (2016),

though used the same dataset, provided different results by

using different techniques (i.e., genetic algorithms).

Brancato et al. (2016) showed a pattern recognition rather

than a predictive outcome, testing whether certain ma-

chine learning techniques performed on a series of signals

(i.e., monitoring data) could estimate the typical distribu-

tion of eruptive activity onset. The authors implemented a

selection of the most predictive monitoring series, reduc-

ing the initial dataset (i.e., 28 variables) usually run for

Bayesian probability estimates to 11 variables (Brancato

et al. 2011).

The dataset here is a revised form of that used to forecast

flank eruptions at Mt. Etna with a Bayesian Event Tree ap-

proach, after an expert elicitation (Brancato et al. 2011). The

current dataset includes only the temporal series (recorded

and/or collected values) of any monitored parameter

(Table 1), neglecting the inertia and anomalies information

needed for the former application (see Brancato et al. 2011).

Brancato et al. (2011) refer to inertia as the timescale during

which the parameter evolves, according to the belief of an

expert, towards a more anomalous value, which indicates a

change in volcanic state (e.g., from a magmatic unrest to an

eruption). For the sake of clarity, different timescales of days

to weeks/months/years were reported (Brancato et al. 2011).

The revision process exploits the capacity of the machine

learning approaches to objectively pinpoint hidden links be-

tween the monitoring data and the state of Mt. Etna (quiescent

or eruptive). The approach allowed also to avoid any model-

ling of the underlying volcanic processes and the associated

dependence on the subjective view of the modeller, primarily

in selecting the thresholds and inertias of the involved moni-

toring parameters. Specifically, the role of machine learning

techniquesis based on detecting anomalies in the dataset with-

out any specific setting for the anomaly.

Seismic monitoring has convincingly demonstrated that

flank eruptions at Mt. Etna are often preceded by earthquake

unrest (e.g., Brancato and Gresta 2003; Patanè et al. 2003;

Feuillet et al. 2006), on timescales of a few days to weeks.

The different seismic parameters are spatially relevant. In oth-

er words, different locations imply different links to the vari-

ous volcanic stages (from unrest phase to eruption) of Mt.

Etna. Earthquakes occurring in the Tyrrhenian slab (Number

of earthquakes (D≥200 km; M= 5+; Tyrrhenian slab);

eqs_slab_Tyrr; Table 1) and along the Pernicana Fault

(NumberofVTearthquakes(M= 3+; Pernicana Fault);

eqs_Pern; Table 1, as well as deep seismicity in the NW sector

(Number of VT earthquakes (D≥20 km; M= 3+; NW sector);

eqs_W_Sect; Table 1) of Mt. Etna, reveal early stages of deep

magma movements (unrest phase). Conversely, shallower

seismicity (depth less than 5 km; Number of VT earthquakes

(D< 5 km); eqs_D < 5 km; Table 1)depictsastrongmagma

involvement (Brancato and Gresta 2003; Patanè et al. 2003).

Such seismicity is mainly clustered (Number of seismic

swarms (> 30 earthquakes day

−1

); eqs_swarm; Table 1), being

likely related to a fracturing field on the flanks of the edifice

(Brancato and Gresta 2003). In particular, eqs_swarm features

a variable with a time and frequency definition (30 events/

day) of earthquakes clustered anywhere on the Mt. Etna edi-

fice, usually indicating the location of the vent zone (flank

eruption occurrence).

Ground deformation sampling campaigns on monthly

timescales, which become daily when magma reaches the vent

zone, are highly useful indicators of existing volcanic activity

(Bonaccorso et al. 2004,2006;Aloisietal.2006;Bonforte

et al. 2007). We differentiate the relative monitoring by con-

sidering GPS, electronic distance measurements (hereafter,

EDM), and tilt variables. The anomalies of the GPS variables

(W flank dilatation and Deformation Pernicana Fault; dil_W

and vel_def_Pern, respectively; Table 1) are usually associat-

ed with a ductile behavior induced by the plumbing system,

while anomalies of the EDM variables (M. Silvestri-Bocche

1792 baseline, Serra Pizzuta-M. Stempato baseline and areal

dilatation; SerPiz_MtStemp, MtSil_Bocche1792, and ar_dil;

Tab le 1) give first-order information about the inflation/

deflation state of Mt. Etna. Specifically, EDM monitors the

horizontal component of ground deformation. From the end of

the 1970s, three separate networks operated at Mt. Etna: on

the northeastern, western, and southern flanks. In particular,

the M. Silvestri-Bocche 1792 and Serra Pizzuta-M. Stempato

baselines (Table 1and Fig. 1) provide insights into the spread-

ing of the SE and the middle part of Rift S, respectively, when

an extension (due to a magmatic intrusion?) occurs on the

well-known NNW-SSE structures. Conversely, tilt data, due

to the timescales of a few hours to days, are indicators of the

rapid evolution of the internal magma movements immediate-

ly preceding the onset of flank activity (Ferro et al. 2011;

Gambino et al. 2014). The different sites cover the sectors of

Mt. Etna (Fig. 1) that underwent most of the recent flank

activity. In particular, tilt_var_0.033_CDV (Table 1)variable

gives information about the early stage of an unrest phase,

whereas CDV and var_CDV (Table 1) variables (similar to

Clinometric measurement (MNR station) or Clinometric var-

iation (MNR station) and Clinometric measurement (MSC

station) or Clinometric variation (MNR station) (MNR,

var_MNR, MSC, and var_MSC, respectively; Table 1) are

linked to the final magma intrusion during the onset of flank

activity at Mt. Etna. On the other hand, tilt_var_3stat and

stat_mean (respectively; Table 1) may describe the stages

linked to the internal movement of the magma towards the

surface of the volcano.

Analysis of gas emissions, both observed remotely from

the volcanic plume as bulk contribution from all summit

Bull Volcanol (2019) 81:40 Page 5 of 19 40

craters (SO

emission, SO

; Table 1) and directly from the soil

(CO

(P39 station) and CO2 (P78 station); CO2_P39 and

CO2_P78; Table 1and Fig. 1), provides insights into the mag-

matic feeding system of Mt. Etna from the deep to the shallow

part of the volcano edifice, with timescales from weeks to

months (e.g., Badalamenti et al. 2004; Caltabiano et al.

2004; Salerno et al. 2018). An increase in bulk SO

emission

has been shown to relate to the ascent of a new batch of gas-

rich magma from a shallow zone of 3–4 km beneath summit

craters (e.g., Sutton et al. 2001; Caltabiano et al. 2004; Salerno

et al. 2018). Conversely, anomalies in CO

flux suggest em-

placement of undegassed magma at ~ 12 km (e.g., Notsu et al.

2006; Spilliaert et al. 2006; Giammanco et al. 2012). In our

study, temporal anomalies at P39 site (Fig. 1)indicateexsolu-

tion from depths of ca. 12 km, while anomalies in CO

flux at

P78 site indicate shallower magma movements from depths of

ca. 4 km (Giammanco et al. 2012).

Anomalies in microgravity measurements (Gravity (FM4

station) and Gravity (PL=Punta Lucia station) variables;

grav_FM4 and grav_PL, respectively; Table 1)havealsobeen

observed a few months before the eruption onset (Carbone

et al. 2003; Carbone and Greco 2007). Both series are record-

ed at PL and FM4 stations (Fig. 1), which represent the sites

where the maximum variation was observed (Carbone et al.

2003). The PL sensor belongs to the N-S profile, which is

aimed at observing magma rising from any particular direc-

tion, while the FM4 sensor belongs to the E-W profile, de-

signed to observe the dynamics of the southern flank of the

Mt. Etna edifice.

Figure 2shows the (normalized) monitoring time series

used for the current analysis, which evidence variations in

both magnitude and temporal scale in connection with the

observed eruptive activity at Mt. Etna. In particular, all the

selected series show significant variations before the July–

August 2001 and October 2002–January 2003 flank erup-

tions. No particular trend (either increasing or decreasing) is

observed, with the sole exception of CDV variable values

(gray solid line; Fig. 2) which shows a continuous decreasing

trend after the end of the July–August 2001 eruption. Finally,

none of the selected data show anomalous values before the

September 2004–March 2005 flank event but instead show

significant variations a few days before the end of the relative

eruptive activity (Fig. 2).

