Explainable Clustering Applied to the Deﬁnition of Terrestrial Biomes

Mohamed Redha Sidoumou

1 a

, Alisa Kim

, Jeremy Walton

3 b

, Douglas I. Kelley

4 c

Robert J. Parker

5 d

and Ranjini Swaminathan

6 e

Amazon Web Services, U.K.

Amazon Web Services, Germany

Met Ofﬁce Hadley Centre for Climate Science and Services, Exeter, U.K.

U.K. Centre for Ecology and Hydrology, Wallingford, U.K.

National Centre for Earth Observation, Space Park Leicester, University of Leicester, U.K.

National Centre for Earth Observation, Department of Meteorology, University of Reading, U.K.

Keywords:

Explainable AI, Explainability, Biomes, Clustering, Segmentation.

Abstract:

We present an explainable clustering approach for use with 3D tensor data and use it to deﬁne terrestrial

biomes from observations in an automatic, data-driven fashion. Our approach allows us to use a larger number

of features than is feasible for current empirical methods for deﬁning biomes, which typically rely on expert

knowledge and are inherently more subjective than our approach. The data consists of 2D maps of geophysical

observation variables, which are rescaled and stacked to form a 3D tensor. We adapt an image segmentation

algorithm to divide the tensor into homogeneous regions before partitioning the data using the k-means algo-

rithm. We add explainability to the classiﬁcation by approximating the clusters with a compact decision tree

whose size is limited. Preliminary results show that, with a few exceptions, each cluster represents a biome

which can be deﬁned with a single decision rule.

1 INTRODUCTION

Natural environment data are complex, noisy and

challenging to analyse. However, interesting

results—see, for example (Ben-Dor et al., 1999)—

can be obtained by the application of data cluster-

ing, which aims to group similar data points accord-

ing to some chosen measure. Clustering is an ex-

ample of unsupervised learning, in which algorithms

ﬁnd structures and relationships in the data without

making use of labels applied to the data, or with any

preconceptions of patterns in the data. Many cluster-

ing algorithms have been developed such as k-means

(Hartigan and Wong, 1979) and hierarchical clus-

tering (Johnson, 1967). However, before computa-

tional clustering methods existed, experts used empir-

ical methods to categorise their data, relying on their

https://orcid.org/0000-0001-6021-0737

https://orcid.org/0000-0001-7372-178X

https://orcid.org/0000-0003-1413-4969

https://orcid.org/0000-0002-0801-0831

https://orcid.org/0000-0001-5853-2673

domain-speciﬁc knowledge and expertise.

Terrestrial biomes are constructs that cluster to-

gether similar geographical areas. More speciﬁcally,

a biome is deﬁned as a community of plants with sim-

ilar functions which form in response to a shared cli-

mate. Examples of biomes include grassland, tropi-

cal rainforest and desert. Biome distributions affect

life on Earth and represent helpful constructs for the

organization of knowledge about ecosystems. Clus-

tering is a natural choice for the characterization of

biomes. Experts have used empirical approaches us-

ing data derived from precipitation and temperature to

make such constructs, leading to the K

oppen-Geiger

(KG) tree model (Peel et al., 2007), built using rules

to decompose the terrestrial map into distinct biomes.

These methods rely on expert assessment and inter-

pretation of observational data to assess future envi-

ronmental change. While this has led to a plethora

of biome representations, very few of these biome

maps target the comparatively coarser scale vegeta-

tion cover changes that are associated with numerical

Dynamic Global Vegetation Models (DGVMs) and

586

Sidoumou, M., Kim, A., Walton, J., Kelley, D., Parker, R. and Swaminathan, R.

Explainable Clustering Applied to the Deﬁnition of Terrestrial Biomes.

DOI: 10.5220/0010842400003122

In Proceedings of the 11th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2022), pages 586-595

ISBN: 978-989-758-549-4; ISSN: 2184-4313

the climate models which incorporate them. Mod-

elling studies are often forced to re-interpret biome

maps designed for very different ecological purposes.

