Methods of cluster analysis in sensor engineering: advantages and faults
We consider the crisp and fuzzy partitioning techniques of cluster analysis bearing in mind their application for classification of data obtained with chemical sensor arrays. The advantage of the cluster analysis techniques is existence of a parameter S(i). This parameter gives quantitative effic...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2010
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| Цитувати: | Methods of cluster analysis in sensor engineering: advantages and faults / Yu.V. Burlachenko, B.A. Snopok // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 393-397. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-1185652017-05-31T03:03:30Z Methods of cluster analysis in sensor engineering: advantages and faults Burlachenko, Yu.V. Snopok, B.A. We consider the crisp and fuzzy partitioning techniques of cluster analysis bearing in mind their application for classification of data obtained with chemical sensor arrays. The advantage of the cluster analysis techniques is existence of a parameter S(i). This parameter gives quantitative efficiency of classification and can be used as optimization criterion for sensor system as a whole as well as the measurement procedure. The crisp and fuzzy techniques give practically the same result when analyzing the data that cluster uniquely. It is shown that big value of the parameter S(i) is not sufficient for adequate data partitioning into cluster in more complicated cases, and the results of clusterization for the above techniques may diverge. In this case, one should apply both techniques concurrently, checking the correctness of partitioning into clusters against the principal component analysis. 2010 Article Methods of cluster analysis in sensor engineering: advantages and faults / Yu.V. Burlachenko, B.A. Snopok // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 393-397. — Бібліогр.: 13 назв. — англ. 1560-8034 PACS 07.07.Df http://dspace.nbuv.gov.ua/handle/123456789/118565 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
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We consider the crisp and fuzzy partitioning techniques of cluster analysis
bearing in mind their application for classification of data obtained with chemical sensor
arrays. The advantage of the cluster analysis techniques is existence of a parameter S(i).
This parameter gives quantitative efficiency of classification and can be used as
optimization criterion for sensor system as a whole as well as the measurement
procedure. The crisp and fuzzy techniques give practically the same result when
analyzing the data that cluster uniquely. It is shown that big value of the parameter S(i) is
not sufficient for adequate data partitioning into cluster in more complicated cases, and
the results of clusterization for the above techniques may diverge. In this case, one
should apply both techniques concurrently, checking the correctness of partitioning into
clusters against the principal component analysis. |
| format |
Article |
| author |
Burlachenko, Yu.V. Snopok, B.A. |
| spellingShingle |
Burlachenko, Yu.V. Snopok, B.A. Methods of cluster analysis in sensor engineering: advantages and faults Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Burlachenko, Yu.V. Snopok, B.A. |
| author_sort |
Burlachenko, Yu.V. |
| title |
Methods of cluster analysis in sensor engineering: advantages and faults |
| title_short |
Methods of cluster analysis in sensor engineering: advantages and faults |
| title_full |
Methods of cluster analysis in sensor engineering: advantages and faults |
| title_fullStr |
Methods of cluster analysis in sensor engineering: advantages and faults |
| title_full_unstemmed |
Methods of cluster analysis in sensor engineering: advantages and faults |
| title_sort |
methods of cluster analysis in sensor engineering: advantages and faults |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118565 |
| citation_txt |
Methods of cluster analysis in sensor engineering:
advantages and faults / Yu.V. Burlachenko, B.A. Snopok // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 393-397. — Бібліогр.: 13 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT burlachenkoyuv methodsofclusteranalysisinsensorengineeringadvantagesandfaults AT snopokba methodsofclusteranalysisinsensorengineeringadvantagesandfaults |
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2025-07-08T14:14:55Z |
| last_indexed |
2025-07-08T14:14:55Z |
| _version_ |
1837088477450076160 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 393-397.
PACS 07.07.Df
Methods of cluster analysis in sensor engineering:
advantages and faults
Yu.V. Burlachenko, B.A. Snopok
V. Lashkaryov Institute of Semiconductor Physics, NAS Ukraine
41 Prospect Nauky, Kyiv 03028, Ukraine
Tel.: (380-44) 525-52-46; e-mail: b_snopok@yahoo.com
Abstract. We consider the crisp and fuzzy partitioning techniques of cluster analysis
bearing in mind their application for classification of data obtained with chemical sensor
arrays. The advantage of the cluster analysis techniques is existence of a parameter S(i).
This parameter gives quantitative efficiency of classification and can be used as
optimization criterion for sensor system as a whole as well as the measurement
procedure. The crisp and fuzzy techniques give practically the same result when
analyzing the data that cluster uniquely. It is shown that big value of the parameter S(i) is
not sufficient for adequate data partitioning into cluster in more complicated cases, and
the results of clusterization for the above techniques may diverge. In this case, one
should apply both techniques concurrently, checking the correctness of partitioning into
clusters against the principal component analysis.
