Enhancing the significance of gravitational wave bursts through signal classification

Abstract

The quest to observe gravitational waves challenges our ability to discriminate signals from detector noise. This issue is especially relevant for transient gravitational waves searches with a robust eyes wide open approach, the so called all- sky burst searches. Here we show how signal classification methods inspired by broad astrophysical characteristics can be implemented in all-sky burst searches preserving their generality. In our case study, we apply a multivariate analyses based on artificial neural networks to classify waves emitted in compact binary coalescences. We enhance by orders of magnitude the significance of signals belonging to this broad astrophysical class against the noise background. Alternatively, at a given level of mis-classification of noise events, we can detect about 1/4 more of the total signal population. We also show that a more general strategy of signal classification can actually be performed, by testing the ability of artificial neural networks in discriminating different signal classes. The possible impact on future observations by the LIGO-Virgo network of detectors is discussed by analysing recoloured noise from previous LIGO-Virgo data with coherent WaveBurst, one of the flagship pipelines dedicated to all-sky searches for transient gravitational waves.

Full text

Enhancing the significance of gravitational wave
bursts through signal classification
S.Vinciguerra1, M. Drago2, G.A. Prodi3, S. Klimenko4,
C.Lazzaro5, V.Necula4, F.Salemi2, V.Tiwari6, M.C.Tringali3, G.
Vedovato5
1University of Birmingham, Edgbaston, Birmingham, B15 2TT,United Kingdom
2Albert-Einstein-Institut, Max-Planck-Institut für Gravitationsphysik, D-30167
Hannover, Germany
3Universitá di Trento, Dipartimento di Fisica, and INFN, TIFPA, I-38123 Povo,
Trento, Italy
4University of Florida, Gainesville, Florida 32611, USA
5INFN, Sezione di Padova, I-35131 Padova, Italy
6Cardiff University, Cardiff CF24 3AA, United Kingdom
Abstract. The quest to observe gravitational waves challenges our ability to
discriminate signals from detector noise. This issue is especially relevant for transient
gravitational waves searches with a robust eyes wide open approach, the so called all-
sky burst searches. Here we show how signal classification methods inspired by broad
astrophysical characteristics can be implemented in all-sky burst searches preserving
their generality. In our case study, we apply a multivariate analyses based on artificial
neural networks to classify waves emitted in compact binary coalescences. We enhance
by orders of magnitude the significance of signals belonging to this broad astrophysical
class against the noise background. Alternatively, at a given level of mis-classification
of noise events, we can detect about 1/4 more of the total signal population. We also
show that a more general strategy of signal classification can actually be performed, by
testing the ability of artificial neural networks in discriminating different signal classes.
The possible impact on future observations by the LIGO-Virgo network of detectors is
discussed by analysing recoloured noise from previous LIGO-Virgo data with coherent
WaveBurst, one of the flagship pipelines dedicated to all-sky searches for transient
gravitational waves.
arXiv:1702.03208v1 [astro-ph.IM] 10 Feb 2017

1. Introduction: signal classification for background rejection
General searches for transient gravitational waves of generic waveform (GW bursts) have
been accomplished exploiting the full sensitivity bandwidth of the Laser Interferometer
Gravitational-Wave Observatory (LIGO) [1, 2] and Virgo [3, 4] detectors. This type
of all-sky search has been performed by analyzing the network detector data with co-
herent methods [5, 6] looking for signals lasting from ms to sscale. These methods
successfully identified the first detected gravitational wave, GW150914 [7, 8]. In burst
searches, the main factor which limits the statistical confidence of a gravitational wave
candidate comes from non Gaussian noise outliers of single detectors, which may ac-
cidentally mimic a coherent response of the network. The implemented strategies to
improve the capability of discriminating between signals and noise include both up-
stream and downstream methods. Upstream methods include data quality flags and
vetoes at single detector level [9, 10] to clean the input of the network analysis. Down-
stream methods apply post processing procedures such as splitting the end results in a
few separate frequency bands: to account for the most evident inhomogeneities of non
Gaussian noise tails, any candidate belonging to a specific frequency band is thus ranked
against the noise outliers characteristic of the same band.
Coherent WaveBurst (cWB) [11] is the flagship pipeline aiming at all-sky burst
searches on LIGO-Virgo data using minimal signal assumptions. cWB has already been
used for the analysis of data collected by the first generation of interferometers [12, 13]
and during the first observation run of Advanced LIGO, O1. In September 2015 cWB
was the first pipeline to identify GW150914 [8]. cWB is based on a likelihood maxi-
mization of the coherent response of the network, which also allows the reconstruction
of the most significant signal characteristics [12, 14]. To further reduce the false alarm
probability at a reasonable cost in terms of false dismissals, additional procedures have
been implemented. These procedures include simpler tests, such as the rejection of
candidate signals in case of unusually high energy disbalance at different detectors, as
well as more elaborate methods. Among them, cWB uses procedures for constraining
the polarization and direction of detectable signals, since noise spectra and directional
sensitivities affect the fraction of detectors which significantly contribute to the coher-
ent response of the network. All the strategies mentioned above preserve the degree of
universality, typical of burst searches.
The performance of the pipeline can also take advantage of priors on the target
signals; however, this is accomplished at the cost of a loss of generality of the search.
Different versions of cWB pipeline have been tailored for, e.g., the search for coales-
cences of intermediate mass binary black holes [15] or of highly eccentric binary Black
Holes [16].
The scope of this work is to demonstrate how signal classification methods can