In addition, the speciﬁc motivation for an ecological

study can affect which variables are selected, causing

this to be less objective.

An alternative approach is to use expert-led deci-

sions to partition a small number of bioclimatic vari-

ables into biomes (Prentice et al., 2011; Sato et al.,

2021). While these are custom-made for climate

model resolutions, they are restricted to a small num-

ber of variables—for example, (Prentice et al., 2011)

uses between two and ﬁve variables, depending on the

biome of interest—due to limits on the number of fea-

tures which can be assessed by human experts. Biome

deﬁnitions can also cut across areas of dense biocli-

mate space, suggesting biome boundaries and expert

assessment for biome deﬁnitions do not necessarily

align.

Despite their shortcomings, these empirical ap-

proaches have the merit of being interpretable—that

is, the reasons for the classiﬁcation of each biome can

be understood. Whilst interpretability is not manda-

tory to validate and use a particular clustering method,

it is a feature which appeals to experts, offering a way

to understand the results and learn from the ﬁndings.

For this reason, we seek a clustering methodology

with an application to terrestrial biomes which, in ad-

dition to being objective, automatic and data-driven,

is also interpretable.

2 RELATED WORK

The biome map of Olson and his colleagues (Olson

et al., 2001) is perhaps the most commonly used in

DGVMs—e.g., (Sellar et al., 2019; Forrest et al.,

2020). This is a meta-analysis of previously pub-

lished ecosystem maps which have been grouped

into biomes in consultation with regional experts and

global ecologists. The map, commissioned by the

World Wide Fund for Nature, is designed speciﬁcally

for the global coordination of regional and local con-

servation efforts—a very different purpose to global

land surface model evaluation. The Olson biome

map provides more detail than can be represented by

DGVMs or climate models, and as a result, global

vegetation studies have aggregated Olson biomes (in

a fashion which is largely inconsistent).

The KG tree model is more targeted to global

biome distributions, and has been considered as the

standard method for biome classiﬁcation (Kottek

et al., 2006). KG uses temperature and precipitation

measurements with decisions based on expert opin-

ion. This type of expert-based model tends to gener-

alise well but can be prone to bias arising from the

prior experience of those designing it. The deﬁnition

of a set of subjective classes is required before the

model is deﬁned. In (Thornthwaite, 1948) the authors

mitigate the KG model’s simplicity by using variables

that are related to moisture and temperature values

(as opposed to direct use of precipitation and tem-

perature), although expert-related biases will still be

present because of the subjective nature of the classi-

ﬁcation approach.

There have been a few attempts to deﬁne biomes

automatically from data. Among them, (Netzel and

Stepinski, 2016) represents variables as a time-series

of mean monthly observations. The time-series data

are then encoded as dissimilarity matrices using dy-

namic time warping dissimilarity functions or Eu-

clidean distances which take every pair of values

from the time series to produce the matrix. Finally,

a clustering algorithm is applied to the dissimilar-

ity matrix to create the clusters. Clustering algo-

rithms used include hierarchical clustering with Ward

linkage (Ward, 1963) and k-medoids (Kaufman and

Rousseeuw, 1987). Finally, (Netzel and Stepinski,

2016) use information theory to deduce that cluster-

ing methods are superior to heuristic approaches such

as the KG model. (DeSantis et al., 2020) encode ob-

servational data as tensors to create a spatial-temporal

link between data. A discrete wavelet transform is

employed to generate coefﬁcients which are then used

in a clustering algorithm. Several scales are used, and

for each the authors note the different clusters pro-

duced along with their variations.

These clustering methods produce biomes that are

not easily achievable by empirical methods because

they take many more features into account and usually

optimise a well-deﬁned objective function. However,

they lack interpretability, a concept often requested by

domain knowledge experts because it can help them

update their knowledge or assess the limits and poten-

tial of interpretable methods.

