Second Asia International Conference on Modelling & Simulation
Recent advances in microarray technology allow scientists to measure expression levels of thousands of genes simultaneously in human tissue samples. This technology has been increasingly used in cancer research because of its potential for classification of the tissue samples based only on gene expression levels. A major problem in these microarray data is that the number of genes greatly exceeds the number of tissue samples. Moreover, these data have a noisy nature. It has been shown from literature review that selecting a small subset of informative genes can lead to an improved classification accuracy. Thus, this paper aims to select a small subset of informative genes that is most relevant for the cancer classification. To achieve this aim, an approach using two hybrid methods has been proposed. This approach is assessed on two well-known microarray data. The experimental results have shown that the gene subsets are very small in size and yield better classification accuracy as compared with other previous works as well as four methods experimented in this work. In addition, a list of informative genes in the best subsets is also presented for biological usage.
Keywords: gene selection, hybrid method, cancer classification, microarray data, gene expression
The problem of cancer in this world is a growing one. It is now the fourth and second leading cause of death among medically certified deaths in Malaysia and the United States, respectively [3][10]. Cancer develops mainly in epithelial cells (carcinomas), connecting/muscle tissues (sarcomas), and white blood cells (leukaemia and lymphomas). A successive mutation in the normal cell that damages the DNA and impairs the cell replication mechanism causes malignant tumours (cancers). There are several numbers of carcinogens such as tobacco smoke, radiation, certain microbes, synthetic chemicals, polluted water, and air that may accelerate the mutations. Thus, there is a need to identify the informative genes that contribute to a cancerous state.
An informative gene is a gene that is useful and relevant for cancer classification.
A traditional cancer diagnosis relies on a complex and inexact combination of clinical and histopathological data. This classic approach may fail when dealing with atypical tumours or morphologically indistinguishable tumour subtypes.
Advances in the area of microarray-based gene expression analysis have led to a promising future of cancer diagnosis using new molecular-based approaches [7]. Microarray is a device used to measure expression levels of thousands of genes simultaneously in a cell mixture, and finally it produces microarray data. Microarray data is also known as gene expression data. The task of cancer classification using microarray data is to classify tissue samples into related classes of phenotypes such as cancer versus normal [9].
Given N tissue samples and expression level of M genes, the microarray data is stored in an N x ( M +1) matrix as shown in Figure 1.
978-0-7695-3136-6/08 $25.00 © 2008 IEEE
DOI 10.1109/AMS.2008.71
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M genes class label g
1,1 g
1,2 g
1,m l
1 g
2,1 g
2,2 g
2,m l
2
N samples g
N,1 g
N,2 g
N,M l
N
Figure 1. The matrix of microarray data. g i,j is a numeric value presenting the gene expression level of gene j in sample i . l i in the last column is the class label for sample i .
Cancer classification using microarray data poses a major challenge because of the following characteristics:
• M >> N . For typical data sets, M is in the range of
10,000-20,000, while N is in the range of 30-200.
• Most genes are not relevant to the classification of different tissue types.
• These data have a noisy nature.
To overcome the problems, gene selection approach is used to select a small subset of informative genes that maximises the classifier’s ability to classify samples accurately [9]. Gene selection has several advantages:
• It can improve classification accuracy.
• It can reduce the cost in a clinical setting. At the moment, expression arrays with thousands of genes are impractical to be employed in medical laboratories.
• It could enable biologists to gain significant insight into the genetic nature of the disease and the mechanisms responsible for it. This would assist in drug discovery and early diagnosis.
Gene selection method can be classified into two categories. If gene selection is carried out independently from the classification procedure, the method belongs to the filter approach. Otherwise, it is said to follow a hybrid approach. Most previous works have used the filter approach to select genes since it is computationally more efficient than the hybrid approach. However, the hybrid approach usually provides greater accuracy than the filter approach [8].
In this paper, gene selection problem is focused on and an approach using two hybrid methods is proposed to select a small subset of informative genes for cancer classification.
Mohamad et al. reported that a hybrid of genetic algorithm and support vector machine (GASVM), and an improved GASVM (NewGASVM) have several advantages and disadvantages [8]. In this paper,
NewGASVM is called as GASVM-II. All information of GASVM and GASVM-II such as flowchart, algorithm, chromosome representation, and parameter values are available in Mohamad et al [8]. The advantage of GASVM is that it can automatically select and optimise a number of genes to produce a gene subset. However, it performs poorly in highdimensional data. In contrast, GASVM-II performs well in the high-dimensional data. Therefore, it can reduce the complexity of search space and maybe able to evaluate all possible subsets of genes. Nevertheless, the drawback of GASVM-II is that it selects a number of genes manually to yield a gene subset.
As a result, this paper proposes an approach using two hybrid methods for selecting informative genes.
This approach is called as GASVM-II+GASVM. It is developed to improve the performances of GASVM and GASVM-II. Figure 2 shows that an algorithm of
GASVM-II+GASVM involves two stages. In the first stage, GASVM-II is applied to manually select genes from the overall microarray data to produce a subset of genes. It is used to reduce the dimensionality of the data, and therefore the complexity of the search or solution space can also be decreased. It also performs well in high-dimensional data.
