published: 21 December 2018
Frontiers in Ecology and Evolution | www.frontiersin.org 1December 2018 | Volume 6 | Article 231
Miles David Lamare,
University of Otago, New Zealand
Geoscience Australia, Australia
This article was submitted to
Biogeography and Macroecology,
a section of the journal
Frontiers in Ecology and Evolution
Received: 28 June 2018
Accepted: 10 December 2018
Published: 21 December 2018
Fiorentino D, Lecours V and Brey T
(2018) On the Art of Classiﬁcation in
Spatial Ecology: Fuzziness as an
Alternative for Mapping Uncertainty.
Front. Ecol. Evol. 6:231.
On the Art of Classiﬁcation in Spatial
Ecology: Fuzziness as an Alternative
for Mapping Uncertainty
Dario Fiorentino 1
*, Vincent Lecours 2and Thomas Brey 1,3
1Helmholtz Institute for Functional Marine Biodiversity at the University Oldenburg (HIFMB), Oldenburg, Germany, 2Fisheries
and Aquatic Sciences, School of Forest Resources and Conservation, University of Florida, Gainesville, FL, United States,
3Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research, Bremerhaven, Germany
Keywords: uncertainty, spatial ecology, discrete classiﬁcation, soft boundaries, mapping transitions
Classiﬁcations may be deﬁned as the result of the process by which similar objects are recognized
and categorized through the separation of elements of a system into groups of response (Everitt
et al., 2011). This is done by submitting variables to a classiﬁer, that ﬁrst quantiﬁes the similarity
between samples according to a set of criteria and then regroups (or classiﬁes) samples in order to
maximize within-group similarity and minimize between-group similarity (Everitt et al., 2011).
Classiﬁcations have become critical in many disciplines. In spatial ecology, for example,
grouping locations with similar features may help the detection of areas driven by the same
ecological processes and occupied by same species (Fortin and Dale, 2005; Elith et al., 2006),
which can support conservation actions. In fact, classiﬁcations have been used with the aim of
investigating the spatial distribution of target categories such as habitats (Coggan and Diesing,
2011), ecoregions (Fendereski et al., 2014), sediment classes (Hass et al., 2017), or biotopes (Schiele
et al., 2015). Sometimes such classiﬁcations were found to act as surrogates for biodiversity in
data-poor regions (e.g., Lucieer and Lucieer, 2009; Huang et al., 2012), some class being known
for supporting higher biodiversity. Many of the traditional classiﬁcation methods were developed
in order to reduce system complexity (Fortin and Dale, 2005) by imposing discrete boundaries
between elements of a system; it is easier for the human mind to simplify complex systems by
identifying discrete patterns (Eysenck and Keane, 2010), and grouping similar elements together
(Everitt et al., 2011). However, in natural environments, spatial and temporal transitions between
elements of a system are often gradual (e.g., an intertidal ﬂat transitioning from land to sea) (Farina,
2010). Those transitions may display distinct properties from those of the two elements they
separate. Despite the particularities and importance of such transitions, they are often disregarded
in ecological research (Foody, 2002), leading to the adoption of approaches that, by deﬁning sharp
boundaries, may fail to appropriately describe natural patterns and groups of a system. Such
approaches have become the norm, despite the existence of approaches such as, fuzzy logic (Zadeh,
1965) and machine learning (Kuhn and Johnson, 2013) that are able to oﬀer a more representative
description of those natural transitional zones. In ecology for instance, machine learning approaces
have gained some traction because of their ability to predict classes distribution (area-wide) in
data-poor conditions (e.g., sparse punctual information) with a relative high performance and
with no particular assumption in building the relationship between targetted classes and physical
parameters (e.g., Barry and Elith, 2006; Brown et al., 2011; Fernández-Delgado et al., 2014).
In the present contribution, we aim at highlighting the limitations associated with classiﬁcation
techniques that are based on Boolean logic (i.e., true/false) and that impose discrete boundaries to
systems. We propose to shift practices toward techniques that learn from the system under study
by adopting soft classiﬁcation to support uncertainty evaluation.