Other monitoring data commonly include petrologic obser-

vations (Ash emission and Sideromelane; ash and

sideromelane, respectively; Table 1) of the volcanic rocks.

Analysis of the physical and chemical properties of emitted

volcanic rocks can provide important constraints for model-

ling. In particular, the presence of sideromelane in volcanic

ash is indicative of a fresh magma injection, hence a possible

Fig. 2 Selected time evolution of the monitoring parameters employed in

the present study. For each series, data are normalized to the relative

maximum value (for graphical display). Also shown (top of the panel)

the eruptive activity at Mt. Etna (in terms of lava flow) which occurred

during the January 2001–April 2005 period. It is evident how the

September 2004–March 2005 flank episode was not heralded by any

anomalous monitoring recording

40 Page 6 of 19 Bull Volcanol (2019) 81:40

precursor of imminent flank activity at Mt. Etna (Andronico

et al. 2009; Corsaro et al. 2017).

Auto-CM algorithm application

Time series, and their relationship with the eruptive activity of

Mt. Etna, was explored performing a two-step analysis. The

first analysis is a classical problem of pattern recognition. For

any day (i.e., any record), we considered the 28 values of the

variables of the day before as input for the K-CM algorithm.

To evaluate the correct learning of a network, it is necessary to

verify its ability to predict cases never seen before. For this

reason, it is usual to divide the sample into two subsets, called

training set and testing set. For both subsamples, we know the

class of belonging of each record (in this case, eruptive or non-

eruptive) called target value. The learning is carried out on the

training set showing to the neural network both the record and

the relative class of belonging. Then, we try to predict the

target value of the testing set in a test called blind. The net-

work, on the basis of what has been learned about the training

set, will assign a class to each of the testing records. At this

point, it will be possible to verify the percentage of correct

forecasts and the percentage of errors. Both training and test-

ing sets include 1580 patterns each. Leave One Out (LOO)

testing protocol (see Appendix 1) was used to validate relative

outcomes. This type of analysis allowed to assess whether the

system is able to predict the state of the volcano the next day,

based on the data recorded the previous day, and provide

volcanologists with essential information and alerts. In the

second step analysis, we applied a moving window with a

length of 6 days to compute the probability of each target

(eruption or rest) for the seventh day. Thus, for each day, we

codified the 28 × 6 = 168 values of the variables and the rela-

tive 2 × 6 = 12 outcomes (both targets for each day) for a total

of 180 inputs. After that, we codified the outcome of the sev-

enth day as output. We then divided the sample of 1574 (=

1580–6) days into two subsamples (787 records each) follow-

ing a chronological scheme. This type of experimentation fo-

cuses upon the possibility to assess whether the system is able

to predict the state of the volcano on the seventh day, based on

the data recorded during the previous week. The information

in this case becomes even more valuable as the time for pos-

sible intervention is longer. For this step analysis, since each

record is linked to the previous one by a time relation, it is not

possible to perform a random training-testing set division, but

it is necessary to consider the time. For this reason, the neural

network was trained on the first 784 records and tested on the

last 784.

The training set spans the period from 7 January 2001 to 4

March 2003 and the testing set from 5 March 2003 to 29 April

2005. The training set includes anomalies in the monitoring,

better interpreted as precursors and linked to the early stages

of the July–August 2001 and October 2002–January 2003

flank eruptions at Mt. Etna. The testing set covers a period

during which no anomalies are present in the relative moni-

toring dataset despite the September 2004–March 2005 flank

eruption occurrence. The dataset analyzed within the first ex-

periment had a total of 44,240 values (i.e., N=28 variables

multiplied by 1580 records) to be processed. When submitted

to the auto-contractive map (Auto-CM) algorithm for the

learning session, the dataset was structured so that the vari-

ables were the hyperpoints and the records were the

hyperpoint coordinates. This is because we are more interest-

ed in understanding how the variables are related to each other

in terms of non-linear correlation rather than records.

After 24,625 epochs (i.e., a classic measure of ANNs learn-

ing phase: the number of times the ANN examines the whole

dataset), the K-CM, with a contraction parameter

C=√N=√28 = 5.292, is fully trained (RMSE = 0.1322). The

Cvalue is the only parameter in the Auto-CM neural network

to be set before learning. It tunes the transmission of the input

into the hidden layer by compressing it with respect to a factor

that depends on Citself and on the values of the connections.

Therefore, the value of the parameter Ccontrols the actual

extent of the contraction, thereby explaining its interpretation

as the contraction parameter (Buscema et al. 2018)from

which the name of the network derives. Experience shows that

the choice of C=√Nis often the optimal one (Buscema et al.

2018).

Once the learning was finished, the Wweight matrix was

determined. As explained in more detail in Appendix 1,the

matrix N×Nof the weights contains, for each entry, the value

of similarity between variable iand variable j. Similarity

denotes a measure of association between two values or how

much two variables tend to be present together (Fig. 3).

Similarity and distance are two closely related concepts be-

cause the more two variables are similar, the less distant they

will be if thought as hyperpoints of a metric hyperspace.

Conversely, the less similar they are, the more distant they

will be. It is therefore possible to calculate the Maximum

Regular Graph (MRG) graph (see Appendix 1)tobetterun-

derstand the hidden relations between the variables and to

perform fuzzy profiling of each record for prediction opera-

tions. As for the graph, all the entries (weights) are scaled with

respect to the theoretic maximum value (i.e., the contraction

parameter C) into the range [0, 1] and all the similarity values

are translated in terms of distances. This technical step is nec-

essary because the algorithms used are based on the minimi-

zation of distances instead of the maximization of similarities

even though they are conceptually the same feature. The clas-

sic method to obtain such a transformation is to consider the

complement to one of the similarity values (i.e., d

=1−s

,so

that high s

values determine low d

values and vice versa).

The dvalue is therefore a distance index providing a value in

the range [0, 1] of how far two variables are from each other.

We point out that we are considering a distance index and not

Bull Volcanol (2019) 81:40 Page 7 of 19 40

distance in the strict metric sense because some of the neces-

sary properties cannot be verified. Then, the highest values

among the variables of the weight matrix entries are consid-

ered in the MRG undirected graph construction. It should be

noted that in the construction of the Minimum Spanning Tree

(MST)(seeAppendix1), and therefore of the MRG, the aim is

to minimize distances. Minimizing distances implies maxi-

mizing similarities, so we can assume that nearby or very

connected nodes have much in common while distant

and not directly connected ones are less well related.

Figure 4shows how non-linear correlation is estimated,

with values even higher than 0.90, mainly associated to

CDV variability. As a matter of fact, some of the values of

the connections have rather weak values, despite the

highest values being selected (Fig. 3; e.g., eqs_slab_Tyrr

−sideromelane = 0.04). Conversely, ground deformation

and geochemical variables show values generally close

to 0.70, with very few exceptions (Fig. 3).

To understand the meaning of the MRG graph, we have

used three known graph indices (Table 1reports all the

relative values):

1. The Association Strength (S

): This index measures the

strength by which each node attracts its neighbors.

2. The Node Centrality (C

) measures how close each node

is to the center of the graph. The higher the centrality of a

node, the more it is a fundamental variable of the dataset

represented by the graph.

3. The Node Degree (D

) measures how far each node is a

mediator (i.e., how many links for each node) among the

other nodes.

The Association Strength S

of each of the displayed nodes

is estimated by:

Si¼li

∑Ni

klk

ð1Þ

where S

= 1 is the baseline (at ith node), l

represents the

number of links of the ith node, N

represents the number

of nodes to which the ith node is directly linked, and l

stands for the number of links of the neighbors of the ith

node. Therefore, the index is proportional to the number

of its links and to the number of links of the nodes

directly connected to it. If S

<1, a not very significant

node is present due to the weak relative force of attrac-

tion for close connections, while a stronger node will

Fig. 3 The semantic map of the 28 variables (for a relative legend, see

Tab le 1) of the dataset that synthesizes their strongest similarity relation-

ships providing important information about the relevance of the vari-

ables and how they relate to each other. It is possible to highlight a group

made up of all the variables of seismological type, connected with the

sideromelane node and weakly integrated with the rest of the variables.

