J. Nig. Soc. Phys. Sci. 4 (2022) 223–230

Journal of the
Nigerian Society

of Physical
Sciences

Statistical Modelling by Topological Maps of Kohonen for
Classification of the Physicochemical Quality of Surface Waters

of the InaouenWatershed Under Matlab

R. El chaal∗, M. O. Aboutafail

Engineering Sciences Laboratory. Data Analysis, Mathematical Modeling, and Optimization Team, Department of Computer Science, Logistics and Mathematics,

Ibn Tofail University National School of Applied Sciences ENSA, Kenitra 14 000 Morocco

Abstract

Self-organizing maps (SOMs) and other artificial intelligence approaches developed by Kohonen can be used to model and solve environmen-
tal challenges. To emphasize the classification of Physico-chemical parameters of the Inaouen watershed, we presented a classification strategy
based on a self-organizing map (SOM) artificial neural network in this study. The use of a self-organizing map to classify samples resulted in the
following five categories: Low quantities of Sodium Na (mg/l), Potassium k(mg/l), Magnesium Mg(mg/l), Calcium Ca(mg/l), Sulfates SO4(mg/l),
and Total Dissolved Solids TDS (mg/l) distinguish Classes 2 and 3. Bicarbonate HCO3 (mg/l), Total Dissolved Solids TDS (mg/l), Total Alka-
linity CaCO3(mg/l), Mg(mg/l), Calcium Ca (mg/l), and electrical conductivity Cond (s/cm) are slightly greater in Classes 1 and 4. Except for
Dissolved Oxygen D.O. (mg/l) and Nitrate NO3(mg/l), Class 5 has exceptionally high values for all metrics. The results suggest that Kohonen’s
self-organizing maps (SOM) classification is an outstanding and fundamental tool for understanding and displaying the spatial distribution of
water physicochemical quality.

DOI:10.46481/jnsps.2022.608

Keywords: Classification, self-organizing maps, SOM, physical-chemical parameters, cluster

Article History :
Received: 24 January 2022
Received in revised form: 29 March 2022
Accepted for publication: 30 March 2022
Published: 29 May 2022

c©2022 Journal of the Nigerian Society of Physical Sciences. All rights reserved.
Communicated by: B. J. Falaye

1. Introduction

Self-organizing maps (SOM) are artificial neural network
techniques based on unsupervised learning algorithms [1].
Because of their classification capabilities and visualization
performance, they have been successfully used in environmen-
tal fields (soil,water, air, etc.). Shen et al. [2] studied the
groundwater chemistry and quality of a multilayered ground-
water system in the Northwest China Coal an approach based

∗Corresponding author tel. no: +212710115110
Email address: rachid.elchaal@uit.ac.ma ( R. El chaal )

on the SOM technique combined with multivariate statistical
tools. Bigdeli et al. [3] applied self-organizing map (SOM)
technique and K-means clustering algorithms to describe
geochemical anomalies in Moalleman district, northeast Iran.
Santos et al. [4] investigated the regional hydrogeochemical
spatialization and controls of the Serra Geral aquifer system in
the southern region of Brazil, using Kohonen’s self-organizing
maps (SOM) in combination with k-means clustering. Amiri
et al. [5] conducted a Spatio-temporal assessment of ground-
water quality in a coastal aquifer, based on Kohonen’s linear
discriminant analysis (LDA) and self-organizing maps (SOM).

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El chaal & M.O.Aboutafail / J. Nig. Soc. Phys. Sci. 4 (2022) 223–230 224

The goal of this study is to use a statistical technique (SOM)
to display and analyze the spatial distribution of water sam-
ples and their Physico-chemical properties at the level of the
Inaouen watershed. To emphasize the distinct classes and detect
the spatial fluctuations of the Physico-chemical characteristics
of the examined watershed, SOM’s hierarchical classification
(SOM-CHA) is utilized.