Fiorentino et al. Soft Classiﬁcation and Uncertainty
The increasing availability of tools and software to semi-
automatically perform classiﬁcations has reduced the amount
of critical thoughts put into the exercise. Classiﬁcation results
are sensitive to a variety of decisions made when establishing
the methodology of a particular application (Lecours et al.,
2017). For instance, (1) the method to compare the objects
to be classiﬁed (e.g., distance-based method), (2) whether or
not the method assigns each object to one single class (i.e.,
Boolean approach) or assigns a membership for one or multiple
classes (e.g., fuzzy logic approach), (3) whether or not the
method uses samples to train the classiﬁcation (i.e., supervised
or unsupervised approach), and (4) the evaluation methods
(see Foody, 2002; Borcard et al., 2011). Furthermore, a number
of other potential sources of errors resulting in potentially
misleading classiﬁcations remains: variation in the data collection
methods, the spatial, temporal, and thematic scales (i.e., the way
the data are categorized/identiﬁed), the spatial and temporal
stability of the observations and the goodness of model ﬁt (Barry
and Elith, 2006).
One of the most challenging parts of using classiﬁcations is to
evaluate how representative of real patterns the classiﬁcation is.
Due to the cumulative eﬀect of the factors listed above (Rocchini
et al., 2011), classiﬁcation results may not adequately represent
natural patterns, making the classiﬁed patterns artiﬁcial, and
misleading, for instance when used to assist decision-making
(Lecours et al., 2017; see Fiorentino et al., 2017). Even
when a robust method is developed to reduce the impact of
these factors, the concept of discrete classes may in itself be
misleading; this type of classes can provide an incomplete,
oversimpliﬁed representation of complex natural patterns, and
thus misrepresent the reality to be described. In spatial ecology,
using discrete classes involves establishing “hard” boundaries
between them, which has been shown to cause misclassiﬁcation
errors (Sweeney and Evans, 2012; Lecours et al., 2017). For
instance, an object may not always belong to one of the deﬁned
classes, thus being forced into one of those deﬁned classes by the
classiﬁer. When doing so, the interpretation that is often made
is that the object was misclassiﬁed or that there was an error
of the algorithm, while in fact, it is a consequence of the often-
erroneous assumption that all objects must belong to a speciﬁc
class. A solution that has been proposed to avoid those errors is
to shift practices toward “soft” classiﬁcations instead of “discrete”
It has been argued in the literature that soft classiﬁcation
approaches better represent and describe natural patterns,
including transitional areas (Ries et al., 2004). Soft classiﬁcation
approaches, which include fuzzy logic (Zadeh, 1965) Bayesian,
neural networks, support vector machines, decision trees,
boosting, bagging, generalized linear models, and multiple
adaptive regression splines, among others (see Fernández-
Delgado et al., 2014 for a comprehensive review on
classiﬁcation and associated problems), acknowledge that
one object may belong to more than one class This enables
the recognition of elements of the real world that are
between classes (i.e., do not belong to one speciﬁc pre-
deﬁned class), such as transitional zones and ﬁne-scale natural
While hard classiﬁers assign an object to a class following
a Boolean, binary system (true/false, in a class or not), soft
classiﬁers assign memberships to objects. Memberships are the
estimated probabilities of objects to belong to a class (Everitt
et al., 2011). Each object will have as many membership values
as there are classes. Membership varies along the continuum
ranging from 0 (not a member) to 1 (deﬁnitely a member). An
object that has relatively high membership values for more than
one class is thus said to be not clearly associated with one speciﬁc
class. This may be an indication that no class adequately describes
this particular object, which could inform and guide further
analyses in order to explain that pattern. Those analyses may for
instance highlight that this data object is an error, or if there are
many objects in the same situation, that a new class needs to be
CAN SOFT CLASSIFICATIONS BE USED
TO ESTIMATE UNCERTAINTY?
In remote sensing, traditional pixel-based classiﬁcations use
image pixels as objects to be classiﬁed. The use of discrete
classiﬁers in land cover studies often oversimpliﬁes the actual
land cover (Foody, 2000). For instance, forested wetlands, which
in nature mark the transition between forested areas and waters
bodies, would most likely be classiﬁed as a “forest” land cover
or a “water” land cover by a hard classiﬁer. For the purpose
of this example, we assume that it classiﬁes it as “forest.” On
the other end, a soft classiﬁer might assign to that same pixel a
“forest” membership of 0.65 and a “water” membership of 0.35.