3 DATA

To determine the distribution of biomes, we used a

mixture of land surface (e.g. tree cover, population

density) and climate (e.g. mean annual precipitation,

mean annual dry days) variables—see Table 1 for de-

tails. We chose the set of variables to reﬂect the

properties of large-scale climate and vegetation dis-

tributions. The selection of variables used consists

of typical parameters that are either measurable from

observations or which can be modelled by DGVMs.

Explainable Clustering Applied to the Deﬁnition of Terrestrial Biomes

587

This allows our approach to be applied in the fu-

ture to biome characterization using data from climate

models (in particular, we are interested in using it for

output from Earth system models—see, for example

(Sellar et al., 2019)—which are climate models that

explicitly model the movement of carbon through the

Earth system).

Table 1: Variables names and their descriptions.

Variable name Description

MADD

Mean annual dry days

(i.e seasonality of rainfall)

MAP Mean annual precipitation

MAT Mean annual temperature

MTCM

Mean minumum temperature

of the coldest month

MTWM

Mean maximum temperature

of the warmest month

MaxWind Mean Maximum windspeed

PopDen Population density

DirectRadiation

Direct downwards shortwave

radiation

DiffuseRadiation

Diffuse downwards shortwave

radiation

TreeCover Tree coverage

Crop Cropland area

nonTreeCover i.e grasses

Pasture Pasture area

Urban Urban area

BurntArea Burnt area

We obtained TreeCover and nonTreeCover from

the MODIS (Moderate Resolution Imaging Spectro-

radiometer) Vegetation Continuous Fields (VCF) col-

lection 6 fractional tree cover (Dimiceli et al., 2015)

regrided as per (Kelley et al., 2019). Although

(Adzhar et al., 2021) have shown VCF underestimates

tree cover in landscapes which have a mixture of tree

and grass, VCF is the only readily available global

tree cover product not based on tile aggregation. We

obtained Urban, PopDen, Crop and Pasture from the

History Database of the Global Environment, Version

3.1 (HYDEv3.1) (Klein Goldewijk et al., 2011). We

selected the Global Fire Emissions Database, Version

4.1 (GFEDv4.1) for BurntArea (Van Der Werf et al.,

2017), and version 4.01 of the Climatic Research Unit

Time Series high resolution gridded dataset (CRU TS

v4.01) (Harris and Jones, 2017) for MADD and MAP.

(Kelley et al., 2021a) have demonstrated that MADD

is likely the best proxy for rainfall distribution con-

trols on vegetation distribution. We used the approach

in (Davis et al., 2017) to calculate DirectRadiation

and Di f f useRadiation from CRU TS v4.03 monthly

cloud cover (Harris and Jones, 2017). MTW M and

MTCM, also from CRU TS v4.03, were used to mea-

sure heat and frost stress. We take MaxWind from

the CRU-NCEP (National Centers for Environmental

Prediction) data (Harris, 2019).

We largely pre-processed variables in the same

way as (Kelley et al., 2021a), and regridded to a N96

(1.25

◦

x 1.875

◦

spatial resolution) climate model grid.

We also aggregated the Olson biome map in the same

way as was done in (Kelley et al., 2021a), but to an

N96 grid instead of a 0.5

◦

x 0.5

◦

grid.

We retain correlation between variables and do not

perform feature selection because this would risk in-

jecting bias. This is not a standard practice in machine

learning problems, which suggests treating correlated

features ﬁrst. However, correlation has different ef-

fects in different algorithms. For example, standard

decision trees algorithms such as CART (Classiﬁca-

tion and Regression Trees) (Breiman et al., 2017) and

C4.5 (Quinlan, 2014) are immune to it and the re-

sulted trees will not be affected. To put correlation

into context, we need to analyse its behaviour in clus-

tering and particularly its effect on our k-means with

the Euclidean distance metric approach.