2. Materials and Methods

2.1. Sample Location and Description

The Oued Inaouene watershed is located in northeastern
Morocco, between the Middle Atlas and the Pre-Rif, and cov-
ers approximately 5109 km2 (Figure 1. The watershed has a
Mediterranean climate with oceanic influences, with great sea-
sonal variations and very evident abnormalities in rainfall due
to its geographic location [6]. With an average annual rainfall
of roughly 600 mm/year, this region is known for its very varied
rainfall from month to month. The rainfall distribution reveals
two bands: the first below 500 meters with an annual rainfall of
roughly 800 mm, and the second between 500 and 1000 meters
with an annual rainfall of 800 to 1500 mm. The rainy season
in the study region lasts from November to April, with Decem-
ber and January being the wettest months. July and August,
on the other hand, are the driest months of the year. The Oued
Inaouène watershed is distinguished by a lithological contrast
between the two banks. The Pre-Rif, whose outcrops are marly
and support a clear sown flora, is on the right bank. The left
bank corresponds to the Middle Atlas’ northern boundary, with
outcrops ranging from Tazzeka’s Paleozoic formations to the
triasi formations [6].

Figure 1: Location and DTM of the study area.

2.2. Data Source

The dataset for this study consists of 16 Physico-chemical
characteristics measured on 100 surface water samples taken in
the Inaouen watershed between 2014 and 2015. The processes
for collecting, transporting, and stocking water samples is done
by our team according to the protocol of the National Office of

Drinking Water.

A portion of the analyses was completed on-site, while the
remainder was completed at the CURI laboratory in Fezby our
team [7].

The parameters used are pH,Bicarbonate (HCO3), Dis-
solved Oxygen (Oxy. Diss), Conductivity (Cond),Temperature
(T◦C), Total Dissolved Solids (TDS), Total Alkalinity
(CaCO3),Potassium (K), Magnesium (Mg), Sodium (Na),
Chlorides (Cl), Calcium (Ca), Sulfates (SO4), Nitrate (NO3),
Phosphorus (P) and Ammoniac (NH3).

2.3. Self-Organizing Maps (SOM)

Kohonen, who was looking for a technique to repre-
sent huge multidimensional data, was the first to introduce
topological maps. To do this, Kohonen uses machine learn-
ing[8]to divide data into ”similar” groups whose neighborhood
structure can be realized and represented using a discrete
low-dimensional (1, 2, or 3D) space called a ”topological
map” [9]. Topological map methods allow data to be projected
onto a low-dimensional environment while revealing the
data’s inherent structures. As a result, the SOM technique
preserves both the topology of the data and the distance
relationship between them (Figure 2). Unsupervised learning
artificial neural network methods[10,11], often known as SOM
maps, are a type of neural network [12]. The samples (input
vectors) are supplied to a grid of d neurons (or nodes, or
units) in these networks [13]. The choice of the parameter
d (the map’s dimension) is chosen ahead of time. The input
vectors are connected to each grid neuron via d synapses
and d weight vectors w. The map neuron in data space is
represented by the vector w, which is also known as the
prototype or referent vector [14]. The BMU is the closest
data referent (the Best Matching Unit). The quantization and
topological preservation capabilities of a self-organizing map
are assessed. Topological error (Te) and quantization error (Qe)
are commonly used to validate the SOM categorization [15,16].

Quantization Error Qe: (or resolution measure) The average
quantization error, which is defined by the average distance of
the data from their referents(BMU), is used to determine the
degree of deployment of the map on the data or the degree of
quantization [1,14]. The better the quality of the SOM algo-
rithm, the lower the value of Qe. It is expressed as follows:

Qe=
1
N

N∑
k=1

∥∥∥∥x(k)−w (x(k))∥∥∥∥2 (1)
where N is the number of data, x(k) is the k-th individual,

and w
(
x(k)

)
is the BMU of the individual x(k)

Topographic error Te [16]: (or a measure of topology preser-
vation) This criterion assesses how well the SOM preserves the
data set’s topology [17]. Which is the percentage of data for
which the two nearest referents do not correspond to adjacent

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El chaal & M.O.Aboutafail / J. Nig. Soc. Phys. Sci. 4 (2022) 223–230 225

map units [18]. In contrast to the Quantification mistake, Te
considers the SOM card’s structure [19].