Moreover, given its location and number of connections, the CDV node

seems to play a key role for the whole system

40 Page 8 of 19 Bull Volcanol (2019) 81:40

have S

>1. It is therefore clear that the CVD variable is

of considerable importance as characterized by S

CVD

4.17 (Table 1). Furthermore, also eqs_swarm, MSC,

and sideromelane variables also feature Si >1 (Table 1).

Interpretation of the structure of the graph is issue in

understanding complex datasets. One of the ways it sim-

plifies visualization is investigating the relative Hfunction

(Buscema et al. 2016). This function is a new index to

measure topological information (i.e., structural complexi-

ty, size measurements, and norms extractable from a graph

without any reference to its relative geometry). In other

words, the Hfunction measures a graph’s complexity.

This function is calculated from a basic value related to

the MST graph. Then, one by one, all discarded links are

added and the function is recalculated. The Hfunction

takes on a maximum value when the number of links added

determines the maximum complexity.

Figure 5shows the value of the Hfunction as a link is

added. The value H(0) corresponds to the original MST,

whereas H(k) corresponds to the MST to which klinks of

those discarded during its construction have been added.

In our case, the Hfunction reaches its peak when the 17th

of the connections skipped during the MST generation is

added back in. So, the MRG needs 17 extra connections to

beaddedtotheMST and, consequently, the Hfunction

value is almost 51.00% higher than its value at the orig-

inal MST (H(0) =0.22 vs. MRG H(17) = 0.45). The MRG

depicts the most relevant associations among the variables

and includes the MST representation, being the former

characterized by links already reported in the MST and

by the skipped 17 values. In particular, notice how the

MRG separates the variables dataset into clear sub-trees

whose boundaries are marked by CDV and stat_mean,

respectively (Fig. 3).

Results

The ground deformation parameter CDV (Table 1)producesa

click (Buscema et al. 2016), a completely regular graph where

each node is directly linked to any other node, including MSC,

tilt_var_0.033_CDV, stat_mean, dil_W (i.e., ground

deformation parameters; Table 1), CO2_P39 (i.e.,

geochemical parameter; Table 1), and grav_PL (i.e.,

gravimetric parameter; Table 1), among which the highest

number of relationships is featured (six, shown in Fig. 3), as

well the highest association values (higher than 0.95, on av-

erage). The minimum (0.89) and maximum (0.99) association

values of the complete regular graph are referred to as dil_W

versus CO

_P39 and stat_mean versus MSC and dil_W ver-

sus tilt_var_0.033_CDV variables, respectively (Fig. 3). The

variables connected through the complete graph show an

Association Strength S

>0.73 (Table 1).

The CDV variable also marks a connection giving the as-

sociation value of 0.90 with ash and sideromelane variables,

both exclusively with a volcanic fingerprint (Fig. 3).

Furthermore, ash versus sideromelane provides the highest

correlation of 1.00 (Fig. 3), indicating that was produced by

volatile-rich fresh magma and occurrence of explosive erup-

tion (as demonstrated by the presence of ash). The

sideromelane variable does not show a significant strength

with any other variable (i.e., variables associated to different

volcanic features are connected among themselves, thus

displaying a kind of non-linear shared quality; Fig. 3).

Other links with weaker clustering strength (i.e., the

AssociationStrengthS

) are marked throughout the MRG

(Fig. 3). This means that the variables belonging to the main

click of the graph represent the outline of the dataset, but the

link between ash and sideromelane remains the main structur-

al connection among data. As for the first step of pattern

Fig. 4 The Hfunction of the

MRG graph. The x-axis denotes

the progressive arc number kthat

is added to the MST, and the y-

axis represents the value of the

function H(k), calculated on this

new graph. The value max

H(k)=H(17) =0.45 implies that

the MRG will have 17 more

connections than the MST.The

maximum of the function

corresponds to the graph of

maximum complexity, that is, the

one that best describes all the

features of the dataset

Bull Volcanol (2019) 81:40 Page 9 of 19 40

recognition task, each record must be characterized by a class

(namely, a target), which the network must learn to recognize.

The target assigned to each of the 1580 records specifies the

state of the volcano on a certain day (i.e., a flank eruption at

Mt. Etna would or would not occur on each day). The results

obtained by the K-CM classifier application were validated

using a LOO testing protocol (Appendix 1). Table 2summa-

rizes the relative calculations, mainly in terms of sensitivity

(how many times the algorithm has correctly classified the

erupting target) and specificity (how many times the algo-

rithm has correctly classified the quiescent target). Following

Brancato et al. (2016),

Sensitivity ¼TP=TP þFNðÞ ð2Þ

Specificity ¼TN=TN þFPðÞ ð3Þ

where TP, TN, FP, and FN stand for true positive, true nega-

tive, false positive, and false negative, respectively.

Fig. 5 Selection of the monitoring values collected during different

periods (see Table 1for relative parameters). Each period spans 30 days

of Mt. Etna volcanic activity. In particular, each time series starts 20 days

before the onset of the July–August 2001 (blue line), October 2002–

January 2003 (red line), and September 2004–March 2005 (green line)

flank eruptions. In each panel, the x-axis represents time, with value x=

20 indicating the onset day of each eruption, while the y-axis indicates the

value recorded in the considered variables

40 Page 10 of 19 Bull Volcanol (2019) 81:40

When considering erupting, a sensitivity of 97.67%

(294 days out of 301 eruptive days in the investigated period)

is estimated (Table 2). When considering the quiescent state, a

specificity of 99.30% (1270 days out of 1279 non-eruptive

days) is estimated (Table 2). The accuracy of classification is

equal to 98.49%, and only 16wrong classifications (seven and

nine, respectively; Table 2) are observed. This means that,

given the values recorded today, the network can predict with

an accuracy of 98.49% if tomorrow there will be an eruption

tomorrow or not. Having a high sensitivity value is essential in

cases where the two classes are not perfectly balanced. In fact,

this parameter takes account of the errors in relation to the

number of elements in that class.

For the second step of this analysis, we estimated probabil-

ities for each target (eruption or rest) for the seventh day, after

an application of a mobile window of 6 days. Table 3reports

the results in terms of sensitivity and specificity for the last

787 days of the dataset (see above) and Table 4compares the

relative targets with the classified days. We should emphasize

that this sample mostly focuses on the 183 eruptive days of the

September 2004–March 2005 flank eruption at Mt. Etna. The

results relating to the July–August 2001 and October 2002–

January 2003 eruptions have to be used as an added value that

completes the analysis in a more global perspective.

When looking at the probabilities of the next day, the most

obvious result is the classification of the September 2004–

March 2005 period, as highlighted in Table 4.Reportedvalues

show how the sample of each day is classified according to

one of the two labels erupting or quiescent. The ANN clas-

sifies each day without knowing the real class to which it

belongs. Most of the 183 eruptive days are classified as

erupting, with the minimum of probability 14.00% occurring

after the end of the eruption (Table 4). The onset of the erup-

tion is classified as 10 September 2004 with a probability of

57.00%. Brancato et al. (2011) showed that the prediction of

the September 2004–March 2005 flank activity failed because

no anomalies were detected in any monitored parameters. The

pattern recognition classified the restricted period as erupting

with a relative sensitivity of 97.81% (179 out of 183 eruptive

days; Table 3)andasquiescent with a specificity of 99.50%

(601 records out 604 rest days). This high accuracy of classi-

fication (i.e., 98.66%) is reflected by only seven misclassifi-

cations (four and three, for erupting and quiescent,

respectively).

These results are in line with those obtained after the first

step (Tables 3and 4). It is noteworthy that during the training

phase of the Auto-CM algorithm, the monitoring dataset re-

ferring to the analyzed period can be regarded as anomalous,

Table 2 K-CM pattern recognition results, following the LOO validation protocol

Eruptive

days (day)

Quiescent

days (day)

Tot al d ay s

(row; day)

Error (day)

Sensitivity

Specificity

A. mean

W. mean

Eruptive days 294 7 301 7 97.67% 98.49% 98.99%

Quiescent days 9 1270 1279 9 99.30%

Total days (column; day) 303 1277 1580 16

Average number of wrong classification

Classified eruptive days

Classified quiescent days

Arithmetic mean (i.e. accuracy of the classification)

Wei g ht ed me an

Table 3 K-CM pattern recognition results of the last 787 records of the dataset, after the application of a mobile window of 6 days (see text for more

details)

Eruptive

days (day)

Quiescent

days (day)

Tot al d ay s

(row; day)

Error (day)

Sensitivity

Specificity

A. mean

W. mean

Eruptive days 179 4 183 4 97.81% 98.66% 99.11%

Quiescent days 3 601 604 3 99.50%

Total days (column; day) 182 605 787 7

Average number of wrong classification

Classified eruptive days

Classified quiescent days

Arithmetic mean (i.e., accuracy of the classification)

Wei g ht ed me an

Bull Volcanol (2019) 81:40 Page 11 of 19 40

with comparable values in line with the preceding flank erup-

tion occurrences (namely, July–August 2001 and October

2002–January 2003). The onset day of the September 2004–

March 2005 flank eruption (namely, 6 September 2004) and

the following 3 days were classified as quiescent (Table 4).