K-means algorithm minimises the variance within

clusters (Lloyd, 1982). As a result, it produces clus-

ters that are near spherical (or hyper-spherical in

higher dimensions). To better achieve this, we ap-

plied rescaling to our variables to ensure ellipses be-

come more spherical. Another implication of using

k-means without any dimensionality reduction is that

correlated features will have a larger impact on clus-

ter formation than uncorrelated features. A variant

of k-means uses the Mahalanobis distance (Maha-

lanobis, 1936) between data points and cluster dis-

tributions instead of the Euclidean distance between

data points. The Mahalanobis distance is the differ-

ence between data points and clusters variances, lead-

ing to correlation-invariant results. We however do

not use this variant because latent features are not nec-

essarily all equal when deﬁning clusters and we want

to keep their inﬂuence proportional to the number of

observed features they are related to.

4 EXPLAINABLE CLUSTERING

METHODOLOGY

We seek to develop a method that can deﬁne biomes

from features in an interpretable way. The goal of in-

terpretability here is to be able to compare with the

empirical biome deﬁnitions produced by experts us-

ing methods such as (Olson et al., 2001). It also al-

lows an evaluation of the rule-based biome deﬁnition

and contrasts it with less explainable methods. Our

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588

Figure 1: Left: Segments (colored according to latitude) after ﬁrst application of Felzenszwalb’s algorithm. Right: Segments

after second pass, and removal of segments with no terrestrial biomes (see text).

Figure 2: Left: Clustering without using segmentation. Right: Clustering after using segmentation. The colors distinguish

clusters, and have no other signiﬁcance.

approach is composed of the following steps:

1. Rescale the data and stack it into a tensor.

2. Use Felzenszwalb’s segmentation algorithm

(Felzenszwalb and Huttenlocher, 2004) on the

tensor data to decompose it into regions. This step

helps to produce smoother biomes and alleviates

the effects of outliers without removing them.

3. Transform the newly formed segments into a tab-

ular dataset D where each segment represents a

row of data. The values of each row are the me-

dian values of the pixels’ segments.

4. Use k-means to cluster D into k clusters.

5. Produce a decision tree taking the inputs as the

dataset D and the labels as the k cluster identiﬁers

(or pseudo-labels) with a set of hyper-parameters

allowing a good compromise between accuracy

and interpretability.

We give details about each step of our approach in the

following sections.

4.1 Data Pre-processing

Our dataset consists of 15 global land surface vari-

ables on a latitude-longitude N96 climate model grid

whose dimensions are 180 (longitude) by 142 (lati-

tude). We recale each variable and then stack them at

each grid cell to produce an image whose pixels have

15 channels. This can be viewed as a 3D tensor whose

dimensions are longitude, latitude and channel.

4.2 Processing Outliers

Some pixels may contain values that could be consid-

ered as outliers, or noise resulting from errors associ-

ated with the data or other conditions. If we cluster

such pixels into groups, neighbouring pixels will be-

long to different clusters which will result in a grained

distribution—for example, tiny clusters represented

by individual pixels within a large cluster. Figure 1

represents such phenomena. To alleviate the effects

of outliers, we use an image segmentation-based ap-

proach. Although our data are not images in the con-

ventional sense, they have an analogous structure—

i.e our data points have a two-dimensional spatial re-

lationship in which proximity and location is signiﬁ-

cant.

Image segmentation methods decompose images

into regions whose pixels have similar characteristics.

The pixels within every segment are rather similar but

Explainable Clustering Applied to the Deﬁnition of Terrestrial Biomes

589

not identical. They also tend to be localized (i.e pixels

which are far apart are unlikely to be part of the same

segment).

We chose Felzenszwalb’s (Felzenszwalb and Hut-

tenlocher, 2004) algorithm as a segmentation that

does not require a ﬁxed number of segments in ad-

vance (unlike SLIC superpixels (Achanta et al., 2012)

for example). Felzenszwalb is a graph-based algo-

rithm that ignores low variabilities in high variability

regions, resulting in segments which appear more nat-

ural. There is no restriction on the shape of the seg-

ments it produces. While images encoded as matrices

typically have three channels (e.g. RGB, or HSL val-

ues), there are no restrictions on the number of chan-

nels this algorithm can work with.