The criterion used to measure the number of observations
where the first winning neuron (ci) and the second winning neu-
ron (si) are not neighbours on the map. The second winning
neuron of observation has its closest referent vector to this ob-
servation after the first winning neuron [20]. The topographic
error is a metric that is determined as follows:

T e=
∑n

i=1 E
n

(2)

E=
{

1 si rci−rsi
2,1

0 si rci−rsi
2= 1

where rc and rs are respectively the locations of neuron c
and neuron s on the map.
The topology is perfectly preserved when this criterion is 0.

Figure 2: Structure of a topological map

The topological map has several advantages over the linear
and classification methods[21] usually used to extract groups
of collected samples, such as Principal Component Analysis
(PCA) [22], Correspondence Analysis (C.A.) and Hierarchical
Clustering (H.C.)[23]. Their limitations are well known. For
example, for each of them, a strong distortion is observed when
there are non-linear relationships between the variables [24].

2.4. Hierarchical Clustering by SOM (SOM-CHA)

Like other data analysis methods, of which it is a part, the
SOM-CHA classification aims to obtain a simple schematic
representation [25]. It consists in calculating a matrix express-
ing the mutual distances between the points to be classified,
which are the nodes of the map, and then, based on this matrix,
grouping together the closest points. This method allows the
construction of a hierarchical tree [26], which reveals several
possible partitions, where each point is assigned to one of the
groups of a given partition. The choice of the best partition is
made once the hierarchical classification is completed [27].

2.5. Algorithm: Kohonen maps (SOM) [16]
Let

(
wt1, . . . ,w

t
N

)
∈(Rn)N be neurons of the vector space Rn.

We designate by V
(
w j

)
the set of neighbouring neurons ofw j

for this Kohonen card. By definition, we have w j∈V
(
w j

)
.Let

(X1, . . . ,XK )∈(Rn)K a cloud of points. We use a sequence of
positive real numbers (αt) checking

∑
t≥0 α

2
t < ∞ and

∑
t≥0 αt <

∞.
initialization
The neurons

(
w01, . . . ,w

0
N

)
are distributed in the space Rn in

a regular way according to the shape of their neighbourhood.
t←−0.
closest neuron
We choose a point of the cloud Xi randomly; then, we define
the neuron wtk∗, so that: w

t
k∗−Xi =min16 j6N w

t
j−Xi .

update
for each wtj in V

(
wtk∗

)
wt+1j ←−w

t
j+αt

(
Xi−w

t+1
j

)
(3)

t←−t+1

As long as the algorithm has not converged, return to the nearest
neuron step.
The update step can be modified to improve the convergence
speed [28] :

wt+1j ←−w
t
j+αth

(
wtj, w

t
k∗
)

wk
(
Xi−w

t+1
j

)
(4)

where h is a function with value in the interval [0,1] which is 1
when wtj=w

t
k′

. And that decreases when the distance between
these two neurons increases. A typical function is :

hck(σ(t)) = exp
(
−

d22 (rc,rk )
2σ2 (t)

)
= exp

(
−
‖rc−rk‖2
2σ2 (t)

) (5)
where rc and rk are respectively the locations of neuron c

and neuron k on the map, and σ(t) is the radius of the neigh-
bourhood at iteration t of the learning process.
Kohonen maps are used in data analysis to project a point cloud
into a two-dimensional space in a non-linear manner using a
rectangular neighbourhood. They are also used to perform un-
supervised classification by clustering neurons where the points
are concentrated. The edges connecting the neurons or vertices
of the Kohonen map are either narrowed to indicate that two
neurons are neighbours or distended to indicate a separation be-
tween classes.