In the second stage, GASVM is used to select and optimise a small subset of informative genes from the subset that is produced from the first stage. If size of the subset is small and the combination of genes is not very complex, then the GASVM can easily find and optimise the subset. GASVM is applied because it can automatically select a number of genes and finally produce an optimised gene subset. This second stage can also remove noisy genes because the first step has reduced the size and complexity of the search space.
Therefore, this proposed approach has totally excluded the testing samples from the classifier building process in order to avoid the influence of selection bias [1]. The fitness of an individual is calculated as follows:
( ) = w
1
× A x +
2
( − ( )) / M ) (1) in which ( ) [0,1] is the leave-one-out-crossvalidation (LOOCV) accuracy on training data using the only expression values of the selected genes in subset x , ( ) is the number of selected genes in x .
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M w
2
is the total number of genes. w
1
.
w
1
and w
2
are two weights corresponding to the importance of accuracy and the number of selected genes, w
1
∈ [0.1,0.9] and
In this paper, accuracy is more important than number of selected genes.
Step 1 : Select a number of genes and produce initial population with each chromosome is represented by integer string.
Step 2 : Evaluate each individual (chromosome) in a population using a fitness function.
Step 2.1
: Sort integer values in a chromosome.
Step 2.2
: Select genes based on position of the integer values in a chromosome (e.g: if integer value=10, then select 10 th gene).
Step 2.3
: Store the selected genes into a subset.
Step 2.4
: ( ) = w
1
× A x +
2
( − ( )) / M )
Step 3 : GA operates on the population to evolve the best solution (a subset of selected genes) until the final generation.
Step 3.1
: Apply the selection strategy and GA operators (crossover and mutation).
Step 3.2
: Repeat Step 2 .
Step 4 : Return a subset of genes (the highest fitness).
Step 5 : Get the total number of genes from the subset of genes that is produced in Step 4, and produce new initial population with each chromosome is represented by bits (0 and 1) string.
Step 6 : Evaluate each chromosome in a population using a fitness function.
Step 6.1
: Select genes based on bit values in a chromosome (bit 1=select; bit 0=unselect).
Step 6.2
: Store the selected genes into a subset.
Step 6.3
: ( ) = w
1
× A x +
2
( − ( )) / M )
Step 7 : GA operates on the population to evolve the best solution (the best subset of genes) until the final generation.
Step 7.1
: Apply the selection strategy and GA operators (crossover and mutation).
Step 7.2
: Repeat Step 6 .
Step 8 : Return the best subset of genes.
Step 9 : Classify the best subset using SVM classifier.
Figure 2. An algorithm of GASVM-II+GASVM.
Two microarray data sets are used to evaluate the proposed algorithm: Lung cancer and Mixed-Lineage
Leukaemia (MLL) cancer. The Lung cancer data set has two classes: malignant pleural mesothelioma
(MPM) and adenocarcinoma (ADCA). There are 181 samples (31 MPM and 150 ADCA), originally analysed by Armstrong et al [11]. The training set contains 32 of them (16 MPM and 16 ADCA). The rest 149 samples are used for test set. Each sample is described by 12,533 genes. It can be obtained at http://chestsurg.org/publications/2002microarray.aspx.
The MLL cancer data set is a multi-classes data set.
It has three leukaemia classes: acute lymphoblastic leukaemia (ALL), acute myeloid leukaemia (AML), and MLL. The training set contains 57 samples (20
ALL, 17 MLL, and 20 AML). While the testing set contains 4 ALL, 3 MLL, and 8 AML samples. There are 12,582 genes in each sample. This data set was published by Gordon et al. [4]. It can be downloaded at http://www.broad.mit.edu/cgi-bin/cancer/publications/ pub_paper.cgi?mode=view&paper_id=63.
Table 1 below contains the parameter values for the
GASVM-II+GASVM. These values are chosen based on the results of preliminary runs. Three criteria following its importance are considered to evaluate the performances of the proposed approach: test accuracy,
LOOCV accuracy, and number of selected genes.
Table 1. Parameters of the proposed approach
(GASVM-II+GASVM).
Parameter
Size of population
Number of generation
Replacement rate (Roulette wheel selection)
Crossover rate (Two-point)
Mutation rate (Gaussian) w
1
Lung data set MLL data set
100 100
1000 1000
0.8 0.8
0.7
0.01
0.7
0.01
0.7 0.7 w
2
Cost for generalization of SVM
Gamma for kernel of radial basis function in SVM
0.3 0.3
0.7 100
0.0000798 0.0000795
The experimental results presented in this section pursue two objectives. The first objective is to show that gene selection using the GASVM-II+GASVM is needed for better classification of microarray data. In additional to that, the second objective is to show that it is better than GASVMs (single-objective and multiobjective) and GASVM-II. To achieve these objectives, several experiments are conducted on the proposed algorithm 10 times on each data set. In the first stage, it is experimented by using different number of pre-selected genes (10, 20, 30,…, 600).