Only on 10 September 2004 did the K-CM algorithm classify

it as erupting (Table 4). At the end of April (the eruption ended

on 8 March 2005), misclassifications occur, classifying the

Table 4 Selected comparison of eruptive activity occurring at Mt. Etna in the January 2001–April 2005 period among real eruption and real rest

targeted (second and third, seventh and eighth columns) and classified (probability; fourth and fifth, nineth and tenth columns) days

Date Classes K-CM Output Date Classes K-CM output

target_1 target_2 target_1 target_2 target_1 target_2 target_1 target_2

1January2001010124November20041010

... ............25November20041010

12 July 2001 0 1 0 1 ... ... ... ... ...

13July2001010121January20051010

14 July 2001 0 1 0 1 22 January 2005 1 0 0.86 0.14

15July2001010123January20051010

16 July 2001 0 1 1 0 ... ... ... ... ...

17 July 2001 1 0 0 1 29 January 2005 1 0 0.86 0.14

18 July 2001 1 0 1 0 30 January 2005 1 0 0.86 0.14

19July2001101031January20051010

8August200110106February20051010

9August2001 1 0 0 1 7 February 2005 1 0 0.86 0.14

10August200101108February20051010

11 August 2001 0 1 0 1 ... ... ... ... ...

... ............7March20051010

25 October 2002 0 1 0 1 8 March 2005 0 1 0.86 0.14

26 October 2002 0 1 0 1 9 March 2005 0 1 0.86 0.14

27 October 2002 1 0 0 1 10 March 2005 0 1 0.57 0.43

28October2002101011March20050101

29October2002100112March20050101

30 October 2002 1 0 1 0 ... ... ... ... ...

31October2002101014April20050101

... ... ... ... ... 15 April 2005 0 1 0.29 0.71

26 January 2003 1 0 0 1 16 April 2005 0 1 0.43 0.57

27 January 2003 1 0 1 0 17 April 2005 0 1 0.43 0.57

28 January 2003 1 0 0 1 18 April 2005 0 1 0.29 0.71

29 January 2003 0 1 0 1 19 April 2005 0 1 0.14 0.86

30January2003010120April20050101

... ............21April20050101

4 September 2004 0 1 0 1 ... ... ... ... ...

5 September 2004 0 1 0 1 ... ... ... ... ...

6 September 2004 1 0 0 1 ... ... ... ... ...

7 September 2004 1 0 0 1 ... ... ... ... ...

8 September 2004 1 0 0 1 ... ... ... ... ...

9 September 2004 1 0 0 1 ... ... ... ... ...

10 September 2004 1 0 0.57 0.43 ... ... ... ... ...

11 September 2004 1 0 1 0 ... ... ... ... ...

12 September 2004 1 0 1 0 ... ... ... ... ...

22 November 2004 1 0 1 0 ... ... ... ... ...

23 November 2004 1 0 0.86 0.14 ... ... ... ... ...

The onset and the end of the flank activities (see text for details) during the investigated time period are marked in bold and italics, respectively

40 Page 12 of 19 Bull Volcanol (2019) 81:40

state of the volcano as erupting (Table 4). Flank activity at Mt.

Etna has been observed to be usually preceded with changes

in the volcano feeder system (Bonaccorso et al. 2004;

Brancato et al. 2011). Figure 5compares three periods, each

of 30 days (i.e., monitoring values), relative to the flank ac-

tivity here analyzed.

It is clear how monitoring parameters reflect the mag-

ma ascent a few days before the flank eruptions of the

2001–2003 period and, conversely, how no monitoring

anomalies (i.e., precursors) were recorded before the

2004–2005 volcanic activity. In the first case, in fact,

there are many sudden changes in the values recorded

before the eruption, while in the second case, the ob-

served variables maintained a constant value before, dur-

ing, and after the eruption, making the event more dif-

ficult to predict.

It is noteworthy that K-CM classifies most of the

2004–2005 flank eruption as erupting (i.e., undergoing

eruption) (Table 4), even though the classified onset is

5 days after the real onset (with a probability of 57.00%;

Tab le 4) and the classified end 3 days after the real end

(Table 4). This is the only relevant error in the K-CM

prediction out of the 1580-day period. In this specific

case, the network, trained on 6 days to predict the sev-

enth, needed more time to provide the correct output.

Since the sample used in training had only two eruptive

flank episodes, the number of cases in which a change of

state at Mt. Etna is present is rather small. It therefore

seems reasonable to believe that with a larger monitoring

dataset, the network could refine its ability to more ef-

fectively predict when the state changes. Furthermore,

misclassifications occur at the end of April 2005,

(Table 4). These are better interpreted as false positives

(i.e., aborted eruptions), due to anomalous seismicity (S.

Alparone, personal communication, 2010) and gas emis-

sions (Brancato et al. 2011). These relate to the closing

phases of a flank eruption at Mt. Etna. Relative confu-

sion is generated because of a diffuse absence of anom-

alous values in the monitoring dataset. In some cases,

this means the classified days have more uncertainty,

the worst case (for decision makers) being when the

ANN anticipates the end.

As further support for our study, we analyzed the behavior

of the Receiver Operating Characteristic (ROC) curve

(Hanley and McNeil 1982;Fig.6) and Molchan diagram

(Zhuang 2010;Schmidetal.2012; de Arcangelis et al.

2016; Fig. 7). By considering that mistakes are likely in clas-

sifying cases, there will be some target patterns correctly clas-

sified as targets (i.e., TP) and some misclassified as non-

targets (i.e., FN). Similarly, there will be non-target patterns

correctly classified as non-targets (i.e., TN) and some

misclassified as targets (i.e., FP).

The solid red line in Fig. 6corresponds to the ROC

curve, relative to the trade-off between the probability of

correctly classifying the erupting class (true positive rate,

also known as sensitivity) and the false positive rate

(1 –specificity) concerning, respectively, the first and

second trials carried out. The Area Under the Curve

(AUC), if compared with the area that lies under the gray

dashed line (i.e., 0.5; no discrimination exists, which

indicates a worthless test where the proportions of TP

and FP are equal), provides a valid measure of diagnostic

performance of the used classifier. In both cases, the area

under the ROC plot, computed by means of the trapezoid

rule (Tallarida and Murray 1987), has an extremely high

value. In the best case, corresponding to the second test

(Fig. 6b), it is equal to 0.9945, meaning that 99.45% of

the classified erupting days are correctly rated for a giv-

en probability of false alarm. Following the Swets clas-

sification (Swets 1988), this value confirms that the di-

agnostic used is highly accurate.

The Molchan diagram features the error. It is drawn by

considering values depending on the quantities TP, TN,

FP, and FN, previously defined. The graph represents the

Fig. 6 ROC curve (red solid line) for the first experiment (a)andsecond

experiment (b), respectively. The dashed line means an AUC equals to

0.5 (i.e., TP and FP proportions are equal). Note that even for high

specificity values, i.e., around zero on the x-axes, the sensitivity is very

high. The value of the AUC is in fact close to 1

Bull Volcanol (2019) 81:40 Page 13 of 19 40

pairs (τ,ν) obtained by varying a threshold value λ.The

quantities τand νare defined as follows:

ν¼FN=TP þFNðÞ ð4Þ

τ¼TP þFPðÞ=TP þTN þFP þFNðÞð5Þ

where νconsiders the amount of missed event and τcorre-

sponds to the alarm time fraction (time covered by the alarms

over the duration of the whole considered period). In our ex-

perimentation, the threshold value λwas varied over the range

[0, 1] with steps of 0.1 (Fig. 7). In the Molchan diagram, the

better the forecast, the closer you get to the theoretical point

(0.0). In our case, in both experiments, we obtained a Molchan

curve that shows excellent network reliability. When the

threshold changes, the points all fall into an area very close

to the theoretical minimum. It should be noted that the output

values of the K-CM network in the first experiment (N=28)

are binary (i.e., 0 or 1), while, in the case of the second exper-

iment, the output values are continuous (i.e., they vary in the

range [0, 1]). For this reason, both the ROC curve and the

Molchan diagram relevant to the first test do not show partic-

ular variations when the threshold changes, maintaining

constant and very good performances (Figs. 6and 7). In the

Molchan diagram, in particular, all the points are

superimposed on a single pair of values τ;υðÞ, with the ex-

ception of the borderline cases (0, 1) and (1, 0).