Keywords: multisensor systems, cluster methods, recognition, classification.
Manuscript received 12.01.10; revised manuscript received 01.02.10; accepted for
publication 02.12.10; published online 30.12.10.
1. Introduction
The development and fabrication of an electronic analog
to biological nose is one of the most interesting practical
tasks of modern science. In recent years, much progress
has been achieved in this area. Now there are many
developments and commercial devices called Electronic
Noses (EN) [1]. However, contrary to biological nose that
provides an organism with all necessary information on
the character of odors from its nearest neighborhood, EN
gives partial information only. Indeed, the multisensor
arrays that serve as basis for EN have a certain selectivity
profile. Therefore, each device of that type can be applied
to solve only limited range of tasks.
Choice of the most efficient sensor array for
solution of a specific problem is one of the most
important tasks in optimization of EN-type devices.
Various generalized mathematical models [2-4],
statistical approaches [5, 6], estimations of information
content via the Fisher information [7, 8], predictions
based on system dynamic behavior [9] etc. have been
proposed in this area and successfully demonstrated in
many cases [9]. All the above approaches are based, up
to a point, on statistical calculations most of which use
the cluster analysis techniques. When classifying data,
various versions of pattern recognition procedures are
used to predict the properties of an object that were not
measured directly (chemical composition) but are related
indirectly to measurements via unknown or
undetermined interrelations.
To estimate the device operation efficiency when
solving a task, one should define a criterion for such
estimation. The objective of any EN-type sensor system
is classification with further recognition of the objects
studied (generally, these are multicomponent mixtures).
Strictly speaking, just classification efficiency could
serve as criterion of array optimization. Moreover,
having a quantitative estimate of classification
efficiency, one could optimize not only the array itself
but the measurement procedure as well, thus ensuring
the choice of the most informative part of response.
However, only some techniques of cluster analysis
make it possible to estimate classification efficiency
quantitatively. In this work, we consider the partitioning
techniques of cluster analysis from the viewpoint of their
application for classification of data from multisensor
arrays. The advantage of these techniques is existence of
a parameter S(i) that expresses the classification
efficiency quantitatively. We consider appropriateness of
this parameter as criterion of sensor array optimization.
The peculiarities of application of partitioning methods
in sensor technique are also considered.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
393
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 393-397.
2. The partitioning methods of cluster analysis
Classification means partitioning of a set of objects or
observations into uniform groups (clusters) whose
elements are similar, while there are quantitative
distinctions between elements belonging to different
clusters [10]. Thus, the objective of cluster analysis is
structuring the multidimensional input data and
attribution of every object from the given set to one of
the clusters. The classical methods of cluster analysis
(crisp techniques) lead to partitioning of the data set into
clusters with well-defined boundaries. This means that,
whatever the input data, they should be ascribed to a
certain class. Contrary to the crisp techniques, those
based on the concept of “fuzzy logic” calculate a
membership for each object, which indicates how
strongly the object belongs to a cluster. Thus,
assignment of an object to a certain class is presented as
something true up to a point only.
Different techniques of cluster analysis are
integrated into most of the modern software packages
used for statistical data processing. This makes
application of such packages simple and obvious. In this
work, comparison of the results of data classification for
multisensor arrays is made using the S-PLUS software
environment, with the partition around medoids (PAM)
and cluster analysis in the fuzzy logic format serving as
examples.
Let us start consideration with PAM. This
technique belongs to the crisp methods: each object is
assigned to one cluster only. The technique is based on
search for a certain number of representative objects
called medoids. The latter are chosen in such a way that
the dissimilarities between all objects and their nearest
medoid are minimal. The number of clusters is set by the
user. S-PLUS has an option of visualization of the
results of objects partitioning into clusters through
construction of a cluster plot (clusplot).
For each i-th objects, a parameter s(i) is calculated,
which characterizes quality of that object clusterization.
Let us dwell on the physical sense of that parameter,
without going into details [11]. The value of s(i) may be
interpreted in the following way:
s(i) ≈ 1 – the i-th object is classified well (into the
given cluster);
s(i) ≈ 0 – the i-th object is between two clusters;
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
s(i) ≈ -1 – the i-th object is classified badly (be-
longs to another cluster rather than the given one).
The s(i) values for all objects are plotted in a
special diagram (the so-called silhouette plot). In this
case, all the objects are partitioned into groups,
depending on their assignment to a certain cluster. The
average value S for all clusters in the silhouette plot is a
parameter that characterizes quantitatively the
classification quality as a whole (for all objects). It is
this parameter that may be applied for optimization of
sensor arrays.