Applying Felzenszwalb’s algorithm with the pa-

rameters values scale = 0.4, sigma = 0.5, minsize = 3

produces 1663 segments (see left hand side of Fig-

ure 1). The scale parameter controls the size of

the segments—larger values produce larger segments.

minsize is the minimum number of pixels which each

segment can contain, and sigma is a pre-processing

parameter that controls the dimensions of the Gaus-

sian kernel. Close inspection reveals that certain

small non-terrestrial (water) regions were mistaken

for noise due to their small size. A second pass of the

segmentation method grouped these non-terrestrial

regions into one segment, which we then removed

(along with segments corresponding to Antarctica)

since these regions have no terrestrial biomes of in-

terest. The right hand side of Figure 1 shows the 1216

segments which remained after this removal; compar-

ing the two sides of the ﬁgure shows the improvement

in the resolution of the coastline arising from the re-

moval of the non-terrestrial regions.

15 values characterise each segment—that is, the

median of each of the 15 variables within the seg-

ment’s boundary.

(segment

) = median(x

ki j

) (1)

where v

is variable k’s value for segment

, j is a point

index within its segment, and x

ki j

is the value of vari-

able k of data point j belonging to segment i.

4.3 Clustering the Map via k-Means

K-means is a distance-based algorithm that groups

points with similar feature values by assigning each

point to the cluster with the nearest centroid. It ﬁnds

centroids that minimise the sum of the squared Eu-

clidean distance between each data point and its asso-

ciated centroid:

argmin

∑

i=0

||x

− µ

(2)

Figure 3: A plot of gap value against cluster count. This is

one of the methods used to determine a suitable cluster size

(see text).

where x

are the vectors representing data points i and

are the centroid vectors associated with data point

We used k-means with all 15 variables for our

analysis. We acknowledge that some of these vari-

ables are correlated as they are inﬂuenced by the same

underlying physical processes and that such correla-

tions might determine cluster associations. However,

we did not see any evidence that the semantic integrity

of our clusters was signiﬁcantly impacted by these

correlations and so we chose to retain all 15 variables.

The k-means clustering algorithm requires the

number of clusters (that is, k) as one of the hyper-

parameters. The selection of a value for this param-

eter requires some consideration. For example, we

could set it to the number of biomes used in an em-

pirical characterization approach for comparative pur-

poses, or to a higher or lower value to obtain a more

generalized or more granular result. We employed

three different evaluation metrics to estimate the op-

timal number of clusters: the Distortion Coefﬁcient,

Gap values and the Silhouette score. We show an

illustration of how we employed one of the metrics

(Gap values) in Figure 3. Based on this metric, we de-

termined that a number between 10 and 15 (clusters)

would optimally represent our data. We found that the

Distortion Coefﬁcient and the Silhouette scores were

in agreement with this range, suggesting a compara-

ble number of clusters.

We ﬁnally chose to employ 11 clusters for deﬁn-

ing biomes in this approach – a number consistent

with both expectations from domain-expertise and the

evaluation metrics we employed.

4.4 Tree-based Interpretability

Machine learning models that are not easy to ex-

plain in simple terms require the application of spe-

ciﬁc extra methods, including SHAP (SHapley Ad-

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590

Figure 4: Results of k-means clustering algorithm, identi-

fying 11 biomes. The key distinguishes 14 clusters, but not

all of them are present.

ditive exPlanations) (Lundberg and Lee, 2017) and

LIME (Local Interpretable Model-agnostic Explana-

tions) (Ribeiro et al., 2016). Models which are more

explainable (for example, a decision tree with a com-

paratively low depth) do not need methods such as

these to be applied. Such models include decision

trees, linear regressions and na

ıve Bayes. These mod-

els belong to the supervised learning family. Explain-

able models in clustering and unsupervised learning

in general are very scarce.