3. Results and Discussion

3.1. Classification of Surface Water Samples by SOM
The concept of the SOM algorithm is to conduct a non-

linear classification of complicated datasets by recognizing
similar patterns. In this work, the input layer consists of
vectors representing individuals., each of which contains 16
components representing the 16 Physico-chemical parameters
of the surface waters studied. The output layer is composed of

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El chaal & M.O.Aboutafail / J. Nig. Soc. Phys. Sci. 4 (2022) 223–230 226

100 neurons (10 rows × 10 columns). This size was chosen
for the output map because it minimizes the two error criteria
(Qe=0.268 and Te=0.03).

The SOM component planes of the data set allow distin-
guishing two types of colors; dark red cells represent high val-
ues, while blue cells represent low values (Figure 3) [16]. The
similar colors between the variables correspond to a positive
correlation; this can be illustrated between the variables Bi-
carbonates (HCO3), Chlorides (Cl), Magnesium (Mg), Sodium
(Na), Sulfates (SO4), Conductivity (Cond), Nitrate (NO3), Am-
moniacal Nitrogen (NH3), Calcium (Ca), Total Alkalinity (in
CaCO3), Potassium (k) and Total Dissolved Solids (TDS). On
the other hand, Dissolved Oxygen (Oxy. Diss) and P.H., To-
tal Alkalinity (CaCO3), and Phosphorus (P) show a negative
correlation. The other variables, especially T(◦C),P, and NO3,
show neither positive nor negative correlations and vary au-
tonomously fromthe others (Figure 3).

Figure 3: Gradient of values of Physico-chemical parameters on the Kohonen

3.2. Principal Component Analysis (PCA)

The PCA Result shows the score road composed of the
two components, PC1 and PC2, which are regarded as the
most informative ones since they contribute to most of the
variance. In our case, PC1 and PC2 respectively contribute
51.1% and 11.2% of the total variance. Therefore, the first two
components of the circle of correlations between variables in
the subspace PC1 vs PC2 contain 62.3% of the data. Figure 4
illustrates the circle of correlations between the variables in the
factor plane (PC1 × PC2).

The correlation circle between variables in the factorial
diagram (PC1 × PC2) shows that the variables Mg, HCO3,
CaCO3, K, SO4, Na, Cl, NH3, and TDS are positively corre-
lated with the PC1 axis with coefficients above 0.6. However,
the element Oxy Diss is negatively correlated with the PC2
axis, with coefficients greater than −0.6. The elements Mg,
HCO3, CaCO3, K, SO4, Na, Cl, NH3, Cond and TDS are

therefore positively correlated with each other.

The other variables do not have positive or negative corre-
lations and are poorly represented in the circle, in particular the
parameters T◦, P, NO3 and P.H. that vary autonomously.

Figure 4: PCA circles of correlation (PC1 × PC2)

3.3. SOM-CHA Hierarchical Classification

Once the Kohonen map is obtained, we use a hierarchical
classification based on the Ward method [29,30]and Euclidean
distance. The hierarchical classification by SOM allows group-
ing the cells of the SOM map into groups of Physico-chemical
parameters of the Inaouen watershed. The dendrogram ob-
tained by SOM-CHA suggests that the 100 neurons should be
grouped into five classes (Figure 5).
The first class contains 13 samples and represents 13% of the
total data, it includes waters with average chemical element
concentration respectively (HCO (105.39 mg/l), TDS (100.54
mg/l) CaCO3(86.38 mg/l), Mg (4.41mg/l), Ca (24.69 mg/l)
and electrical conductivity (201.08 µs/cm)) which are a little
high and (NH3 (31.23 µg/l) and (Na (11.60 mg/l) which are low.

