=Paper=
{{Paper
|id=Vol-3038/paper16
|storemode=property
|title=Evaluation of the Gene Expression Profiles Complex Proximity Metric Effectiveness Based on a Hybrid Technique of Gene Expression Data Extraction
|pdfUrl=https://ceur-ws.org/Vol-3038/paper10.pdf
|volume=Vol-3038
|authors=Lyudmyla Yasinska-Damri,Igor Liakh,Sergii Babichev,Bohdan Durnyak
|dblpUrl=https://dblp.org/rec/conf/iddm/Yasinska-DamriL21
}}
==Evaluation of the Gene Expression Profiles Complex Proximity Metric Effectiveness Based on a Hybrid Technique of Gene Expression Data Extraction==
https://ceur-ws.org/Vol-3038/paper10.pdf
Evaluation of the Gene Expression Profiles Complex Proximity
Metric Effectiveness Based on a Hybrid Technique of Gene
Expression Data Extraction
Lyudmyla Yasinska-Damria, Igor Liakhb, Sergii Babichev c and Bohdan Durnyak a
a
Ukrainian Academy of Printing, Pid Goloskom street, 19, Lviv, 79000, Ukraine
b
Uzhhorod National University, University street, 14, Uzhhorod, 88000, Ukraine
c
Kherson State University, University street, 27, Kherson, 73000, Ukraine
Abstract
Gene expression data processing in order to develop the systems of complex diseases
diagnostic or/and gene regulatory networks (GRN) reconstruction is one of the actual
direction of modern bioinformatics. One of the important stages of this problem solving is an
extraction of mutually correlated gene expression profiles (GEP) considering the used
proximity metric. Within the framework of our research, we evaluate the complex metric of
GEP proximity calculated as the combination of modified mutual information criterion and
Pearson's chi-squared test using OPTICS clustering algorithm implemented using principles
of the objective clustering inductive technique (OCIT). The examined objects classification
accuracy was used as the main criterion to access the applied method effectiveness. The
simulation results have shown that the proposed technique allows us to form an optimal GEP
cluster structure in terms of maximum values of the patterns classification accuracy quality
criterion.
Keywords 1
Gene expression profiles, proximity metrics, OPTICS clustering algorithm, gene expression
profiles classification, inductive methods of objective clustering, clustering quality criteria,
classification accuracy
1. Introduction and literature review
The development of models of diseases diagnostics or/and gene regulatory networks (GRN)
reconstruction using gene expression data (GED) is one of the actual directions of modern
bioinformatics. As a rule, the initial GED is formed as a high dimensional array with components
represented the studied patterns and genes. The value of gene expression is depended on the amount
of this type of gene that determines the appropriate properties of the examined biological organism.
Gene expression profile (GEP) means the vector of gene expressions the values of which are
evaluated for the examined patterns.
Reconstruction of gene regulatory network (GRN) which adequate reflect the nature of genes
interaction under the different states of a biological organism in order to develop both effective
medicine and disease diagnostic and treating methods is possible provided the extraction of groups of
highly and mutually expressed genes. For this reason, the stage of gene expression data pre-
processing is very important at the early stage of GRN forming or under the development of a disease
diagnosing model. Figure 1 illustrates a stepwise procedure for implementing this process. The
filtration procedure, in this case, involves removing genes with zero expression at the first step and
genes with low expression in terms of the empirically established threshold at the second step.
IDDM-2021: 4th International Conference on Informatics & Data-Driven Medicine, November 19–21, 2021 Valencia, Spain
EMAIL: Lm.yasinska@gmail.com (L. Yasinska-Damri); ihor.lyah@uzhnu.edu.ua (I. Liakh); sbabichev@ksu.ks.ua (S. Babichev);
durnyak@uad.lviv.ua (B. Durnyak)
ORCID: 0000-0002-8629-8658 (L. Yasinska-Damri); 0000-0001-5417-9403 (I. Liakh); 0000-0001-6797-1467 (S. Babichev); 0000-0003-
1526-9005 (B. Durnyak)
©️ 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
Moreover, data can contain gene expression profiles that are statistically significantly different from
the GEP of the main group. It is obvious that such genes do not correlate with the profiles of other
genes and they can also be removed from the data. Qualitative implementation of this stage allows
significantly reducing the number of genes for further research. This fact also contributes to
enhancing the quality of further steps of GED processing for the solving hereinafter described
problem.