Chirping signals in GW burst searches 3
complement all-sky burst searches to enhance the significance of selected signal classes
without losing the generality of the search. The proposed signal classification method
is based on machine learning techniques [17] to identify such signals against the non
Gaussian noise outliers recorded in LIGO-Virgo observations. The signal vs. noise dis-
crimination based on the use of machine learning techniques on single detector data has
been discussed in several papers. For instance [18, 19, 20] address the classification of
transient noise outliers and [21] the whitening of the detector output. A signal recog-
nition approach based on boosted decision trees has been tested for the case of a burst
search triggered by astrophysical events in a network of detectors [22]. Similarly, in [23],
the authors developed a multivariate classification with random forests in the context
of matched filtering searches for high-mass black hole binaries.
The novelty of our work lies in its integration into all-sky burst searches and
on the implementation of new strategies for signal classification, taking advantage of
pattern recognition in the framework of the time-frequency (TF) representation of
the candidate signals. The latter is accomplished by averaging the response of more
artificial neural networks (ANNs), as explained in Section 2. As a case study, we
focus on the recognition of signals consistent with coalescences of compact binaries
(Section 3). Section 4 and Section 5 discuss respectively the effectiveness of the ANN
analyses of the TF representations and its robustness against changes in the target
signal distribution. Section 6 explores the potentiality of a further multivariate step:
we test a new ranking statistic built by combining the discrimination variables, adopted
in a standard cWB analysis, with the output parameter describing the recognition of
time-frequency patterns. By comparing the receiver operating characteristics, we show
the achievable enhancement of GW burst searches through our signal classification
strategies. In Section 7, we give more general remarks about the impact of signal
classification approaches on all-sky searches for GW bursts.
2. Methodology
With the purpose of enhancing the significance of GW bursts in all-sky searches, we
complement the standard analysis pipeline cWB with a new discrimination variable
based on ANNs, dedicated to signal classification according to their TF characteristics.
In its standard operation, cWB uses two main post-processing statistics to discriminate
gravitational waves from noise artifacts (glitches): the network correlation coefficient
(cc) and the effective correlated SNR (ρ) [8]. The latter is used to rank candidate events
and assign them a false alarm rate. The former measures the consistency of the candidate
with a coherent response of the network to a GW. cWB uses TF transformations [24] at
different resolutions (or levels) and defines the TF characterisation for each candidate,
through e.g. a Principal Component Analysis (PCA) [25]. We use a PCA since it
summarises the main TF characteristics of each candidate in the least number of TF
pixels from different resolutions.

Chirping signals in GW burst searches 4
To perform the ANN classification, the resulting TF representations in the whitened
data domain are converted by a post-processing algorithm into a frame made by 8×8
pixels, each described by a scalar amplitude proportional to the fraction of total likeli-
hood †(see Fig 1). Each frame carries no information about the absolute scale of the
candidate strength, duration or frequency band and keeps only the uncalibrated shape
information of the candidate’s TF trace (for more details see Appendix A).
The 64 entries of the 8×8frame feed the ANNs dedicated to the classification of
Figure 1. Schematic representation of the proposed event classification. The
procedure is based on the reconstructed time-frequency map of candidates. ANNs are
trained to produce an output number close to 1for events are classified as belonging
to the target distribution, and close to 0otherwise. Our procedure does not constrain
the output value to be limited to [0,1] and overflows and underflows are possible.
the TF pattern. ANNs are informatic tools composed of calculation units (neurons -
represented by circles in Fig. 2), connected together by synapses (represented by lines
in Fig. 2), which acquire specific values (weights) accordingly to a supervised training
procedure‡(see [26] and references therein). The ANNs adopted for this study are mul-
tilayer perceptrons defined within ROOT [27] (the object oriented framework developed
at CERN). Every ANN is composed of an input layer, fed by the 8×8frame, and of 3
hidden layers, requiring the definition of about 2×103synapses. Each ANN is trained
against a set of ∼104target signals (type1 class) and a set of ∼104complementary
events (type0 class) composed of either noise glitches or signals belonging to alternative
†In the algorithm dedicated to the definition of the frame, we also allow the rejection of late TF
pixels with low likelihood. Starting from the pixels that appeared at the latest times, the procedure,
which defines the 8×8frame, discards a fraction of the TF pixels, corresponding to at most 10%
of the total likelihood. This selection prevents the occurrence of problematic distortions of patterns
in the 8×8frames. Noisy pixels selected after the merger time would indeed shrink and move the
characteristic trace left by chirping events on the 8×8frame. This operation is particularly useful for
the classification in real noise. In fact, it favours a neater TF map by rejecting any weak structures
appearing after the merger time, which will then dominate the last column of the frame (see Fig 1).
‡A supervised training procedure consists in an optimization rule tailored to minimize the error
between actual and desired output over the selected target and complementary sets of signals.