As a result, diﬀerent users could interpret those classiﬁcations
according to the following statements:
A) Based on the hard classiﬁcation result, the pixel represents
“forest” land cover. In the absence of a ground-truth point data
for that particular pixel, it could be assumed that this result is
B) Based on the soft classiﬁcation result, the pixel represents a
mixture of “forest” land cover and “water” land cover.
C) Based on the multiple memberships from the soft
classiﬁcation, the pixel has an associated level of ambiguity
(e.g., it is 35% ambiguous that the pixel represents a “forest”
land cover and 65% ambiguous that it represents a “water”
D) Based on the multiple memberships from the soft
classiﬁcation, it is possible that the pixel belongs to a
distinct class characterized by a mixture of forest and water
(the transition), perhaps “wetland.” After validation or a
re-run of the soft classiﬁcation with a new class, it could
potentially be possible to say that the pixel represents a
“wetland” land cover with much less ambiguity. While we
argue that soft classiﬁcations are more appropriate than hard
classiﬁcations, we note that a re-run of the hard classiﬁcation
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Fiorentino et al. Soft Classiﬁcation and Uncertainty
TABLE 1 | Methods for synthesizing membership values (p) resulting from soft classiﬁcations at each location (i) for a given number of classes (K).
Name Confusion index (CI) Pielou evenness index (J) Red Green Blue (RGB)
Interpretation 0 1 0 1 red, green and
yellow, violet and
full dominance of one
full dominance of one
classes have similar
full dominance of
two classes evenly
all classes have
Number of classes 2 k 3
References (Burrough et al., 1997; e.g., in Lucieer and
(Pielou, 1975; e.g., in Fiorentino et al., 2017) (Boughen, 2003; e.g., in Hass et al., 2017)
We note that the Red Green Blue (RGB) method only provides a visual representation and it is not quantitative. It combines the ﬁrst three highest memberships into a composite three-band RGB image, that is the geographic overlay of
the three bands.
with a class corresponding to wetlands would also be more
accurate than the initial hard classiﬁcation.
The interpretation in “A” is not fully representative of the
reality as the water component of the pixel is not reported
or acknowledged at all. In “B” a nuance is added to the
interpretation as the potentially mixed nature of the pixel is
acknowledged. In “C,” that nuance is interpreted as a measure of
ambiguity, i.e., that it is acknowledged that the classiﬁer could
not distinguish between the two classes. Finally, in “D,” the mixed
nature of the pixel is used to redeﬁne the classiﬁcation based
on ecological knowledge (e.g., that wetlands can be a mixture
of forest and water from a remote sensor’s perspective), and to
guide further analyses about the nature of the land cover. That
simple example illustrates uncertainty as deﬁned by Zhang and
Goodchild (2002), i.e., as the ambiguity of a classiﬁcation. Since
membership quantiﬁes the probability of an object to belong to
multiple classes, it can be used as a measure of ambiguity, and
therefore as a measure of uncertainty (Yager, 2016).
Depending on the nature of the analysis, the spatial
representation of membership can be used to display spatial
uncertainty of classiﬁcations, or to identify transitions between
existing classes. Traditional fuzzy and model-based approaches
thus acknowledge transitions among classes.
However, such approaches have the limitation to be
algorithmic, i.e., not explicitly accounting for data statistical
properties such as randomness (Warton et al., 2015) and mean-
variance trends (Warton et al., 2012)–although resampling
or ﬁnite mixture approaches may provide likelihood-based
foundations to the clustering (Pledger and Arnold, 2014). In
fact, methods based on a single classiﬁer oﬀer only one piece
of evidence, which does not provide any conﬁdence interval
of the membership estimation (Huang and Lees, 2004; Liu
et al., 2004). In turn, ensemble modeling approaches overcome
such problems in a consistent environment (Elder IV, 2003).