Figure 1: Block-chart of a step-by-step procedure of GED processing to form clusters of highly and
mutually expressed GEP
In [1], the authors presented the “limma” module (Linear Models for Microarray and RNA-Seq
Data), which contains various functions for generating, filtering and interpreting gene expression data
obtained using both DNA microchips experiments and mRNA molecules sequencing method. This
module is to some extent an alternative to the “Bioconductor” package, implemented in the data
mining and machine learning R software [2] and it is based on the use of linear models to allocate
differently expressed genes in a multifactor experiment. This module also contains functions for the
genes ontology analysis, which is very important for adequate GRN reconstruction, because the
interpretation of genes and their interactions based on the analysis of conceptual interconnections
allows identifying target genes, to establish the nature of interconnections between target and other
genes taking into account appropriate disease.
The papers [3-5] considered a various tools and techniques of GED filtering that are available in
the "Bioconductor" package using quantitative quality criteria for GED received by DNA microarray
method [3,4] and mRNA molecules sequencing [5]. As a simulation result, the authors proposed a
stepwise algorithm for extracting highly and mutually expressed gene expression profiles for their
further grouping into clusters. In a review [6], the authors conducted a comparative analysis of current
software to process the GED for purpose of extracting the most informative genes. The analysis of the
authors' research allows concluding on the feasibility of using the R software for GEP processing in
order to form clusters of highly and mutually expressed genes because this software contains all
necessary modules and functions to process gene expression data according to the solved task.
The review [7] presents the research results focused on the study of various hybrid techniques to
extract the clusters of mutually correlated GEP to solve the problem of creation of the system of
cancer disease diagnostic. In the reviewed works, various combinations of filtering, clustering and
classification techniques using various types of statistical criteria and gene expression profiles
proximity metrics were applied. The examined objects classification accuracy was applied as the
principal quality metric to assess the appropriate hybrid model effectiveness. The following filtration
techniques and methods to estimate the gene expression profiles proximity were analyzed in this
review: mutual information maximization method [8], 2 Pearson's test [9], correlation-based feature
selection technique [10], Laplacian and Fisher score [11], information gain method [12], Fisher
criterion [13], independent component analysis [14], maximum relevance minimum redundancy [15],
probabilistic random function [16], random forest ranking [17], Fisher-Markov selector [18],
symmetrical uncertainty [19] and logarithmic transformation [20] method. However, we would like to
note that in the analyzed research high classification accuracy in most cases is achieved when using a
low number of the extracted GEP. Moreover, the parameters of the respective technique used in the
appropriate hybrid models are set upped empirically when the simulation process is performed.
Undoubtedly, this fact is one of the main disadvantages of the analyzed models.
The works [21,22] presents the partial decision of this task. A stepwise procedure of GEP
extraction on the basis of the joint application of Shannon entropy, statistical criteria, clustering
technique based on the SOTA clustering algorithm and random forest binary classifier was developed
in these papers. The suitable algorithm parameters considering the classification accuracy were set a
priory according to the OCIT principles. However, only correlation proximity metric was used within
the framework of the authors' research. Thus, the presented hereinbefore brief review allows
concluding that an effective model of GEP extraction based on joint application of various proximity
metrics, clustering and classification techniques is absent now. This problem can be solved on the
basis of joint application of various techniques used successfully in current data science directions of
scientific research nowadays [23-26].
In this work, we consider the GEP hybrid proximity metric calculated as a combination of
modified mutual information maximization method and Pearson's 2 test. The modified mutual
information maximization method, in this instance, takes into account various methods of Shannon
entropy evaluation.
The objective of the research is the development and evaluation of a hybrid model of GEP
extraction on the basis of joint application of hybrid proximity metric, OPTICS clustering algorithm
implemented using principles of OCIT and random forest binary classifier.
2. Materials and methods
In the general instance, the clustering internal quality criterion should consider both the gene
expression profiles allocation inside clusters and clusters' medians allocation relative to each other.
Thus, this criterion should be complex and contains two components. If we assume that K is the
number of clusters, then the formula for assessing the first component of this criterion can be
calculated in the following way:
1 K 1 Nk
QCW d (ei , Ck ) (1)
K k 1 N k i 1
where: N k and C k are the number of GEP in k-th cluster and the median of k-th cluster respectively;
d (ei , C k ) is the distance between i-th profiles and median of this cluster calculated using complex
proximity metric which contained both the modified mutual information maximization method
(considered various methods of Shannon entropy calculation) and Pearson’s 2 test the effectiveness
of which is proved in [27].