Now let us consider the fuzzy partitioning
technique that is based on the concept of “fuzzy logic”.
Contrary to PAM where assignment of an object to a
certain class is either 0 or 1, in the fuzzy partitioning
technique it may take any value from 0 up to 1. The
results of analysis with the fuzzy partitioning technique
also may be presented as a clusplot and silhouette plot;
to this end, the closest crisp partitioning is chosen. As a
rule, the results obtained with fuzzy partitioning and
PAM are the same, if separation of the objects into
classes is sufficiently unambiguous. If, however, there
are some objects in a data array whose assignment to a
certain class is not well-defined, then different
techniques may give different results. Therefore, it
seems to be of importance that comparative analysis of
adequacy of these data classification should be made
with the crisp as well as fuzzy techniques.
3. Experimental
A set of experimental data was obtained using an array
of three QCM sensors (AT-cut quartz resonators with
resonance frequency of 10 MHz) modified with
phthalocyanine (H2Pc, CuPc, PbPc) films 100 nm thick.
The following analytes were used: (1) ethanol; (2)
triethylamine; (3) propylamine; and (4) water. Three
repeated measurements were performed with each
analyte. For the features of the measurement procedure
as well as the experimental set-up design see [12].
4. An example of application of PAM and fuzzy
partitioning
Figure 1 shows, as an example, the typical experimental
curves for three sensors exposed to ethanol vapor (these
curves were used in further calculations). Table 1
presents the normalized values of sensor responses, Snm,
at a moment t = 35 s since the beginning of
measurements:
∑
=
n
nm
nm
nm F
FS .
Here, Fnm is the response of the n-th sensor (taken
in the m-th measurement) to the same analyte; m = 1…3
numbers of measurements, while n = 1…3 numbers of
sensors.
As was noted earlier, availability of a priori
information on the number of classes is presumed when
applying the cluster methods. At the same time, in many
cases it is necessary to evaluate data quality bearing in
mind possible classification (how the data are clasterized
per se). To solve this task, one usually applies the
principal component analysis (PCA) [10]. This makes it
possible to project the response space onto a plane with
minimum distortions, visualize the data in the
transformed space of sensor coordinates, and estimate
qualitatively the degree of inherent data clusterization.
The data from Table 1 obtained with PCA are presented
in Fig. 2. (The numbers correspond to those of
experiments.)
394
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 393-397.
Table 1. Normalized sensor responses Snm at t = 35 s since
the beginning of measurement.
Analyte Measureme
nt # Sensor 1 Sensor 2 Sensor 3
1 0.316058 0.270269 0.413674
2 0.274731 0.273789 0.451479Ethanol
3 0.311210 0.280612 0.408178
4 0.133913 0.564111 0.301976
5 0.154681 0.564090 0.281228Triethylam
ine
6 0.149661 0.553314 0.297026
7 0.322383 0.205610 0.472007
8 0.294352 0.211957 0.493691Propylami
ne
9 0.298338 0.202595 0.499067
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
One can see from Fig. 2 that the objects (4, 5, 6) –
triethylamine – make a clearly pronounced separate
group. The object 2 (ethanol) is closer rather to the
group (7, 8, 9) than its own class (1, 3). This fact makes
the task of its correct classification much more difficult.
We used intentionally the data whose classification is
not apparent. Our aim was to demonstrate the fact that,
in such a situation, two different cluster analysis
techniques may give different results.
Shown in Fig. 3 are the silhouette plot and clusplot
constructed with PAM using the data from Table 1. One
can see that the object 2 (ethanol) is assigned to the class
(7, 8, 9) - propylamine, just as according to PCA, i.e., its
classification is wrong. In fact, negative s(i) value for
this object suggests that it belongs to another class rather
than this one.
Figure 4 presents a silhouette plot constructed with
the fuzzy partitioning technique using the same data. In
this case, all the objects are in their own classes. One can
see from Fig. 4 that just the second technique gives
correct classification. This is in spite of the fact that S
takes a bigger value in the first case rather than the
second one (0.67 for PAM and 0.66 for fuzzy
partitioning). Thus, one can state that bigger S value is a
necessary but not sufficient condition for correct data
classification.
0 200 400 600
-500
-400
-300
-200
-100
0
fre
qu
en
cy
s
hi
ft,
H
z
time, s
H2Pc
CuPc
PbPc
Fig. 1. Responses to ethanol vapor of QCM-sensors coated
with 100 nm films of phthalocyanines (H2Pc, CuPc and PbPc).