Discussion

Analyses of pattern classification (both supervised and

unsupervised) have previously been performed at Mt.

Etna by Langer et al. (2009)andCorsaroetal.(2013).

In particular, the artificial neural networks were applied

to volcanic tremor data recorded between July and

August 2001 (Supporting Vector Machine (SVM) and

Multi-Layer perceptron (MLP); Langer et al. 2009)and

to geochemical data collected from 1995 to 2005 (Self-

Organizing Map (SOM) and fuzzy clustering; Corsaro

et al. 2013). The analyzed periods cover both summit

eruptive activity (lava fountains) and flank eruptions.

Even though both datasets represent a much reduced

sample of that used here, the authors conclude that clas-

sification methodology is a suitable tool for understand-

ing the non-linear relationships between volcanic data

and the internal dynamics of a volcano. In particular,

Langer et al. (2009), by applying the LOO testing

scheme as used in this study, yielded high performances

of 94.80% and 81.90% (for SVM and MLP, respective-

ly), though with a slightly lower score relative to our

value of 97.67% (Table 2). In addition, Corsaro et al.

(2013)proposedthatclassificationsperformedbySOM

and fuzzy clustering are extremely useful for an accurate

interpretation of magma composition, its origin, and be-

havior during future eruptions at Mt. Etna, thus allowing

a direct comparison between old and new erupted

products.

This study applies and presents the theory behind an

emerging supervised method for volcanological pattern recog-

nition, named the K-CM, as applied to detecting the change

from Bin a flank eruption^(i.e., erupting)totheBnot in a flank

eruption^state (i.e., quiescent) at Mt. Etna. A two-step anal-

ysis was performed. First, the applied methodology exploits

the variable connection weights provided by the Auto-CM

neural network strategy to obtain the z-transforms (see

Appendix 1) on which the kNN classifier is applied for class

membership evaluation. The Auto-CM system reshapes the

distances between variables or records in any dataset, consid-

ering their global vectorial similarities, and consequently

drawing out the specific warped space (i.e., a non-Euclidean

space) in which such variables or records lie, thereby provid-

ing a proper theoretical representation of their actual variabil-

ity. We have shown how a known filter like the MST can be

used to cluster a distance matrix, generated by means of Auto-

CM from a dataset. In particular, how the MST can be regarded

Fig. 7 Molchan diagrams for the first (a) and the second experiment (b),

respectively. The dashed line means a random guess (i.e., the curve of

modelequivalence;deArcangelisetal.2016). The red solid line shows

the confidence level

40 Page 14 of 19 Bull Volcanol (2019) 81:40

as the minimal representation that takes into account the basic

level of information below which the structure of the indepen-

dence among variables loses coherence. We have used the H

index, a function that evaluates the topological complexity of

any kind of undirected graph, its mathematical consistency,

and the potential for its applications (Fig. 4and Table 1).

Finally, by using the Hfunction, we have represented our

results on the MRG semantic graph. From an MST,generated

from any metric, the MRG reshapes the links between nodes in

order to maximize the fundamental and the most regular struc-

tures implicated in any dataset.

After analyzing the MRG graph, very robust relation-

ships were found among variables (Fig. 3). In detail, the

role of the CDV parameter (which monitors ground de-

formation) is predominant, around which a click is creat-

ed featuring the highest number of connections with dif-

ferent parameters of the volcanic framework (Fig. 3).

Further, an immediate link with ash and sideromelane

variables generates one of the highest non-linear correla-

tions (i.e., 0.90; Fig. 3).

Indeed, the most outstanding novelty concerns the

September 2004–March 2005 flank eruption (Table 4).

Brancato et al. (2011) failed to predict this activity because

of the total absence of anomalies (due to fuzzy parameters) in

the monitoring dataset. In contrast, the approach used in this

study performs a high accuracy evaluation, with only a very

few exceptions (only seven wrong classifications out of a total

of 787 days; Table 3).

Brancato et al. (2011) performed a Bayesian Event Tree

(BET) approach on the same time-interval analyzed here. A

larger dataset, including also the volcanic tremor parameter

(not used here because unavailable for the entire period),

allowed the probabilistic volcanic hazard to be quantified, in

terms of occurrence of flank eruptions. The results showed the

major role of monitoring in forecasting short-time flank activ-

ity at Mt. Etna. It is worth noting that probability estimates of

an impending flank eruption were affected by anomalous

values in CO

emission at P39 site. Indeed, the presence of

relative anomalies generated a sequence of long-lasting false

alarms. Thus, Brancato et al. (2011) suggested that CO

emis-

sion at P39 site was incorrectly elicited by experts.

Conversely, the K-CM approach points to the fundamental

role of the parameter in the dataset, based on the Association

Strength S

value of 1 and the highest C

value of 4 (Table 1),

thus avoiding the relative confusion about the predicting aim

of the parameter after the BET approach. In other words, even

though the expert elicitation set the CO

emission at P39 site

as one of the potential parameter to be used for predicting

flank eruptions at Mt. Etna, the BET approach rose to the

question about its reliability. The present approach highlights

that a parameter, as discarded by previous approaches, might

be a significant loss in terms of hidden links as better associ-

ated to the internal volcanic processes.

Conclusion

This study highlights the performance of the modified K-

CM classifier, applied for the first time to a volcanic

context, using Mt. Etna as case study. We presented a

new method to interpret the results of data represented

on the MRG graph and to forecast flank eruptive activity.

Improvements are mainly due to a many-to-many vari-

able relationship. Given the complex nature of the phe-

nomenon, in fact, we cannot be satisfied with the simple

relationship between two or three variables, but we must

investigate how a multiplicity of variables (many),

interacting with others (to many), determines the phe-

nomenon. Only by this approach, it will be possible to

obtain a reliable predictive model. A lone parameter may

not be anomalous (based on the mean variance), but the

entire dataset of parameters, when defining the same

non-linear function, can contribute incrementally to re-

veal deep global effects (the so-called meta-stable vari-

ables, whose behavior is strongly affected by the values

of the other variables). Indeed, by comparing results by

the K-CM from those obtained by the Bayesian approach

(Brancato et al. 2011), the predominance of the algo-

rithms of automatic learning becomes clear. This is due

to the ability of the machine learning techniques to iden-

tify objectively the subtle links between the monitoring

data and the state of Mt. Etna (quiescent or eruptive),

thus avoiding the subjectivity of external operators, pri-

marily in selecting thresholds and inertias for the moni-

toring parameters involved.

K-CM opens the possibility for bottom-up algorithms to

provide a symbolic explanation of their paths and behavior.

The symbolic level of the K-CM system is not, however, a

set of naïve Bif…then^rules traditionally applied to all

training data. Understanding this symbolic level is relative-

ly simple: the increase of a non-linear functional, from

interpolation of the training set, results in the exponential

growth of explicit rules suitable for deriving a description.

A more interesting symbolic level is that which allows the

explanation of the Bfuzzy mental map^through which the

learning algorithm is represented based on training data

and, simultaneously, the subjective similarities on which

the same algorithm can operate in new cases. In other

words, a bottom-up algorithm can work in a symbolic

way when it is able to self-generate a mental representation

(weighted graph) of what it has learned (from the training

set) and dynamically place it in a chart of new experiences

(the test set), by inducing it to reorganize the initial map.