The second component of the internal criterion can be assessed as the average distance between
the allocated clusters’ medians:
K 1 K
2
QCB d (Ci , C j )
K ( K 1) i 1 j i 1
(2)
In [21], the authors performed modelling to assess the performance of different types of internal
criteria, containing (1) and (2) as the components. As a result, a hybrid internal criterion formed as a
ratio of Calinski-Harabasz criterion and WB index has been proposed:
K ( K 1)QCW 2
QC int (3)
( N K )QCB2
where N is the number of objects that should be grouped. This criterion was used as the internal one
during the modelling procedure performing.
Assessment of the efficiency of both the GEP hybrid proximity metric and quality criteria when
the profiles grouping into clusters was performed based on the application of density clustering
algorithm Optics [28], which is a logical development of DBSCAN density algorithm and allows us to
form a multicluster structure based on the application of respective proximity metric. The feasibility
of using the OPTICS clustering algorithm is determined by the fact that its application allows us not
only to form a multicluster structure containing clusters of close gene expression profiles by density
in their allocation in feature space but also to allocate profiles identified as noise because of density of
their allocation relative to other GEP is much lower compared to the density of the main groups of
GEP distribution.
We would like to note that the criterion calculated by formulas (1) – (3) does not always allow us
to objectively form an adequate clustering due to the reproducibility error, which is inherent to most
prevailing clustering algorithms. In other words, satisfactory results of data grouping gotten using one
dataset are not always repeated when applying another similar dataset. In [29], the authors proposed
the idea of reducing the reproducibility error by using “fresh data” (not used when creating the model)
during the process of verifying the obtained model of object distribution into clusters and making the
final decision regarding the cluster structure formation by joint using the internal, external and
balance criteria, which considered possible discrepancies between internal and external criteria. This
idea was further developed in [30,31] where the objective clustering inductive technology was
described and implemented. The authors proposed an external quality criterion assessed in the form of
normalized distinction of the internal criteria assessed on two equivalent subsets (contained the same
number of pairwise similar objects) at the appropriate hierarchical level of cluster structure formation:
QC1int QC2int
QC ext
(4)
QC1int QC2int
The main idea was as follows. The minimal reproducibility error matches the maximum degree of
the similarity of objects allocation in clusters obtained on two equivalent subsets. Since the internal
criteria consider the nature of both the patterns distribution in clusters and the clusters' medians
allocation relative to each other, objective clustering (minimum value of reproducibility error) in this
case corresponds to the minimal difference between the corresponding values of the internal criteria.
The normalizing correction in formula (4) transforms the range of the external criteria values variation
from 0 (zero reproducibility error) to 1 (maximum error). The balance criterion was calculated using
the Harrington desirability function according to the algorithm described in detail in [30,31].
The random forest classifier was used to implement this step. This choice is determined by the
previous authors' research, presented in [21], where various types of binary classifiers were studied to
classify the samples of patients examined on lung cancer. These samples contained gene expression
data as attributes too. The effectiveness of the respective model was assessed using the examined
samples classification accuracy.
Figure 2 shows a block chart of the stepwise procedure performed within the framework of the
modelling procedure executing. The practical implementation of this algorithm assumes the following
stages:
Stage I. Formation of GEP data and functions to calculate respective criteria.
1.1. Forming a array of GED, the components of which represent the assessed patterns and genes
whose expression determines the relative amount of a given type of gene for the examined patterns
respectively.
1.2. Formation of the function to estimate the proximity metrics between GEP on the basis of the
joint application of the modified mutual information maximization proximity metric and Pearson's 2
test [28].
1.3. Formation of the functions to calculate the internal, external and hybrid balance quality
criteria.
1.4. Formation of the function to calculate the examined samples classification accuracy.
1.5. Formation of two equivalent subsets of GEP by the iterative distribution of the two nearest
GEP according to a hybrid proximity metric into two equivalent subsets.
Stage II. Setup of density-based OPTICS clustering algorithm.
2.1. Setup of range for changing the minimum number of points within the ε-neighborhood:
MinPtsmin, MinPtsmax.
2.2. Creating a reachability chart. Setup of both the range and step of variation of the ε-
neighborhood values: Epsmin, Epsmax, dEps.
2.3. Calculation of distances between all pairs of gene expression profiles in equal-power subsets
and formation of matrixes of distances between the corresponding profiles. The obtained distance
matrixes will be used as input data when the clustering procedure is implemented by applying the
OPTICS algorithm.
Figure 2: Structural block-chart of the algorithm for forming a multicluster structure based on the
OPTICS algorithm implemented using the principles of OCIT
Stage III. Stepwise clustering of GEP within the specified ranges of the algorithm appropriate
parameters variation.
3.1. MinPts value initialization: k = MinPtsmin.
3.2. Eps value initialization: e = Epsmin.
3.3. Clustering of gene expression profiles contained in equivalent subsets, forming the partitions
with the number of clusters K1 and K2.