Despite some criticisms to ensemble modeling approaches like
the lack of interpretation capability and some tendency to
overﬁt (see Elder IV, 2003 for a discussion on the topic),
ensemble modeling approaches were shown to outperform other
methods (Elder IV, 2003; Fernández-Delgado et al., 2014). The
conﬁdence interval around the membership values provided by
such models may be used to acknowledge natural transitions
in addition to the error estimates around those membership
THE ADVANTAGE OF MAPPING
The concepts of uncertainty and error have often mistakenly
been used interchangeably (Zhang and Goodchild, 2002; Jager
and King, 2004). As a consequence, uncertainty is often perceived
negatively because of its association with the idea of error and
inaccuracy. Uncertainty is inherent to any and all data and
cannot necessarily be removed or minimized to get closer to
the truth the same way errors can (Zhang and Goodchild,
2002; Beale and Lennon, 2012). Uncertainty is part of our
perception of natural patterns (e.g., temporal dynamics, spatial
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Fiorentino et al. Soft Classiﬁcation and Uncertainty
FIGURE 1 | Example of learning classiﬁer workﬂow using a fuzzy clustering. The learning phase is linked to the data acquisition because fuzziness may highlight data
weakness, thereby areas where new data acquisition is required. Note that the same workﬂow can be translated to any other methods that allow uncertainty.
variability), data representation (e.g., positional uncertainty,
measurement uncertainty, thematic uncertainty), and modeling
(e.g., error introduced by the model) (e.g., Barry and Elith,
Maps of uncertainty, or maps of ignorance, help to identify
areas where the classiﬁcation has a stable, consistent, and distinct
solution and can be used further to target the areas where
uncertainty is higher, thus highlighting the need to deepen the
investigation in those areas (Rocchini et al., 2011). It has been
demonstrated that maps of uncertainty enhance decision-making
in conservation contexts by solving issues that often appear when
hard classiﬁcations are applied (Regan et al., 2005; Langford et al.,
2009). In fact, maps of uncertainty permit a more realistic and
natural delineation of boundaries between classes (Zhang and
Soft classiﬁcations and ensemble models allow users’
knowledge of the system to grow by providing an estimation
of uncertainty. When classes cannot provide an appropriate
description of the system under study (for example in cases
of high fuzziness), the investigator can choose to change the
classiﬁer or deepen the investigation to better understand
the patterns in the system and how it translates into the
data representation. On the opposite, Boolean (true/false)
approaches only oﬀer a static view, and while measures of
accuracy can be calculated to quantify misclassiﬁcations, they
have been shown to sometimes misrepresent the amplitude of
the misclassiﬁcations (e.g., Lecours et al., 2016) and often cannot
guide further investigations to better understand the dynamics
To assist with the interpretation of uncertainty resulting from
the application of a soft classiﬁer, at least three solutions based
on membership assignations of objects to classes can be used
(Table 1). These solutions can be used to display uncertainty
spatially in a map, which can be interpreted, discussed, and then
used to further enhance the classiﬁcation in an iterative process
We acknowledge that classiﬁcation methods need to be reliable
and appropriate for the intended use, and adequately represent
the natural complexity of the systems under study. However, we
think that the main challenge of classiﬁcations is the proper and
meaningful interpretation of the associated uncertainty rather
than the method itself.
The use of soft classiﬁers to provide the visual and spatial
display of classiﬁcation uncertainty enhances the value of
classiﬁcations. Providing a measure of uncertainty associated
with classes leads to the fulﬁllment of classiﬁcations’ potential,
which goes beyond the simple identiﬁcation and separation of
classes. Classiﬁcations based on concepts of fuzzy logic, model-
based approaches, and ensemble modeling approaches, will help
move away from classes with hard, discrete boundaries, yielding
better solutions to represent accurately and better understand
complex systems. Acknowledging uncertainty encourages
learning from the classiﬁcation process by encouraging
further investigation and hypothesizing about its causes (e.g.,
inappropriate spatial resolution, data quality, inappropriate
number of classes).
Whether the aim of an exercise is to communicate results
or to start the investigation of a system through exploratory
analyses, the spatial display of uncertainty provides directions
on which actions need to be undertaken. While stakeholders
may use map of uncertainty to ﬁnd for instance the proper
conservation measure and therefore to better handle areas where
high uncertainty is displayed, scientists may use the same
information to build new hypotheses and shed light on processes
that underpin such uncertainty.
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Fiorentino et al. Soft Classiﬁcation and Uncertainty
DF conceived and organized the manuscript. DF, VL, and TB
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We would like to thank the reviewer and Dr. Casper Kraan whose
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Conﬂict of Interest Statement: The authors declare that the research was
conducted in the absence of any commercial or ﬁnancial relationships that could
be construed as a potential conﬂict of interest.
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