Fig. 2. PCA plot related to the responses of a three-sensor
array to ethanol, triethylamine and propylamine.
It should be noted that analysis of different
situations with data classification for multisensor arrays
testifies unambiguously that one cannot say in advance
what technique (crisp or fuzzy) will be more appropriate
for consideration of a specific case. Therefore, it seems
reasonable to perform classification using both
techniques in parallel to improve reliability of results. In
this case, the PCA method can serve for both
visualization and check of the results given by the
cluster analysis techniques because, contrary to the
partitioning techniques, it does not require availability of
a priori information on the number of clusters.
5
4
6
2
7
9
8
1
3
0.0 0.2 0.4 0.6 0.8 1.0
Silhouette width
Average silhouette width : 0.67
a
-2 -1 0 1 2
Component 1
-0
.4
-0
.2
0.
0
0.
2
0.
4
C
om
po
ne
nt
2
These two components explain 100 % of the point variability.
b
Fig. 3. Silhouette plot (а) and clusplot (b) constructed
according to PAM using sensor responses to ethanol,
triethylamine and propylamine.
395
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 393-397.
0 100 200 300 400
0,40
0,45
0,50
0,55
0,60
0,65
0,70
0,75
0,80
0,85
0,90
0,95
S
t, sec
1
2
Fig. 5. The classification efficiency curves S(t) constructed
using the sensor array responses to analytes: 1 - ethanol,
triethylamine and propylamine; 2 - water, triethylamine and
propylamine.
7
8
9
5
4
6
2
1
3
0.0 0.2 0.4 0.6 0.8 1
Silhouette width
Average silhouette width : 0.66
a
.0
-2 -1 0 1
Component 1
-0
.4
-0
.2
0.
0
0.
2
0.
4
0.
6
0.
8
C
om
po
ne
nt
2
These two components explain 100 % of the point variability.
b
Fig. 4. As in Fig. 3 but made with the fuzzy partitioning
technique.
5. Use of parameter S for optimization of sensor
array and measurement procedure
The parameter S can serve not only for array
optimization (i.e., for comparison of efficiencies of
individual sensors in an array) but for choice of the most
representative (i.e., ensuring the best classification)
region of response surface as well. Classification
efficiency may vary considerably in the course of time
of measurement. The reasons for this are the effects of
kinetic discrimination, on the one hand, and those of
reproducibility (different portions of adsorption curve
are affected differently by the external factors), on the
other hand [13]. Indeed, the calculation of S value for
every instant of time of experiment makes it possible to
obtain time dependence of classification efficiency, S(t).
Shown in Fig. 5 are the examples of such
dependences for classification of two sets of analytes:
ethanol, triethylamine and propylamine (curve 1) and
water, triethylamine and propylamine (curve 2). The
same multisensor arrays were used in both cases. Such a
presentation makes it possible to determine the most
informative (from the viewpoint of analyte distinctive
features) part of array response with respect to any of the
analytes used. To illustrate, for the first set of analytes, it
seems more reasonable to consider the stationary
response amplitudes (the peak of S(t) dependence is in
the saturation region of the adsorption curves). At the
same time, for the second set of analytes (that differed
from the first one by a single analyte only), the peak of
discrimination efficiency is observed in the kinetic
region. (Note once more that the same multisensor array
was used in both cases.)
Of course, the curve S(t) can be used only after
check for classification adequacy in different points of
the curve. To this end, one should construct silhouette
plots for sampling instants using the partitioning
techniques. It is expedient to recall here that, as shown
earlier, PAM gives wrong classification for the first set
of analytes at t = 35 s (see Fig. 3).
6. Conclusions
The approaches of mathematical statistics and
experiment optimization are widely used in analytical
chemistry practice to obtain information from big
analytical data arrays. The techniques of cluster analysis
are necessary and extremely convenient tool for solving
such tasks with respect to multidimensional data
obtained with sensor arrays made for various purposes.
As a rule, the results of classification obtained with the
crisp and fuzzy techniques coincide. If, however, the
data are classified ambiguously, it is reasonable to apply
both approaches in parallel, checking the result obtained
with PCA. In this case, availability of the parameter S
makes it possible to use the cluster methods for sensor
array optimization as well as choice of the most
informative region of the response surface. This will
enable one to increase efficiency of the analytical
procedures based on multisensor arrays to solve various
tasks of gas analysis via minimization of costs and time
required for analytical signal measurement and
extracting chemical information on analyte using the
databases for reference specimens.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Acknowledgements
396
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 393-397.
This work got a financial support from the National
Academy of Sciences of Ukraine.
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