3.4. If K1 = K2 > 2, calculation of internal and external quality criteria by formulas (1) - (4).
Otherwise, increase the value of Eps parameter (e = e + de) and go to step 3.3 of this procedure.
3.5. Classification of objects that contain gene expression profiles in each of the allocated clusters.
Calculation of the classification quality criterion (Accuracy).
3.6. If e Eps max , go to step 3.3 of this procedure. Otherwise, calculate the hybrid balance
criterion and increase the MinPts value by one: k = k + 1.
3.7. If k MinPts max , go to step 3.2 of this procedure. Otherwise, the creation of charts of the
clustering and classification quality criteria depending on the Eps value for each of the MinPts values.
Stage IV. An analysis of the obtained results.
4.1. An analysis of the obtained charts. Forming conclusions regarding the effectiveness of hybrid
metrics of GEP proximity in the process of forming subsets of informative genes for their further use
when the creation of disease diagnosing systems or/and GRN reconstruction.
3. Experiment, results and discussion
The practical implementation of the proposed algorithm was carried out using the GSE19188 gene
expressions dataset of patients studied for the early stage of lung cancer [32]. The data were obtained
using a DNA microchips experiment and contained 156 microchips, 65 of them contained GED of
healthy patients and 91 ones included the GED of patients with lung cancer tumor (mild form). 400
the most informative GEP in terms of classification accuracy (approximately 93%) [20,21] were used
during the simulation procedure implementation.
The MinPts value was changed within the limits of 3 to 5. This interval was established empirically.
The results of the modelling showed that a larger quantity of points within the Eps neighborhood
degrades the simulation results both in terms of the number of clusters in the equal over subsets and in
terms of gene expression profiles clustering quality criteria and the samples classification accuracy.
The Eps values were varied from the minimum, which was calculated as the minimum distance
between gene expression profiles in equal-power subsets to a 1.5 minimum distance. This range was
also set empirically. When the Eps values was larger, the GEP were allocated into 2 clusters, and the
clustering results were repeated. The resulting range of the Eps values variation was divided into 20
equal sections. The width of the section was equal to the step of the Eps value changing. According to
the hereinbefore presented algorithm, the clustering and classification quality criteria were calculated
only for cases where the number of clusters allocated on equal-power subsets was equal. This
condition minimizes the reproducibility error. Tables 1 and 2 and Figures 3 and 4 present the
modelling results.
Table 1
The result of the division of GEP into clusters when MinPts = 3
Clusters
EPS,*10-3
1 2 3 4 5 6
0.66435 24 311 6 14 6 7
0.69525 24 322 6 14 6 –
0.71070 24 323 6 14 6 –
0.72615 24 329 6 14 6 –
0.74160 24 332 6 14 6 –
0.91155 24 359 6 – – –
0.92700 24 359 6 – – –
Table 2
The result of the division of GEP into clusters when MinPts = 4 and 5
EPS,*10-3 MinPts = 4 EPS,*10-3 MinPts = 5
Clusters Clusters
1 2 3 4 1 2 3 4
0.64890 24 158 115 11 0.64890 23 155 115 11
0.69525 24 322 14 – 0.66435 24 308 14 –
0.71070 24 323 14 – 0.67980 24 314 14 –
0.72615 24 326 14 – 0.69525 24 321 14 –
0.74160 24 331 14 – 0.71070 24 322 14 –
– – – – – 0.72615 24 326 14 –
– – – – – 0.74160 24 331 14 –
Figure 3: The simulation results regarding the criterial analysis of cluster structure using OPTICS
algorithm implemented on the basis of OCIT: distribution of the internal criteria assessed on the first
(a) and second (b) equivalent subsets of GEP; external (c) and hybrid balance criterion (d) when the
Eps and MinPts values are varied from minimum to maximum values
The analysis of the obtained results allows concluding on the feasibility of using the proposed GEP
proximity metric for the selection of mutually correlated profiles in the case of using a multicluster
structure which is formed by applying the OPTICS clustering algorithm. The proposed method crate
the condition to assess the algorithm suitable parameters in terms of the optimal nature of the GEP
grouping into clusters on the one hand, and the minimum value of the reproducibility error on the
other hand. As can be seen from Tables 1 and 2, when the MinPts parameter value is 3, there are
seven clusters' structures. The first clustering contains six clusters, the four clustering contain five
clusters, and the last two clustering contain three clusters. In the cases when MinPts values are 4 or 5,
the first clustering contained four clusters, in other cases, three clusters were obtained in each
clustering. It should be noted that the initial data contained approximately 400 gene expression
profiles that were carefully selected by stepwise application of the SOTA clustering algorithm
[20,21]. The accuracy of the samples classifying when the full set of gene expression profiles was
used as attributes was approximately 93%.