Chirping signals in GW burst searches 5
classes. The classification rule consists in obtaining output values close to 1/0for ele-
ments of type1/type0 class respectively. For more details on the structure and training
procedure used for the present study, see Appendix B and [27].
We mitigate the impact of the statistical fluctuations intrinsic to the ANN response
by averaging the output of 4 (unless otherwise specified) independently trained ANNs
and so introducing the ANN average, as shown in Fig. 2. Every considered ANN
is built with the same fixed training procedure, but each of them is trained over an
independent set of events sampled from the same distributions. The time required
for the definition of a single ANN varies by several orders of magnitude according to
the adopted training. However, once defined, ANNs are able to quickly evaluate cWB
triggers, providing an effective discriminating variable, as illustrated in Fig. 3. In this
ANN average
hANN i
Figure 2. Schematic representation of the algorithm adopted to obtain the ANN
average. In the square it is summarised the structure of each ANN: the black filled
circles compose the input layer, while the empty ones represent elaborating units. Each
of them sums the output values of the previous layer, by weighting them with the
correspondent synapse’s (lines) strength. The new classification parameter is obtained
by averaging the result of 4 independent ANNs (ANN average).
preliminary test, we considered a population of target signals (type1) made by compact
binary coalescences (see Tab. 2) and a population of accidental coherent responses of
the initial LIGO-Virgo network of detectors (network glitches, type0). The former is
produced by software injections of signals in a few days of initial LIGO and Virgo data
from S6D-VSR3 runs [6, 28], recolored according to the early phase spectral sensitivity
of advanced detectors [29]. The set of network glitches is produced by running the
standard cWB all-sky search on the same recolored data streams after applying a set of

Chirping signals in GW burst searches 6
time-shifts among different detectors so to cancel any physical correlation present. The
use of actual data is necessary to model the non Gaussian noise features that dominate
the performances of all-sky burst searches. Fig. 3 shows that ANNs can be effective
in discriminating these target signals from network glitches, to a much more efficient
degree than the more general criteria used by cWB.
Figure 3. Distributions of 5×104target CBC signals (red, see Tab. 2) and 5×104
network glitches (blue) as seen in different analysis variables.
y axis: fraction of events in the xbin.
x axis, from left to right: network correlation coefficient, correlated SNR and average
of 4 trained ANN outputs. The first two are the main test statistics used by cWB in
GW burst searches.
3. Case study: classification of chirping signals
In this Section we focus on the classification of a specific signal class, emitted by
compact binary coalescences. The results will be highlighted in Section 4 while their
robustness will be discussed in Section 5, proving that the enhancement provided by
our classification still holds over a much wider signal parameter space than that used to
train the ANNs.
3.1. Type1 or target signal class
The results of the first observing run of advanced LIGO [30] and the measured rate
for binary black hole (BBH) mergers of 9−240 Gpc−3yr−1[31] confirm that compact
binary coalescences are the most numerous sources for current ground based detectors.
In this study, we focus on the classification of the inspiral phase of the binary evolution.
During the inspiral, the gravitational emission is mainly determined by the chirp-mass
M=(m1m2)3/5
(m1+m2)1/5, where m1and m2are the masses of the two companions. The chirp-
mass drives:

Chirping signals in GW burst searches 7
•the frequency evolution ˙
f∝ M5/3f11/3of the gravitational waves, which sets the
chirping behaviour commonly associated to these signals;
•the gravitational wave strain amplitude, which in time domain is: A(t)∝f2/3M5/3;
•the time spent in the most sensitive part of the spectral sensitivity of the detectors,
which scales as tdet ∝ M−5/3. This time is also strongly dependent on the noise
spectral density (PSD) of detectors at lower frequencies.
Since the classification procedure depends on these properties, we investigated different
distributions of chirp-masses. In particular, we mainly tested two signal populations:
•alow-mass distribution (see Tab. 1) composed of signals characterised by a clear
chirping feature in the TF representation, which is dominating the detectable signal
within the spectral sensitivity of the detectors.
Mass distribution uniform in Mtot and m1/m2
Total mass range [MJ]Mtot∈[3,50]
Mass ratio range m1/m2∈[1,11]
Distance range d[Mpc] ∼[70,225]
number of Shells∗[32] 3
Distribution in each shell uniform in volume
Table 1. main parameters of the low-mass CBC signal distribution.
∗The subdivision in shells is performed to decrease the computational load while
ensuring more homogeneous statistical uncertainties on detection efficiency. The
reference shell range is [100−150] Mpc and by rescaling signal amplitudes we populate
the two contiguous shells ([∼70,100] Mpc and [150,225] Mpc).
•awide mass range distribution (see Tab. 2), composed of a CBC population
including more massive systems and therefore shorter detectable signals, in which
the inspiral phase plays a weaker contribution within the spectral sensitivity
considered in this study (early phase of advanced detectors).
Mass distribution uniform in log(m1),log(m2)
Mass range [MJ]m1,2∈[1.5,96.0],Mtot∈[3.0,136.0]
Distance range d[Mpc] ∼[45,500]
number of Shells∗[32] 6
Distribution in each shell uniform in volume
Table 2. Main parameters of the wide-mass range signal distribution.
∗As described in Table 1, but rescaling signal amplitudes to populate five contiguous
shells from ∼45 Mpc to ∼500 Mpc. Detection efficiencies are listed in table 3.
As CBC signals models, we adopt EOBNRv2 waveforms [33, 34]. They rely on
the effective-one-body (EOB) formalism and describe all the phases (inspiral, merger
and ring-down) of the coalescence. The actual distributions of the detected signals

Chirping signals in GW burst searches 8
used in this study are a convolution between the signal population (from Tab. 1 or
Tab.2) and the cWB detection efficiency. Fig. 4 illustrates the selection effect due to
this convolution on the wide-mass-range signal distribution (Tab.2). As expected the
detection pipeline is more sensitive to louder signals, i.e. for more massive systems
(Fig. 4). Indeed the gravitational wave amplitude scales as A(t)∝f2/3M5/3and
M(M, q) = Mq3/5(q+ 1)−6/5, where q=m1/m2is the mass ratio. Tab.3 lists the
overall detection efficiencies of cWB in the different shells. As expected, the pipeline
efficiency decreases as the distance range increases.
Figure 4. Event distribution of injected signals (violet) and reconstructed by
cWB (green) for mass-ratio (left panel) and chirp-mass (right panel). cWB pipeline
reconstructed ∼6.5×104out of about 1.7×105signals, injected according to Tab.2.
Shell distance range [Mpc] Efficiency %
[∼45,∼65] 72.3±0.3
[∼65,100] 57.8±0.2
[100,150] 42.5±0.1
[150,225] 29.2±0.2
[225,∼340] 18.3±0.3
[∼340,∼505] 10.2±0.1
Table 3. cWB detection efficiency per shell [32], for CBC signals belonging to the
wide-mass-range distribution (see Tab.2 and Fig. 4)
3.2. Type0 or alternative signal class
Our case study requires to test the classification procedure with respect to both network
glitches and alternative GW signals. The network glitch distribution has been described
in Section 2. As alternative signal class we considered a mixture of GW signal
waveforms widely used in simulations of GW burst searches, i.e. the BRST set described
in [35], which includes Gaussian pulses, sinusoidal signals with Gaussian amplitude
envelope as well as White-Noise-Bursts waveforms. Such alternative signals lack of a