In other comparative studies (Buscema et al. 2014), K-CM

showed the best valid classification performance for most of

the considered datasets and, on average, out-performed the

other classification methods. In practice, K-CM can improve

the classification results especially in those cases where non-

Bull Volcanol (2019) 81:40 Page 15 of 19 40

linear relationships among variables are relevant. We are

aware that this new approach, although very promising, leaves

many questions unanswered and needs further scrutiny to in-

vestigate its properties and potential shortcomings. In forth-

coming research, we plan to develop it from both the theoret-

ical and the empirical angles, by better exploring and charac-

terizing the structural features of the Auto-CM and the math-

ematical properties of the Hfunction and the MRG.Onthe

empirical side, we plan to apply this methodology to state-of-

the art problems that are relevant in the literature of specific

disciplines. It is, of course, of particular interest to evaluate

how our approach performs against traditional methods in the

analysis of networks, be they of a physical or social nature.

All the connections among variables (in particular, the click

generated by CDV; Fig. 3) indicate that monitoring is funda-

mental for quantifying short-term volcanic hazard. In the same

way, it is important to bear in mind that the pattern recognition

approach improves the sensitivity, specificity, and accuracy

estimated in previous applications of the ANN methodology

(Brancato et al. 2016), thus confirming the high non-linear

behavior of an open conduit volcanic complex system, such

as Mt. Etna.

In light of this, thisstudy represents one of the few attempts

in processing long-time records of monitoring data collected

at an active volcano by artificial neural network methodology.

Results may offer a tool when decision makers face challenges

in volcanic emergencies in terms of planning and/or mitiga-

tion of potential effects in areas prone to volcanic risk, mostly

due to a robust near real-time estimate. Furthermore, results

achieved here show how a supervised K-CM approach per-

forms a reliable data mining when applied to a high-quality

monitoring dataset. This might be a limiting factor in a poorly

monitored volcano.

Acknowledgments The authors are deeply grateful to Alessandro

Bonforte, G. Di Grazia, F. Greco, and S. Gambino of the INGV-OE for

having provided data, beliefs, and theoretical models. The authors are

also grateful to the Technical Staff of the INGV-OE for maintaining the

monitoring networks. Semeion Research Center of Sciences of

Communication is also thanked for providing the specialist ANN soft-

ware for all the elaborations. Sylvie Vergniolle is sincerely acknowledged

for the continuous encouragement and the constructive criticism. Andrew

Harris is acknowledged as well for suggestions that deeply improved the

final version of the paper. The authors wish to thank two anonymous

reviewers for the careful revision of earlier versions of the manuscript.

AB benefited from funding provided by GEOMONITOR Project.

Semeion Research Center of Sciences of Communication funded PMB,

GM, and FDT for this research. The authors kindly acknowledge Stephen

Conway for the initial language revision of the manuscript.

Appendix 1

K-CM method overview

K-CM is a supervised version of Auto-CM neural networks

(Buscema et al. 2014,2018). K-CM has a training phase in a

completely unsupervised way and then a blind testing valida-

tion, using the kNN algorithm (Hastie et al. 2009)toestimate

to which of Nclasses each tested record belongs. Furthermore,

by using the parameters derived from the Auto-CM learning,

it is possible to obtain a graph that reflects the non-linear

correlation values assumed by the neural network. The whole

process is summarized in Fig. 8.

Fig. 8 Flow chart of all the analyses carried out with K-CM

40 Page 16 of 19 Bull Volcanol (2019) 81:40

The entire dataset is initially used as input for an unsuper-

vised neural network (i.e., Auto-CM), which synthesizes the

non-linear correlation relationships between the variables in

the Wconnection matrix of its weights, as identified in the

data. This matrix represents the Auto-CM knowledge about

the whole dataset and can be used in two different ways: to

rewrite the dataset through the function called z-transform or

as a matrix of the weights to be linked to the graph whose

nodes are the variables. The z-transformation allows the fuzzy

profile of each record to be determined, taking into account

the information about the relationships between the variables

which emerged during the learning phase. The rewritten

dataset is therefore more informative than the previous one.

The kNN classifier is used on the new dataset to perform the

pattern recognition task. The dataset is randomly subdivided

into two subsets A and B. The subset A is trained and the

subset B is blind tested, but the algorithm also works in re-

verse, with the subset B trained and the subset A subsequently

blind tested. The average of these two tests represents the

accuracy of the algorithm.

The semantic map: data graphical visualization

The K-CM classifier is able to support its classification task

projecting each tested record as a node of a weighted graph,

where the more similar records are closer to each other. In other

words, the resulting graph is a map of similarities among the

predicted records and this map is very useful in understanding

which records represent a general prototype of the whole

dataset and which ones are outliers. On the other hand, Auto-

CM is an ANN architecture that forces the non-linear correla-

tion among variables into an embedding space where the rela-

tive associations are accurately reflected as closeness. Because

of the Auto-CM architecture, the weight matrix has a dimension

(N×N), where Nis the number of variables. It is then possible

to consider the graph G(n,E), where nis the set composed of

all the Nvariables (nodes of the graph) and Eis the set contain-

ing all the arcs (i.e., the couple (i,j) if the variables iand jare

linked in the graph). All nodes are connected to each other and

the weight of the connection between nodes iand jdepends on

the value of the w

weight of the Wmatrix (w

values express

similarities; therefore, it is necessary to make a transformation

to translate them into terms of distance).

Since it is not easy to read a graph where all nodes are

connected, filters are used to display only the most relevant

connections, in particular the MST and the MRG. These two

graphs work as an effective filter on the dataset correlation,

drastically reducing the number of connections shown, and

both of them have already shown promising applications in

many fields (Buscema et al. 2014,2016,2018). While MST is

a known algorithm for its application to real problems (an

undirected graph without circuits or loops; see Mantegna

1999), MRG is a new one (see Buscema et al. 2014). The

MST connects all the Nvariables to each other, selecting the

highest N−1 connections that avoid the creation of cycles.

MRG adds to MST those circuits representing the most impor-

tant fingerprints of the whole analyzed dataset until the max-

imum of a complexity function is reached (the Hfunction, see

below for details). In particular, the MRG reshapes the links

between nodes in order to maximize the fundamental and

most regular structures, thus highlighting the features of a

dataset (Buscema et al. 2018).

Working with classification methods, it is common to deal

with the overfitting phenomenon. This arises when the num-

ber of degrees of freedom of the classification technique (i.e.,

its complexity) is large enough to not be constrained in a

stable way by the available data. To this end, cross-

validation schemes represent a basic tool for the diagnosis of

this overfitting. In a validation protocol, part of the patterns

with a priori known class membership is set aside and not used

during the training phase. These patterns represent the test set,

which is used after the training to evaluate the performance of

the classifier. If the degrees of freedom are well balanced with

respect to the size of the dataset, then the classifier perfor-

mance for patterns used during training and test phases will

be comparable.

The K-CM classification method, used here, is modified

according to a new validation protocol, namely the LOO

estimator. This represents a particular case of the K-fold

cross-validation estimator, when the number of patterns in-

to which the original dataset is subdivided equals the num-

ber of cases of the same dataset. The model is then trained

with all the patterns of the dataset but one (i.e., that is, the

one on which the error is estimated), and the procedure runs

for all the patterns. The average of the estimated errors for

the entire pattern will provide the average error of the

model.

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record of the conditions of ascent, degassing, and extrusion of

volatile-rich alkali basalt during the powerful 2002 flank eruption

of Mount Etna (Italy). J Geophys Res 111. https://doi.org/10.1029/

5742005JB003934

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Historical Developments and Perspectives of Muography

Chapter

Mar 2023

Hiroyuki K. M. Tanaka

Seismic precursors to the Whakaari 2019 phreatic eruption are transferable to other eruptions and volcanoes

Article

Full-text available

Apr 2022

Volcanic eruptions that occur without warning can be deadly in touristic and populated areas. Even with real-time geophysical monitoring, forecasting sudden eruptions is difficult, because their precursors are hard to recognize and can vary between volcanoes. Here, we describe a general seismic precursor signal for gas-driven eruptions, identified through correlation analysis of 18 well-recorded eruptions in New Zealand, Alaska, and Kamchatka. The precursor manifests in the displacement seismic amplitude ratio between medium (4.5–8 Hz) and high (8–16 Hz) frequency tremor bands, exhibiting a characteristic rise in the days prior to eruptions. We interpret this as formation of a hydrothermal seal that enables rapid pressurization of shallow groundwater. Applying this model to the 2019 eruption at Whakaari (New Zealand), we describe pressurization of the system in the week before the eruption, and cascading seal failure in the 16 h prior to the explosion. Real-time monitoring for this precursor may improve short-term eruption warning systems at certain volcanoes.