Analysis of the results shows also that in all cases, some of the gene expression profiles are
identified as noise. These genes are not contained in any cluster. The presence of "noise" genes can be
explained by the fact that the density of these GEP in terms of the used proximity metric is less than
the conditional boundary value assessed by the OPTICS clustering algorithm. Analysis of the charts
presented in Figure 3 has also shown that the internal and external criteria do not optimal to assess the
OPTICS algorithm suitable parameters because the minimum values of these metrics do not matched
to the maximum values of the object classification accuracy in the corresponding clusters. The
maximum value of the hybrid balance criterion, which contains as components both the internal and
external criteria is achieved in the case in a three-cluster structure with the parameters of the OPTICS
algorithm: MinPts = 3, Eps = 0.00091155 or Eps = 0.00092700 (the same results are achieved in these
instances). The results of the classification of objects contained in the corresponding clusters and
presented in Figure 4, confirm the hereinbefore conclusions. As it can be seen from the charts, with
these parameters of the algorithm, the classification accuracy is maximal for the first two clusters,
while the second cluster contains the largest number of genes, i.e. it is the main in terms of the
number of gene expression profiles. The third cluster contains only six genes. The classification
results in the fourth, fifth and sixth clusters are not adequate because they are the same in all cases and
slightly worse than the classification results in the first three clusters. It should be noted that the
maximum values of the hybrid balance criterion that determines the quality of gene expression
profiles clustering correspond to the maximum values of the samples classification accuracy that
contain as the attributes the extracted gene expression profiles. This fact indicates the high efficiency
of the proposed hybrid proximity metric and technique to asses the quality of GEP clustering.
Figure 4: The results of the simulation regarding assessing the objects classification accuracy whose
attributes are the gene expression profiles allocated to clusters using the OPTICS algorithm: a) the
first cluster; b) the second cluster; c) the third cluster
4. Conclusions
A hybrid model of GEP clusters formation in order to extract the groups of mutual similar GEP in
terms of applied proximity metrics based on the application of OPTICS clustering algorithm
implemented on the basis of OCIT principles has been described in this paper. The hybrid proximity
metric to access the distance between GEP has been applied during the simulation. This metric has
been calculated on the basis of the joint applying the modified mutual information maximization
metric (considered various methods of Shannon entropy evaluation) and Pearson's 2 test. The
effectiveness of this hybrid proximity metric has been proved in [27]. The structural block chart of the
stepwise algorithm for set the OPTICS algorithm suitable parameters in terms of a hybrid balance
clustering quality criterion, which contains as components the internal and external clustering quality
criteria has been presented. The high efficiency of the proposed model has been confirmed by the
convergence of quality criteria for clustering gene expression profiles and the classification of objects
that contain these GEP as attributes.
An analysis of the simulation results has indicated that the internal and external clustering quality
criteria do not allow determining the OPTICS algorithm optimal parameters. The minimal values of
these criteria do not matched to the maximum values of the object classification accuracy in the
corresponding clusters. The maximal value of the hybrid balance criterion, which is formed
considering both the internal and external criteria has been achieved for a three-cluster structure with
the parameters of the OPTICS algorithm: MinPts = 3, Eps = 0.00091155 or Eps = 0.00092700 (the
same results are achieved in these instances).
The analysis of the results of objects classification has confirmed the high effectiveness of the
proposed technique since the classification accuracy is maximal for the first two clusters, while the
second cluster contains the largest number of genes, i.e. it is the main in terms of the number of gene
expression profiles. The third cluster contains only six genes. The fourth, fifth and sixth clusters
contained the same number of gene expression profiles. Additionally, classification accuracy in these
cases is slightly worse than the classification results in the first three clusters. It should be noted that
the maximum values of the hybrid balance criterion that determines the quality of GEP clustering
matched to the maximum values of the samples classification accuracy that contain as the attributes
the extracted gene expression profiles. This fact indicates the high efficiency of the proposed hybrid
proximity metric and model to assess the quality of GEP clustering. However, we would like to note
that the proposed proximity metric is appropriate for high dimensional gene expression profiles. In the
case of the other data use, it is necessary to investigate other more suitable for this type of data
metrics. This is the limitation of the proposed model.
The further perspectives of the authors' research are an application of the proposed hybrid
proximity metric within the framework of gene expression profiles hybrid clustering and classification
techniques implemented based on other clustering and classification algorithms.
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