Chirping signals in GW burst searches 9
proper astrophysical model and therefore their amplitude distribution at earth has been
modeled by scaling their nominal amplitude value (hrss ≡qR∞
−∞ h2(t)dt = 2.5×10−21)
by a grid of logarithmically distributed scaling factors (0.075,0.15,0.3,0.6,1.2,2.4,4.8,
9.6,19.2), see [6, 12]. All these signals have been injected on the same recolored data
set used for the target signals injections.
4. Classification performance results
The main three tests of classification performances are summarized in Tab. 4.
type1 class type0 class
Test 1 chirp-like GWs from low-mass distribution (Table 1) network glitches
Test 2 chirp-like GWs from low-mass distribution (Table 1) alternative BRST GWs
Test 3 chirp-like GWs from wide-mass distribution (Table 2) network glitches
Table 4. Summary of type1 and type0 classes used for the main three tests of
classification performances.
The results are described in terms of the fraction of type1 (type0) events which are
correctly classified (miss-classified) as belonging to the target class, F1→1(F0→1)defined
by:
Fk→1=1
Nk
Nk
X
i=1
δi(1)
Here Nkis the total number of tested events drawn from the kclass (where k= 1,0for
type1,type0) and δiis defined for each event iby:
δi=(1,if ρi≥ρth ∧cci≥ccth ∧ hANN ii≥ hAN N ith
0,otherwise (2)
where the subscript “th” refers to threshold value on the related variable. Events
with δi= 1 (δi= 0) are classified as belonging to the type1 (type0) class. Fig. 5-
7summarise the results of each test and provide a comparison of the effects of the
standard test statistics of cWB (correlated SNR and network correlation coefficient)
with the ANN average. Each figure is made by four plots, whose y-axis reports F1→1
and F0→1respectively in the top ones and bottom ones. The plots to the left show
F1→1and F0→1as a function of the threshold on the correlated SNR, ρth. The red
lines represent results obtained without applying a threshold on the ANN average (or
hANN ith =−∞), while green curves show the effects of selected threshold values,
namely hANN ith ={0.0,0.5,1.0}. The plots to the right show F1→1and F0→1as a
function of the threshold on the ANN average. Here blue curves are computed by
applying different thresholds on the correlated SNR ρth ={5,6,7}. In all the plots a
constant threshold on the network correlation coefficient is used, ccth = 0.6, which is

Chirping signals in GW burst searches 10
a common choice in standard GW burst searches [8]. This cc threshold makes all the
plotted fractions F1→1and F0→1lower than 1.
4.1. Test1: low-mass chirp-like GWs vs glitches
The first classification test aims to discriminate network glitches from chirp-like signals
of the low-mass distribution (first line of table Tab. 4). The results on a population
of 5×104events per each type are reported in Fig. 5: both correlated SNR and the
ANN average are effective classifiers but their joint use shows advantages. In fact,
TARGET SIGNALS TARGET SIGNALS
GLITCHES GLITCHES
hANN ith
hANN ith
⇢th
⇢th
F0!1
F0!1
F1!1
F1!1
Figure 5. Left plots: F1→1(top) and F0→1(bottom) as a function of ρth. Right
plots: F1→1(top) and F0→1(bottom) as a function of hAN N ith . A constant threshold
for ccth ≥0.6is used. In the left plots, the red lines show the results obtained by a
standard cWB analysis, while the green curves use also the signal classification with
hANN ith ={0.0,0.5,1}, from top to bottom. In the right plots, the blue lines are
computed for ρth ={5,6,7}from top to bottom. The results refer to 5×104events
from the low-mass GW distribution and to the same number of network glitches.
it is possible to enhance the statistical confidence with a much smaller cost in terms
of detection efficiency. For instance, considering the left plots, at any selected value
of ρth, by adding hANN ith = 0.5almost the same fraction of chirp-like signals are
recovered, while the fraction of mis-classified glitches F0→1is reduced by about one
order of magnitude. The right plots lead to similar considerations. F1→1depends very

Chirping signals in GW burst searches 11
weakly on hANNith as long as hAN Nith ≤0.8, while the mis-classified fraction of events
F0→1drops substantially in the same hANNith range.
4.2. Test2: low-mass chirp-like GWs vs alternative GWs
The signal classes considered for this test are the low-mass distribution and the
BRST simulation set introduced as alternative signal class in 3.2. The results of the
classification are reported in Fig. 6, which shows the performances in terms of F1→1
and F0→1with the same structure of Fig. 5. In particular, the right plots illustrate that
the ANN average provides an efficient separation of the two GW populations, while the
correlated SNR is instead agnostic with respect to the GW waveform class. In this test
we selected a population of alternative GWs which are louder than the target GWs, to
test an opposite condition with respect to what described in the previous subsection.
The results are consistent with the ANN average being agnostic with respect to the
loudness of the events, as it was designed to be. The chosen loudness of the alternative
F0!1
F0!1
F1!1
F1!1
hANN ith
hANN ith
⇢th
⇢th
TARGET SIGNALS TARGET SIGNALS
ALTERNATIVE SIGNALS ALTERNATIVE SIGNALS
Figure 6. The Figure is structured as Fig. 5. The right plots clearly illustrate that
the ANN average provides an efficient separation of the two GW populations. Results
refer to 104type1 signals from the low-mass distribution and an equal number of type0
events from the alternative signal class, formed of BRST simulation. All the signals
have been injected in recoloured detectors data. For this test, the ANN average is
computed from the outputs of just 2 ANNs.
GW class carries no specific physical meaning, and the difference between F1→1and