Automatic precursor recognition and real-time forecasting of sudden explosive volcanic eruptions at Whakaari, New Zealand

Article

Full-text available

Jul 2020

Sudden steam-driven eruptions strike without warning and are a leading cause of fatalities at touristic volcanoes. Recent deaths following the 2019 Whakaari eruption in New Zealand expose a need for accurate, short-term forecasting. However, current volcano alert systems are heuristic and too slowly updated with human input. Here, we show that a structured machine learning approach can detect eruption precursors in real-time seismic data streamed from Whakaari. We identify four-hour energy bursts that occur hours to days before most eruptions and suggest these indicate charging of the vent hydrothermal system by hot magmatic fluids. We developed a model to issue short-term alerts of elevated eruption likelihood and show that, under cross-validation testing, it could provide advanced warning of an unseen eruption in four out of five instances, including at least four hours warning for the 2019 eruption. This makes a strong case to adopt real-time forecasting models at active volcanoes. In this study, the authors investigate the predictability of sudden eruptions, motivated by the 2019 eruption at Whakaari (White Island), New Zealand. The paper proposes a machine learning approach that is able to identify eruption precursors in data streaming from a single seismic station at Whakaari.

Pilot study of eruption forecasting with muography using convolutional neural network

Article

Full-text available

Mar 2020

Muography is a novel method of visualizing the internal structures of active volcanoes by using high-energy near-horizontally arriving cosmic muons. The purpose of this study is to show the feasibility of muography to forecast the eruption event with the aid of the convolutional neural network (CNN). In this study, seven daily consecutive muographic images were fed into the CNN to compute the probability of eruptions on the eighth day, and our CNN model was trained by hyperparameter tuning with the Bayesian optimization algorithm. By using the data acquired in Sakurajima volcano, Japan, as an example, the forecasting performance achieved a value of 0.726 for the area under the receiver operating characteristic curve, showing the reasonable correlation between the muographic images and eruption events. Our result suggests that muography has the potential for eruption forecasting of volcanoes.

Large and Powerful ANNs Versus Small, Numerous, and Diverse ANNs

Chapter

Mar 2025

Convolutional Neural Networks (CNNs) have proven to be one of the state-of-the-art systems in image understanding and other complex tasks where input patterns must undergo convolutions. CNNs have highlighted the “vertical” development of a classical ANN significantly increasing the number of processing layers between the input (its pattern) and the output (its correct classification). Its intermediate layers including convolutional, pooling, and dropout layers are inspired by how the visual cortex processes light signals.

Specialized Nodes Versus Conscious Nodes

Chapter

Mar 2025

Both supervised and unsupervised artificial neural networks each have nodes within the hidden layers that tend to specialize during the learning phase. This specialization involves encoding specific features of the observed patterns while disregarding others. This phenomenon is inherently linked to the technique of gradient descent and the chain rule used for backpropagating errors from the output layer.

Machine Learning with Muographic Images as Input

Chapter

Feb 2022

The application of machine learning techniques on remote sensing data has opened new possibilities in automated classification and forecasting of geophysical phenomena, including those triggering natural hazards, such as landslides or volcano eruptions. Muographic imaging can reveal the structural and density changes in geological bodies in connection with subsurface geophysical phenomena. We present the recent progress in machine learning‐based muographic image processing and discuss how it may reveal subsurface volcanic phenomena and contribute to volcano eruption forecasting. Our analysis is based on data sets collected by the Multi‐Wire‐Proportional‐Chamber‐based Muography Observation System during the eruption episodes of Minamidake crater of Sakurajima volcano between October 2018 and July 2020. The area under the curve score of 0.761, provided by the receiver operating characteristic curve analysis of a convolutional neural network, shows correlation between the impending vulcanian eruptions of Minamidake crater and the muographic images captured on the previous days.

Seismic Precursors to the Whakaari 2019 Phreatic Eruption detected in Five Other Volcanoes

Preprint

Full-text available

Nov 2021

Volcanic eruptions that occur without warning can be deadly in touristic and populated areas. Even with real-time geophysical monitoring, forecasting sudden eruptions is difficult because their precursors are hard to recognize and can vary between volcanoes. Here, we describe a general seismic precursor signal for gas-driven eruptions, identified through correlation analysis of 18 well-recorded eruptions in New Zealand, Alaska and Kamchatka. We show that the displacement seismic amplitude ratio, a ratio between high and medium frequency volcanic tremor, has a characteristic rise in the days prior to eruptions that likely indicates formation of a hydrothermal seal that enables rapid pressurization. Applying this model to the fatal 2019 eruption at Whakaari (New Zealand), we identify pressurization in the week before the eruption, and cascading seal failure in the 16 hours prior to the explosion. This method for identifying and proving generalizable eruption precursors can help improve short term forecasting systems.

Mt. Etna: Volcano laboratory

Book

Full-text available

Jan 2004

For thousands of years man has marveled at the gigantic structure that makes up Mt. Etna, the largest active volcano in Europe, and has lived side by side with the mountain, which despite its intense eruptive activity has always been considered a "friendly giant". After the Second World War, with its frequent but non-life-threatening eruptions, Mt. Etna represented an ideal location for volcanological research for the national and international scientific community. Numerous scientists from Belgium, Germany, France, the United Kingdom, and the United States of America have taken part in volcanological research aimed at understanding the volcano.

Pattern Recognition for Flank Eruption Forecasting: An Application at Mount Etna Volcano (Sicily, Italy)

Article

Full-text available

Aug 2016

A volcano can be defined as a complex system, not least for the hidden clues related to its internal nature. Innovative models grounded in the Artificial Sciences, have been proposed for a novel pattern recognition analysis at Mt. Etna volcano. The reference monitoring dataset dealt with real data of 28 parameters collected between flank eruptions. There were 301 eruptive days out of an overall number of 1581 investigated days. The analysis involved successive steps. First, the TWIST algorithm was used to select the most predictive attributes associated with the flank eruption target. During his work, the algorithm TWIST selected 11 characteristics of the input vector: among them SO2 and CO 2 emissions, and also many other attributes whose linear correlation with the target was very low. A 5 × 2 Cross Validation protocol estimated the sensitivity and specificity of pattern recognition algorithms. Finally, different classification algorithms have been compared to understand if this pattern recognition task may have suitable results and which algorithm performs best. Best results (higher than 97% accuracy) have been obtained after performing advanced Artificial Neural Networks, with a sensitivity and specificity estimates over 97% and 98%, respectively. The present analysis highlights that a suitable monitoring dataset inferred hidden information about volcanic phenomena, whose highly non-linear processes are enhanced.

Geological evolution of Mount Etna volcano (Italy) from earliest products until the first central volcanism (between 500 and 100 ka ago) inferred from geochronological and stratigraphic data

Article

Full-text available

Jan 2009

An Introduction to Natural Computation

Book

Jan 1999

Dana H. Ballard

This book provides a comprehensive introduction to the computational material that forms the underpinnings of the currently evolving set of brain models. It is now clear that the brain is unlikely to be understood without recourse to computational theories. The theme of An Introduction to Natural Computation is that ideas from diverse areas such as neuroscience, information theory, and optimization theory have recently been extended in ways that make them useful for describing the brains programs. This book provides a comprehensive introduction to the computational material that forms the underpinnings of the currently evolving set of brain models. It stresses the broad spectrum of learning models—ranging from neural network learning through reinforcement learning to genetic learning—and situates the various models in their appropriate neural context. To write about models of the brain before the brain is fully understood is a delicate matter. Very detailed models of the neural circuitry risk losing track of the task the brain is trying to solve. At the other extreme, models that represent cognitive constructs can be so abstract that they lose all relationship to neurobiology. An Introduction to Natural Computation takes the middle ground and stresses the computational task while staying near the neurobiology. Bradford Books imprint

Monitoring the December 2015 summit eruptions of Mt. Etna (Italy): Implications on eruptive dynamics