Decision rules provide an explainable way to de-

ﬁne categories. Each category is bounded by a set

of conditions, generally Boolean. A number of al-

gorithms exist that can generate decision rules for a

given problem. (Chavent, 1998) builds decision rules

directly for clustering purposes on unlabelled data. It

uses a similarity measure to decide on dividing clus-

ters of data by ﬁnding the optimal splitting value on

features. The process is similar to the splits used in

decision trees. The method builds hyper-cubic shaped

clusters but does not put a restriction on the number

of rules or the number of features used. This method

optimises the decisions at each level instead of opti-

mising the whole structure of the clusters. (Dasgupta

et al., 2020) uses ﬁrst k-means to build clusters, and

then builds a minimum set of decision rules on top

of these clusters to approximate them. The simpler

the rules, and the smaller the set, the more explain-

able the clustering will be. Another method of build-

ing explainable clustering is to approximate k-means

clusters with a decision tree while restricting the size

of the tree via its hyper-parameters. We use this ap-

proach. Since decision boundaries in decision trees

are made of vertical and horizontal lines and k-means

clusters boundaries are spherical-like, we would not

expect them to be exactly equivalent. Instead, we

choose hyper-parameters that allow a good compro-

mise between interpretability and equivalence. We

deﬁne two models as equivalent if they assign the

same label (or cluster) to a given data point—i.e. if

the models agree on the classiﬁcation of all the data

points. We adopt the following algorithm to generate

interpretable decision trees:

1. Generate k clusters using k-means (see §4.3). Re-

sults are presented in ﬁgure 4.

2. Use the resultant clusters identiﬁers as pseudo la-

bels for the data.

3. Build a decision tree using:

min samples per node=30, max depth=9

4. Recursively trim the resulting tree if the predicted

classes do not change in sibling leaves

It is worth noting that there is a set of de-

cision trees that can approximate the clustering

results while producing explainable rules. The

above algorithm generates one among several pos-

sibilities. Tweaking the hyper-parameters such as

min samples per nodes and max depth will produce

slightly different trees. We note that the algorithms

we used to build the trees are (Breiman et al., 2017)

and C4.5 (Quinlan, 2014), other clustering or tree-

based algorithms will produce different trees.

(Dasgupta et al., 2020) describe a k-means cluster-

ing result along with a possible decision tree approxi-

mation. Our aim here, however is to explore the effect

of the addition of interpretability to k-means cluster-

ing, in particular whether it enhances the comparison

with results from empirical classiﬁcation methods for

terrestrial biomes. To better satisfy interpretability,

we have two goals that will guide us during the tree’s

construction. The ﬁrst one is to produce short rules,

which is equivalent to the decision tree length. The

second aim is to reduce the number of rules per clus-

ter to as close to one as possible. These goals will help

deliver the deﬁnition of biomes in a fashion which

is more accessible to the domain knowledge experts

who can examine, strip, augment, or even discard

them. Such rules will also be comparable in struc-

ture to the empirical rules from models such as KG

tree or expert knowledge such as (Olson et al., 2001).

4.5 Results

Having applied the methodology described in (§§4.1–

4.4) to generate explainable biomes, we present our

results and compare them to those from the empirical

biome attributions. Upon a partial application of our

method, without selecting the hyper-parameters that

account for short and small numbers of rules and tree

trimming, the resultant decision tree (called TreeA)

approximates k-means clustering with an agreement

of 95%. Although the decision tree gives a very good

Explainable Clustering Applied to the Deﬁnition of Terrestrial Biomes

591

Figure 5: Final reduced decision tree after application of recursive trimming algorithm (i.e. TreeB), resulting in 14 leaf nodes.

representation of the original clusters, it uses around

80 rules to deﬁne all the biomes. This is a compara-

tively large number, representing a challenge for the

usability of the classiﬁcation scheme, and for compar-

isons with the results from the empirical characteriza-

tion approach. Therefore, we compromise agreement

with the clusters and usability by setting values for

the hyper-parameters in the decision tree algorithm,

deﬁning the minimum number of samples per leaf

min samples per nodes to 30, limiting the tree depth.