Chirping signals in GW burst searches 12
F0→1in the left plots cannot be used to classify type1 and type0 events in an actual
GW search.
4.3. Test3: wide-mass chirp-like GWs vs glitches
The task of the last classification test is separating network glitches from chirp-like
signals, drawn from the wide-mass range simulation (Table 2). We report the results
in Fig. 7. The plots of Fig. 7 and Fig. 5 exhibit very similar trends. The main
F0!1
F0!1
F1!1
F1!1
hANN ith
hANN ith
⇢th
⇢th
TARGET SIGNALS TARGET SIGNALS
GLITCHES GLITCHES
Figure 7. The image is structured as Fig. 5. The test is applied on 5×104type1
signals from the wide-mass range distribution and 5×104type0 events from the set of
recolored network glitches.
difference is that F1→1values are generally slightly higher, since the wide-mass event
distribution includes also louder GWs. Instead, even if the chirping character is weaker
for the wide-mass signals distribution, the results show that the ANNs can be trained
to give comparable performances with respect to the low-mass case.
5. Robustness
When the learning is supervised [26], as in our case, the ANN structures are defined
thorough procedures mainly driven by the selected type0 and type1 samples. Since
the astrophysical distribution of chirp-like GWs is unknown, we need to investigate the

Chirping signals in GW burst searches 13
robustness of our approach against biases in the training distributions. To this purpose,
we consider Receiver Operating Curves (ROC) computed as F1→1vs F0→1by varying
the value of ρth, while keeping constant ccth = 0.6, at selected hAN N ith values. Fig. 8
shows ROC curves for hANNith =−∞ and hAN Nith = 0.25. The robustness is tested
by comparing the improvement related to the application of the hANNith = 0.25 on the
ROC in two different cases:
•classification results are performed on chirp-like signals belonging to the same type1
distribution used for the training;
•classification results are performed on chirp-like signals belonging to a distribution
different from that of the type1 used for the training.
Training set We build a simulation of GW emissions from three fixed equal-mass bi-
naries (10 −10)MJ,(25 −25)MJand (50 −50)MJ(see Table C1). From each of
these three sources, we collect an equal number of reconstructed events to compose
the training set for the target (type1) signals. The type0 training class is again de-
fined with a sample of network glitches recoloured to mimic the spectral sensitivity
in the early phase of the advanced detectors.
Testing sets The first one is composed of samples of the same type1 and type0
populations used to define the training set just described, while the other one
is formed by events drawn from the type1 and type0 classes of line 3 in table 4.
For both cases, the tested type0 events are independent samples of the recoloured
network glitches.
As expected, the ROC curves for a testing set different from the training set are worse,
see Fig. 8. However, the improvement on the ROC achieved by implementing the
threshold on the ANN average are significant and of comparable value in both testing
sets. In this sense, Fig. 8 demonstrates the robustness of our approach against biases in
the population-model. Since the mismatched type1 testing set has a much wider range
of chirp-masses than the matched one, we present the achieved results of Fig. 8 as rep-
resentative of the effect produced by increasing the assumed volume in the parameter
space of the source population.
6. Multivariate analysis
The last versions of the cWB pipeline include an estimation of the binary chirp-mass
Mest, computed as a best fit of the signal TF trace resulted from the PCA. To compute
the fit, the algorithm considers all the pixels obtained with the TF decomposition at
different levels, discarding the ones flagged as noise artifacts, according to the proce-
dure defined in [8, 36]. Applying such post-processing analysis significantly improves
the signal to noise discrimination achieved by cWB for CBC signals [36].

Chirping signals in GW burst searches 14
Figure 8. F1→1vs F0→1measured with (blue squares and green void cycles) and
without (red filled circles and teal triangles) the application of a threshold on the
ANN average of 0.25. Symbols correspond to the same grid of ρth values. The red and
blue curves (matched) are the results performed by testing the same signal population
used to train the ANNs. The green and teal lines (mismatched) trace the ROC for
a different test set built selecting CBC signals from the wide-mass range distribution.
In both the cases, 5×104CBC signals form the type1 class and the same number of
network glitches form the type0 one.
The joint distribution of the estimated chirp-mass and the ANN average (see Fig. 9)
demonstrates that the two variables are not fully correlated. This gives the opportunity
to further improve the results by a joint use of these variables. In addition we can con-
sider other signal parameters estimated by cWB to implement a multivariate analysis
(MVA).
For the morphological discrimination we are interested in, we implement an addi-
tional classification stage, using four MVA-ANNs (see Fig. 10). They are characterised
by approximately 300 synapses and independently trained on ∼103events per class.
The input quantities listed in Fig. 10 are then used to define a MVA-ANN average
(hMV Ai). We evaluated the effectiveness of the multivariate approach by comparing
the ROC obtained from this MVA ranking statistic (MVA-ANN average) with the one
driven by different values of correlated SNR, accordingly to the standard cWB analysis.
Fig. 11 clearly demonstrates that cWB’s performances in discriminating signals from
glitches can be considerably improved by adopting the MVA-ANN average as ranking
statistic. In fact, at fixed F1→1values F0→1is lowered down by three orders of magnitude,
when switching the ranking statistic from the correlated SNR to the MVA-ANN average.