Article

Apr 2017
J VOLCANOL GEOTH RES

A lengthy period of eruptive activity from the summit craters of Mt. Etna started in January 2011. It culminated in early December 2015 with a spectacular sequence of intense eruptive events involving all four summit craters (Voragine, Bocca Nuova, New Southeast Crater, and Northeast Crater). The activity consisted of high eruption columns, Strombolian explosions, lava flows and widespread ash falls that repeatedly interfered with air traffic. The most powerful episode occurred on 3 December 2015 from the Voragine. After three further potent episodes from the Voragine, activity shifted to the New Southeast Crater on 6 December 2015, where Strombolian activity and lava flow emission lasted for two days and were fed by the most primitive magma of the study period. Activity once more shifted to the Northeast Crater, where ash emission and weak Strombolian activity took place for several days. Sporadic ash emissions from all craters continued until 18 December, when all activity ceased. Although resembling the summit eruptions of 1998–1999, which also involved all four summit craters, this multifaceted eruptive sequence occurred in an exceptionally short time window of less than three days, unprecedented in the recent activity of Mt. Etna. It also produced important morphostructural changes of the summit area with the coalescence of Voragine and Bocca Nuova in a single large crater, the “Central Crater”, reproducing the morphological setting of the summit cone before the formation of Bocca Nuova in 1968. The December 2015 volcanic crisis was followed closely by the staff of the Etna Observatory to monitor the on-going activity and forecast its evolution, in accordance with protocols agreed with the Italian Civil Protection Department.

Diagnosis of autism through EEG processed by advanced computational algorithms: A pilot study

Article

Feb 2017
COMPUT METH PROG BIO

Background: Multi-Scale Ranked Organizing Map coupled with Implicit Function as Squashing Time algorithm(MS-ROM/I-FAST) is a new, complex system based on Artificial Neural networks (ANNs) able to extract features of interest in computerized EEG through the analysis of few minutes of their EEG without any preliminary pre-processing. A proof of concept study previously published showed accuracy values ranging from 94%-98% in discerning subjects with Mild Cognitive Impairment and/or Alzheimer's Disease from healthy elderly people. The presence of deviant patterns in simple resting state EEG recordings in autism, consistent with the atypical organization of the cerebral cortex present, prompted us in applying this potent analytical systems in search of a EEG signature of the disease. Aim of the study: The aim of the study is to assess how effectively this methodology distinguishes subjects with autism from typically developing ones. Methods: Fifteen definite ASD subjects (13 males; 2 females; age range 7-14; mean value = 10.4) and ten typically developing subjects (4 males; 6 females; age range 7-12; mean value 9.2) were included in the study. Patients received Autism diagnoses according to DSM-V criteria, subsequently confirmed by the ADOS scale. A segment of artefact-free EEG lasting 60 seconds was used to compute input values for subsequent analyses. MS-ROM/I-FAST coupled with a well-documented evolutionary system able to select predictive features (TWIST) created an invariant features vector input of EEG on which supervised machine learning systems acted as blind classifiers. Results: The overall predictive capability of machine learning system in sorting out autistic cases from normal control amounted consistently to 100% with all kind of systems employed using training-testing protocol and to 84% - 92.8% using Leave One Out protocol. The similarities among the ANN weight matrixes measured with apposite algorithms were not affected by the age of the subjects. This suggests that the ANNs do not read age-related EEG patterns, but rather invariant features related to the brain's underlying disconnection signature. Conclusion: This pilot study seems to open up new avenues for the development of non-invasive diagnostic testing for the early detection of ASD.

A new Bayesian Event Tree tool to track and quantify volcanic unrest and its application to Kawah Ijen volcano: A NEW TOOL TO QUANTIFY VOLCANIC UNREST

Article

Jul 2016
GEOCHEM GEOPHY GEOSY

Although most of volcanic hazard studies focus on magmatic eruptions, volcanic hazardous events can also occur when no migration of magma can be recognized. Examples are tectonic and hydrothermal unrest that may lead to phreatic eruptions. Recent events (e.g., Ontake eruption on September 2014) have demonstrated that phreatic eruptions are still hard to forecast, despite being potentially very hazardous. For these reasons, it is of paramount importance to identify indicators that define the condition of nonmagmatic unrest, in particular for hydrothermal systems. Often, this type of unrest is driven by movement of fluids, requiring alternative monitoring setups, beyond the classical seismic-geodetic-geochemical architectures. Here we present a new version of the probabilistic BET (Bayesian Event Tree) model, specifically developed to include the forecasting of nonmagmatic unrest and related hazards. The structure of the new event tree differs from the previous schemes by adding a specific branch to detail nonmagmatic unrest outcomes. A further goal of this work consists in providing a user-friendly, open-access, and straightforward tool to handle the probabilistic forecast and visualize the results as possible support during a volcanic crisis. The new event tree and tool are here applied to Kawah Ijen stratovolcano, Indonesia, as exemplificative application. In particular, the tool is set on the basis of monitoring data for the learning period 2000-2010, and is then blindly applied to the test period 2010-2012, during which significant unrest phases occurred.

Statistical physics approach to earthquake occurrence and forecasting

Article

Mar 2016
PHYS REP

There is striking evidence that the dynamics of the Earth crust is controlled by a wide variety of mutually dependent mechanisms acting at different spatial and temporal scales. The interplay of these mechanisms produces instabilities in the stress field, leading to abrupt energy releases, i.e., earthquakes. As a consequence, the evolution towards instability before a single event is very difficult to monitor. On the other hand, collective behavior in stress transfer and relaxation within the Earth crust leads to emergent properties described by stable phenomenological laws for a population of many earthquakes in size, time and space domains. This observation has stimulated a statistical mechanics approach to earthquake occurrence, applying ideas and methods as scaling laws, universality, fractal dimension, renormalization group, to characterize the physics of earthquakes. In this review we first present a description of the phenomenological laws of earthquake occurrence which represent the frame of reference for a variety of statistical mechanical models, ranging from the spring-block to more complex fault models. Next, we discuss the problem of seismic forecasting in the general framework of stochastic processes, where seismic occurrence can be described as a branching process implementing space–time-energy correlations between earthquakes. In this context we show how correlations originate from dynamical scaling relations between time and energy, able to account for universality and provide a unifying description for the phenomenological power laws. Then we discuss how branching models can be implemented to forecast the temporal evolution of the earthquake occurrence probability and allow to discriminate among different physical mechanisms responsible for earthquake triggering. In particular, the forecasting problem will be presented in a rigorous mathematical framework, discussing the relevance of the processes acting at different temporal scales for different levels of prediction. In this review we also briefly discuss how the statistical mechanics approach can be applied to non-tectonic earthquakes and to other natural stochastic processes, such as volcanic eruptions and solar flares.

Modeling long-term volcanic hazards through Bayesian inference: an example from the Tohoku arc, Japan

Article

Jan 2004

A.J. Martin

Data Mining Applications Using Artificial Adaptive Systems

Book

Apr 2013

W.J. Tastle

This volume directly addresses the complexities involved in data mining and the development of new algorithms, built on an underlying theory consisting of linear and non-linear dynamics, data selection, filtering, and analysis, while including analytical projection and prediction. The results derived from the analysis are then further manipulated such that a visual representation is derived with an accompanying analysis. The book brings very current methods of analysis to the forefront of the discipline, provides researchers and practitioners the mathematical underpinning of the algorithms, and the non-specialist with a visual representation such that a valid understanding of the meaning of the adaptive system can be attained with careful attention to the visual representation. The book presents, as a collection of documents, sophisticated and meaningful methods that can be immediately understood and applied to various other disciplines of research. The content is composed of chapters addressing: An application of adaptive systems methodology in the field of post-radiation treatment involving brain volume differences in children; A new adaptive system for computer-aided diagnosis of the characterization of lung nodules; A new method of multi-dimensional scaling with minimal loss of information; A description of the semantics of point spaces with an application on the analysis of terrorist attacks in Afghanistan; The description of a new family of meta-classifiers; A new method of optimal informational sorting; A general method for the unsupervised adaptive classification for learning; and the presentation of two new theories, one in target diffusion and the other in twisting theory. © Springer Science+Business Media New York 2013. All rights are reserved.

K-CM application for supervised pattern recognition at Mt. Etna: an innovative tool to forecast flank eruptive activity

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