We also recursively trim the tree, using the following

algorithm:

Order pairs of sister leaves based on length

for each pair of sister leaves a,b:

if majority_class(a) == majority_class(b):

c=merge(a,b)

d=find_sister_leaf(c)

insert pair(c,d) in list of sister

leaves keeping the order

end

Applying the algorithm with the hyper-parameter

values mentioned above and using recursive trim-

ming produces decision tree TreeB which is in 85%

agreement with the original clusters. However, the

tree contains 14 leaves, which makes it considerably

smaller than TreeA—see Figure 5. In a trimmed tree

all biomes (except three) are explained by a single leaf

and thus a single rule. This supports the hypothesis

that most biome deﬁnitions can be deﬁned in an ex-

plainable way. We then re-clustered the regions of the

map according to TreeB. In this tree, leaves are num-

bered from 0 to 10. Leaves are assigned to biomes

according to the index of the maximum value in the

leaf’s segments array—for example, a leaf with seg-

ments array of [2, 55, 3, 0, 1, 0, 4, 4, 1, 1, 0] would rep-

resent biome 1.

5 DISCUSSION

By comparing our results to the empirical biomes de-

ﬁned by experts in the literature, we can observe a

number of biomes that are in accordance with our re-

sults such as the tropical rainforest, the tundra, the

taiga, the desert, the steppe, the savanna and the

mixed forest with some variations on their bound-

aries. However, we also observe a couple of extra

biomes, one of which is mainly present in the Indian

subcontinent, while the other is a semi-arid biome

similar to desert. The biome present in the Indian sub-

continent seems to be inﬂuenced by agriculture and

suggests an anthropogenically-induced change. Fur-

ther analysis of these results is required to compare

the boundaries of the discovered biomes to those de-

rived by empirical methods. Figure 7 shows a com-

parison between Olson’s biomes (Olson et al., 2001)

and the biomes derived from the explainable cluster-

ing methodology. Typically there is a strong overlap

between our derived biomes and those from Olson

(for example, the desert biome has a 92% overlap,

tropical forest has 87%). Interestingly, when there is

some disagreement, a biome is still often attributed

as belonging to a similar biome (e.g. boreal forest

and tundra) suggesting the boundary between biomes

is somewhat ﬂuid. Applying an image segmenta-

tion algorithm helped in making biomes more con-

tinuous in space, thus ignoring localized small vari-

ations. An examination of the decision rules and t-

distributed stochastic neighbour embedding (t-SNE)

visualizations of the biomes reveals the following:

• Most biomes require only one rule to deﬁne them.

• Two leaves do not have a clear majority decision.

• Three biomes (biomes number 4, 6 and 9) each

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592

(a) t-SNE projection for the ﬁnal clusters (b) t-SNE projection for k-means clusters

Figure 6: t-SNE projections.

Figure 7: A comparison of biomes obtained from explainable clusters against Olson’s biomes (Olson et al., 2001). The

numbers show the % of clustering biomes that fall in each Olson biome. In biome names, trop = tropical, med = Mediterranean,

frst = forest, wood = woodland, shrub = shrubland, shrub = scrubland, grass = grassland, bl = broadleaf. The color of each cell

denotes the type of biome (green = forest, blue = woodland, purple = grassy, orange = barren); color intensity is proportional

to the value in the cell.

require two rules to be deﬁned.

Biome 6 (represented by the pink leaves in Figure

5) covers a large part of the map. Most of its region

is governed by a single rule covering 185 segments

from the map, whilst the second rule covers only 25

segments. The 25 segments appear to be close to the

borders with other biomes.

Similarly, biome 9 represented by the yellow leaf

is deﬁned by two rules as well. One rule governs 134

segments, while the other governs 18 segments and

another 12 segments from biome 6. Both rules are

characterized by a high tree coverage and adjacent in-

tervals of mean annual temperatures. This may allow

these two rules to be fused in one single rule.

Looking at the t-SNE plot in ﬁgure 6 of the de-

cision tree, we note that biomes 1 and 4 are highly

mixed with other biomes in the spatial representation

while the t-SNE graph of the k-means clusters does

not shows this mixtures. This suggests that these two

biomes may not be easily deﬁned by simple rules.