Chirping signals in GW burst searches 15
Relative frequency Relative frequency
TARGET SIGNALS
GLITCHES
hANN i
hANN i
Mest[M]
Mest[M]
Figure 9. Distributions on plane defined by ANN average and the estimated chirp-
mass of candidates belonging to the wide-mass signal class (Top panel) and S6D
recoloured glitches (Bottom panel). The colour scale represents the fraction of recovered
events, over a total of 5×104per class. Negative values estimated chirp-mass are
automatically set to zero.
We finally performed checks to point out the sensitivity of our MVA-ANN average
to the different inputs. These tests show that the estimated chirp-mass and the ANN
average are by far the ones that impact more the results. Much smaller contributions
comes from the central frequency, the correlated SNR and the network correlation
coefficient, while duration and frequency bandwidth are the parameters which appear
to be the least effective for our multivariate analysis.
7. Final Remarks
In the previous sections we presented the application of the signal classification to the
selected case study, i.e. CBC-like transient signals with an inspiral stage chirping up in
frequency. The resulting enhancement of the significance of the detected signals in this
class is improved by orders of magnitude, at least in the confidence range investigated
here (see Fig. 11). Alternatively, the gain can be interpreted as a significant increase
of the detected fraction of sources at a given confidence, e.g. we recover ∼25% more

Chirping signals in GW burst searches 16
ANN average
Estimated chirp-mass
Central frequency
Frequency band-width
Duration
Network correlation coefficient
Correlated SNR
yi,MVA
MVA-ANN
average
ANNi,MNA
1
4
4
X
i=1
yi,MV A
hMVAi
y1,MVA
y2,MVA
y3,MVA
y4,MVA
Figure 10. Schematic representation of the algorithm adopted to define the MVA-
ANN average. In the left square, we list all the input quantities elaborated by all the
four ANNi,MVA to obtain hM V Ai.
signals at a mis-classification of 0.01% of noise events. The current approach could
be further improved by considering more candidate parameters (cc,ρ,Mest, etc ), as
proposed in Section 6 by defining a new ranking statistic hMV Aiand by generalising
the classification to other signal classes.
This search can be easily integrated within the framework of an all-sky search,
where the search is general and open to every kind of GW-like signals with no partic-
ular assumptions on the morphology. In this situation, we can split the overall set of
interesting triggers, W, in two classes, the say class A⊂Wof CBC-like signals and the
complementary class (W−A)of triggers belonging to Wbut not to A. Following this
approach for many waveform classes, all-sky searches can be managed as more separate
searches on the same observation time, similarly to the more traditional case of all-sky
searches performed on separate frequency bands. To account for the increased number
of trials, a relative weight on these searches has to be chosen to portion out the overall
false alarm probability of the all-sky search.
Signal classes of astrophysical interest can be, for example, ring-down-like signals
as emitted in quasi normal modes of NSs [37] - say class Bsignals, or, more generically,
signals with a reconstructed duration longer than a number of typical cycles, allowing
for a diversity of waveform amplitude envelopes and phase evolutions in time - say class
Csignals. In addition, glitch classification methods can also be implemented for vetoing

Chirping signals in GW burst searches 17
Figure 11. ROC using the MVA-ANN average (red) and the correlated SNR (blue)
as a ranking statistic. In the last case, F1→1and F0→1are obtained considering a
constant threshold on the network correlation coefficient ccth >0.6and ignoring the
ANN average. The testing set, as well as the training one, has been defined by 5×104
samples of S6D recoloured glitches (type0) and by 5×104signals drawn from the
wide-mass range distribution (type1).
purposes, i.e. to reject the more frequent noise transient families at the detectors - say
class Z. The most straightforward implementation of the all-sky search would then be
a hierarchical signal classification scheme in subsequent steps, such as e.g. selecting
A⊂(W−Z), then B⊂(W−Z−A), then C⊂(W−Z−A−B)and finally analysing
the rest (W−Z−A−B−C). Such a hierarchical implementation would ensure that
the considered classes are disjoint, both for signal and for glitches. Of course the more
background rejection is accomplished in the first classification steps, the higher will be
the resulting background left to the last ones.
In the framework of all-sky searches, the optimization strategy is not defined, both
because we are lacking reliable source population models for most source classes and
because we want to be leave room for unexpected detections. The prioritization of sig-
nal classes and the portioning of the overall false alarm probability among the classes is
subjective and has to be agreed upon, as a balance between boosting detection probabil-
ity of better known sources and preserving suitable detection chances for signals in the
widest accessible duration-frequency range. The former requires to take into account
the detectable source number within the visible volume of the search; therefore, it would
prioritize e.g. the frequency band of best spectral sensitivity and/or some waveform or
polarization class. The latter instead calls for the consideration of the entire spectral