The second class includes the largest number of samples (48)
and represents 48 % of the total database. It is characterized
mainly by low concentrations of chemical elements such as:
Na (9.00 mg/l), K (1.02 mg/l), SO4(4.61 mg/l) and TDS (58.33
mg/l) and by high dissolved oxygen concentration (6.24 mg/l).
The third class contains 13 samples and represents 13% of the
total database. It is characterized mainly by low concentrations
of chemical elements (SO4 (4.87 mg/l), Cl (3.19 mg/l) and Na
(4.91 mg/l)), Mg (1.81 mg/l), K (0.84 mg/l), Ca (9.95 mg/l),
NH3 (17.69 mg/l), and TDS (43.38 mg/l) and a very high con-
centration of P(225.39mg/l) and dissolved oxygen(6.30 mg/l).
The fourth class contains 23 samples that represent 23 % of the
database. It is characterized by medium high concentrations of
chemical elements HCO3 (117.76 mg/l), Cl (47.98 mg/l), Mg
(4.85 mg/l), CaCO3 (96.52 mg/l), Ca (29.83 mg/l), Na (38.90

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El chaal & M.O.Aboutafail / J. Nig. Soc. Phys. Sci. 4 (2022) 223–230 227

Figure 5: Classification tree (Dendrogram) of the Physico-chemical parame-
ters of the surface waters of Inaouen watershed accessed with the method of
topological maps (SOM)

mg/l), NH3(74.17 mg/l), electrical conductivity (375.87 µs/cm)
and TDS (188.74 mg/l)
Finally, the Fifth class includes the smallest number with 3
samples that represent 3% of the database. It is characterized
by very high concentrations of chemical elements NH3(770
mg/l), electrical conductivity (1801.33 µs/cm), TDS (901 mg/l),
HCO3 (435.13 mg/l), Na (303.33 mg/l), Cl (47.98 mg/l),
Mg(4.85 mg/l), CaCO3 (356.67 mg/l), Ca (31.40 mg/l), K (9.70
mg/l), SO4 (59.67 mg/l) (Table 1 and Figures 6-8.
This enrichment would probably have a triple origin, on the one
hand, the geological nature of the crossed grounds, the differ-
ence of altitude and on the other hand, the domestic discharges
of the neighbouring communes.

Figure 6: Picture of the five clusters with the samples accessed by the SOM
hierarchical clustering.

Figure 7: Projection of the samples relative to the five clusters on the plan
factorial PC1 × PC2

Figure 8: The five clusters generated by the SOM hierarchical clustering are
illustrated. The number of patterns given to each neuron is indicated.

Table1.Statistics on-base quantities (Min, mean, maximum)
for Physico-chemical parameters, respectively, for the whole
database and for classes 1, 2, 3, 4 and 5.

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El chaal & M.O.Aboutafail / J. Nig. Soc. Phys. Sci. 4 (2022) 223–230 228

Table 1: Statistics on-base quantities (Min, mean, maximum) for Physico-chemical parameters,respectively, for the whole database and for classes 1, 2, 3, 4 and 5.

STAT OF ALL DATA STAT OF DATA FROM CLUSTER 1 STAT OF DATA FROM CLUSTER 2
Name Min Mean Max Min Mean Max Min Mean Max
T ◦C 16,3 19,9 23 17,1 18,9846 21 16,3 19,7042 23
pH 5,21 7,1923 9,61 6,36 7,56462 9,42 5,21 7,04458 9,61
OxyDiss 0,09 5,0408 14,01 0,08 2,85 7,76 0,08 6,24229 13,26
Cond 20 233,69 2959 134 201077 315 20 116729 629
TDS 45 117,15 1480 67 100538 157 10 58,3333 314
HCO3 3,66 80,6298 634,4 68,32 105389 170,8 6,1 45,1654 170,8
CaCO3 3 66,09 520 56 86,3846 140 5 37,0208 140
Mg 0,2 3,1735 25 1 4,40769 11 0,2 1,82542 6,8
Na 1 24513 540 2,4 11,6 31 1 9,00208 76
K 0,1 1,7211 13 0,34 1,63615 4 0,1 1,01563 6,4
Cl 0,4 25,8394 550 0,6 5,98462 22 0,4 8,62792 99
Ca 1 17794 110 3 24,6923 54 1 11,4333 45
SO4 275 7,83175 150 1,65 7,08462 13 275 4,60781 15
NO3 0,02 0,4805 4,8 0,1 1,15846 4,8 0,02 0,464167 4,5
P 10 58,5 900 20 30,7692 80 10 33,3333 80
NH3 11 62,93 1000 11 31,2308 130 11 34,1875 130