Biome 1 which appears to represent the desert is less

prone to this effect than biome 4. The latter, which

to date appears to be the only biome that the decision

tree approach is unable to identify. The fact that it

is related to agricultural regions suggests that “non-

natural” biomes may not follow the same structure as

the others, and the effect of these man-made environ-

mental changes are more complex than those repre-

sented by natural observable features. Biome 4 ap-

pears to share some characteristics with neighbour-

ing biomes but is sufﬁciently different to be charac-

terized as a new biome by k-means. However, it is

not distinctive enough to be fully explainable. We

note that most of the other irregularities in the deci-

sion tree-based clustering are located near the borders

of biomes in data space.

We also note that decision trees that can approx-

imate k-means are not unique. For this, a further

analysis of the different ways of approximating the

k-means clusters is required. For example, changing

the weights of certain instances will result in a differ-

ent tree with a possibility of a different interpretability

level. There are also tree construction methods that

are not based on CART or C4.5 such as the methods

presented in (Dasgupta et al., 2020) that can applied

to this use case.

6 CONCLUSION

In this work we have deﬁned a methodology for ex-

plainable clustering which we have applied to 3D ten-

sor data. Our motivation is the production of explain-

able deﬁnitions of terrestrial biomes. After rescaling

Explainable Clustering Applied to the Deﬁnition of Terrestrial Biomes

593

the data, we superpose them as 3D tensors and ap-

ply an image segmentation algorithm to decompose

the tensor into homogeneous segments. We apply k-

means clustering to the segments, and introduce ex-

plainability by approximating the clusters with a de-

cision tree, which we subsequently trim to a manage-

able number of leaves.

This method allowed for the building of continu-

ous biomes in space with one rule per biome in most

cases. Three biomes required more than one rule to

deﬁne them. Four of these rules could be fused into

two rules thus making the clustering simpler. How-

ever, despite using all 15 features in the construction

of the decision tree, the resulting rules used at most

four features. This is due to underlying latent fea-

tures inﬂuencing more than one correlated feature.

It is worth noting that a decision tree which is rel-

atively small and can approximate clustered data is

not unique. Different methods with different hyper-

parameters will produce different trees. We also no-

ticed that certain biomes that are man-made such as

the Indian subcontinent biome cannot be easily de-

ﬁned by rules without affecting the rules of adjacent

biomes. This indicates that this biome has an irregular

shape (in data space) and indeed requires more than

one rule to be deﬁned. One ﬁnal observation is that

decision trees are not perfect in building simple rules

for clustering. Because rules are constrained to be

connected at different node levels, simplicity may be

traded for this property. For future work, we suggest

augmenting this method with a strategy for merging

rules that not only merges rules when they are con-

nected via a feature but also when features are corre-

lated and there is a possibility for such a merge. These

may lead to a loss in precision depending on the cor-

relation level but it will improve the interpretability.

We believe that this study demonstrates the strong

potential possible for advancing our understanding of

Earth system science by utilising machine learning

methods, such as explainable clustering. By expand-

ing this work in the future and applying these methods

to climate projections from Earth system models, we

will be able to provide analyses which complement

existing insights from experts about how the Earth’s

biomes may alter in response to a changing climate.

7 DATA AVAILABILITY

The data used (Table 1) are archived at

https://doi.org/10.5281/zenodo.5736407 (Kelley

et al., 2021b).

ACKNOWLEDGEMENTS

This project originated as a collaboration between the

Met Ofﬁce and Amazon Web Services (AWS) under

the AWS Machine Learning Embark program. JW

is supported by the Met Ofﬁce Hadley Centre Cli-

mate Programme funded by BEIS and Defra. RS

and RJP are funded by the UK National Centre for

Earth Observation (UKESM, NE/N018079/1). DIK

was supported by the UK Natural Environment Re-

search Council (UKESM, NE/N017951/1).

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