Chirping signals in GW burst searches 18
range of the detectors, including disadvantaged spectral sensitivity bands, and for un-
modelled waveforms and polarization states.
This issue has to be addressed anyway, regardless of the implementation of signal
classification methods. In past all-sky searches, the portioning of the false alarm prob-
ability has been driven by uniform priors, i.e. by accounting a-posteriori for the trial
factor coming from multiple sub-searches on different bandwidths or, in other words, by
ranking signal candidates according to a quantity closely related to their inverse false
alarm rate, as measured within the related sub-search. A portioning close to uniform
makes sense also for the hierarchical search depicted here.
Acknowledgment
We would like to thank Ilya Mandel for the useful suggestions concerning this work.
The research leading to these results has received funding from the People Programme
(Marie Curie Actions) of the European Union’s Seventh Framework Programme
FP7/2007-2013/ (PEOPLE-2013-ITN) under REA grant agreement n ◦[606176]. It
reflects only the author’s view and that the Union is not liable for any use that may be
made of the information contained therein.
Appendix A. Conversion of TF representations into 8×8frames
ANNs are here trained to recognise the common patterns in the TF representation
of chirping signals. ANNs input layer are feed with the values of an 8×8frame
constructed starting from the Time-Frequency Principal Component Analysis run by
cWB 2G. The TF representation is defined by applying the Wilson-Daubechies-Meyer
(WDM) transformation to the data [38] at different time (∆T) and frequency (∆F)
resolutions (related to each other by ∆T×∆F= 1/2). Then the algorithm applies the
PCA to the most energetic pixels of each map (core pixels) to represent a particular
event. From this multiple map representation, we analyse the possibility of discarding
pixels, according to the rule mentioned in the first footnote of Section 2. With this
information we are able to focus (“zoom”) on the TF region really involved by the event.
This selected region is divided into fundamental units, i.e. the minimum time resolution
of the selected core pixels and half of the minimum frequency resolution (according to
the application of WDM transformations). We finally group all the resulted units so to
obtain a 8×8frame. In order to adjust the “zoomed” region to the 8×8frame, each
of the 8×8squares can contain more fundamental units, or a fraction of them. The
corresponding 64 values are therefore obtained by summing or spreading the likelihood
of the all fundamental units used to define each frame square. These values are then
normalised and used to feed the ANNs. More details can be found in [27].

Chirping signals in GW burst searches 19
Appendix B. Analysis and parameters
Table B1 reports the cWB-parameters adopted for the transient searches described in
the paper.
PARAMETER VALUE PARAMETER VALUE
ρthreshold 5cc threshold ∼0.5
search type idetector network V1H1L1
range of f from 64Hz to 2048Hz data set S6D
range of δt from ∼3.90ms to 250ms range of δfmax from 2Hz to 128Hz
∆tcluster 3s∆fcluster 130Hz
Table B1. Main cWB parameters used to analyze the recolored data [39], [24].
The training procedure, applied to construct the ANNs used for classifying TF
patterns, is defined by the parameters reported in Table B2 (for more details on the
parameters and their choice see [40] and [27]).
Training set 16384 BKG-events, 16384 SIG-events
Epoch number 650
Normalization to the total of each matrix representation
to the maximum for each matrix element on the training set
Architecture IN: 64; H: 16/32/16; OUT: 1
Learning method Conjugate Gradients with F.R. updating formula
Table B2. The training set includes the examples used for the preliminary tests. The
architecture describes the input (IN), the hidden (H) and the output (OUT) layers
through their numbers of neurons.

Chirping signals in GW burst searches 20
Appendix C. Other signal distribution
To test robustness of the proposed analysis against the uncertainty over the chirp-like
signal distribution, we introduced another class of chirping signals, whose distribution
is defined by the parameters reported in Tab. C1.
Mass range [MJ]mi∈{10,25,50}i∈{1,2}, m1=m2
Mass distribution uniform in the 3 mivalues
Distance range d[Gpc] ∼[10−4, Rf], Rf∈{0.7,1.5,2.6}
Distance distribution uniform in d3
Table C1. Main parameters and correspondent values adopted to construct the
distribution of chirp-like events used in Sec. 5.Rf’s values are calculated taking
into account the relation SNR ∝M5/6
d.

Chirping signals in GW burst searches 21
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