STAT OF DATA FROM CLUSTER 3 STAT OF DATA FROM CLUSTER 4 STAT OF DATA FROM CLUSTER 5
Name Min Mean Max Min Mean Max Min Mean Max
T ◦C 18 20,8231 23 17,5 20,3174 23 19 19,8 21
pH 5,41 6,70692 8,86 5,63 7,44826 9 6,62 8,08333 9,04
OxyDiss 1,25 6,3 14,01 1.32 3,59913 10,24 0,7 0,906667 2,2
Cond 0.09 84,8462 198 100 375,87 1118 980 1801,33 2959
TDS 23 43,3846 99 50 188739 559 490 901 1480
HCO3 7,32 39,3215 82,96 3,66 117757 329,4 231,8 435133 634,4
CaCO3 6 32,2308 68 3 96,5217 270 190 356667 520
Mg 0,53 1,80923 4,5 0,61 4,84826 23 3,1 12,4667 25
Na 1,5 4,90769 13 1,4 38,8957 180 140 303333 540
K 0,16 0,84 2,4 0,43 2,6987 7,6 6,8 9,7 13
Cl 0,7 3,19231 11 0,4 47,9783 260 77 315667 550
Ca 1,9 9,95385 30 14 29,8261 110 2,4 31,4 86
SO4 1,65 4,86538 18 1,65 9,89783 37 11 59,6667 150
NO3 0,03 0,133077 0,4 0,02 0,364348 2,4 0,1 0,2 0,4
P 20 225385 900 20 34,7826 80 20 40 70
NH3 11 17,6923 50 11 74,1739 250 530 770 1000

Figure 9: Variation of chemical elements in surface waters of the Inaouen wa-
tershed

Figure 10: Variation of the total dissolved solids and conductivity in surface
waters of Inaouen watershed

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El chaal & M.O.Aboutafail / J. Nig. Soc. Phys. Sci. 4 (2022) 223–230 229

Figure 11: Variation of the Na, Cl and SO4 in surface waters of Inaouen water-
shed.

3.4. The U Matrix Classification:

For the U Matrix classification map, the hexagonal topology
was chosen to achieve a better resolution and speedierresults.
The rectangular topology needed many fewer neurons to get a
small quantization and topography error. The result of the U-
matrix (Figure 12) from the selected SOM parameters.
The precision of the classification via the BMUs in the U-matrix
is considered almost exact and produces a high quality and very
smooth mapping.

Figure 12: U-matrix representation of SOM. The training samples are the 16
Physico-chemical parameters taken from 100 Inaouen watershed sources.

4. Conclusion

Statistical analysis based on Kohonen’s self-organizing map
(SOM) approach was applied to a database consisting of 16
Physico-chemical parameters carried out on 100 samples of
the surface waters of the Inaouen watershed between Febru-
ary 2014 and December 2015. It highlighted the different pos-
itive, and negative correlations between the different Physico-
chemical parameters studied. The hierarchical classification of
the SOM map (SOM-HC) detected spatial variations from one
source to another, identifying the physicochemical behaviour of

the waters of the Inaouen watershed. This differentiation would
probably be related to the geological nature of the land crossed,
the difference in altitude and the domestic discharges of neigh-
bouring municipalities.

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