Furthermore, in the second stage, GASVM chooses a
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number of the final selected genes automatically.
Lastly, it produces an optimised gene subset that contains the final selected genes. The subset that produces the highest LOOCV accuracy with the possible least number of selected genes is chosen as the best subset. SVM classifier, GASVMs, and
GASVM-II are also experimented for comparison.
Additionally, the GASVM-II+GASVM is also compared with other previous works in order to obtain better findings. Finally, a list of informative genes in the best subsets is presented for biologist usage.
In this paper, a value of the form x ± y represents average value x with standard deviation y.
Furthermore, #Pre-Selected Genes, #Final Selected
Genes, and Run# represent number of pre-selected genes, number of the final selected genes, and run number, respectively.
Figure 3 shows that the highest averages of
LOOCV and test accuracies for classifying Lung cancer samples are 100% and 94.16%, respectively , while 100% and 92%, respectively, for MLL data set are shown in Figure 4.
LOOCV Test #Final Selected Genes
110
100
90
80
70
60
50
40
100±0 100±0 100±0 100±0 100±0 100±0 100±0 100±0 100±0 100±0 100±0 100±0 100±0
94.16±6.85
90.71±14.07
69.33±31.43
75.37±21.68
70.94±28.83
78.32±20.04
20
17.9±1.52
16
76.38±30.11
12
64.16±30.75
3.7±1.25
4.1±2.89
68.99±16.58
2.1±0.32
3.2±0.79
67.45±23.87 69.33±28.12
3.3±0.68
2.4±0.52
64.43±27.85
2.5±0.53
6.3±0.82
8
4
10 20 30 40
3.2±0.92
50 60
3.5±1.09
70 80
2.7±0.82
#Pre-Selected Genes
90
2.2±0.42
50.13±30.52
100 200 400 600
0
Figure 3. Correlation between classification accuracies and numbers of selected genes
(#Pre-selected genes and #Final selected genes) on Lung data set (10 runs on average)
Only 2.1 average genes were finally selected to obtain the highest average of the accuracies of Lung data set, whereas 6.5 average genes of MLL data set.
Almost all the different numbers of pre-selected genes and the final selected genes have obtained 100%
LOOCV accuracy, and this has proven that the proposed approach search and select the optimal solution (the best gene subset) in the solution space successfully. However, test accuracy in both data sets was much lower than LOOCV accuracy due to overfitting problem. This problem happened because of the number of samples is much smaller than the number of genes, and many expression values of test samples may be different from those of the training samples.
110
90
80
70
60
100
99.3±01.23
99.65±1.11
77.33±14.47
7.4±1.9
10
8.4±1.9
20
99.65±0.74
8.2±2.25
30
LOOCV
99.65±0.74
100±0
83.33±9.56
75.33±8.92
80±9.43
8.4±1.78
8.6±2.12
40 50
Test
99.82±0.55
74±12.35
8.7±1.57
100±0 cx
#Final Selected Genes
99.47±0.85
79.33±11.95
79.33±12.35
72.67±11.53
7.7±2.31
8.3±1.49
99.65±0.74
8.1±2.33
60 70 80
#Pre-selected Genes
100±0
92±8.2
76±10.52
6.5±0.71
100±0
100±0
29.1±1.79
6.7±1.16
100±0
86.67±7.7
85.33±6.89
13.5±1.08
90 100 200 400 600
30
25
20
15
10
5
Figure 4. Correlation between classification accuracies and numbers of selected genes
(#Pre-selected genes and #Final selected genes) on MLL data set (10 runs on average)
Table 2. Results of the best gene subsets in 10 runs.
Data set
#Pre-
Selected
LOOCV
(%)
Test
(%)
#Final
Selected
Run#
Genes Genes
Lung 40 100 98.66 2 2,6,7,8,9,10
MLL 100 100 100 6 1,2,6,9
Table 2 shows that the best performances (LOOCV and test accuracies) of the proposed approach in the best subsets were 100% and 98.66%, respectively for
Lung data set using the only two genes. For MLL data set, the highest results (LOOCV and test accuracies) were 100% using the only six genes. The best performances for Lung data set have been found in the second, sixth, seventh, eighth, ninth, and tenth runs, while the first, second, sixth, and ninth runs of MLL data set.
The selected genes in the best gene subsets as founded by the GASVM-II+GASVM in Table 2 are shown in Table 3. The probe-set name, gene description, and gene accession number of the selected informative genes are also given. Interestingly, all of the best gene subsets of Lung data set have similar type of genes. However, for MLL data set, the best subsets have same and different kind of genes. From this finding, the existences of some kinds of correlations among the two selected genes of Lung data set and six selected genes of MLL data set are noted (gene description). Based on graph in Figures 3 and 4, different number of selected genes in a subset has produced dissimilar test accuracy. Thus, the
GASVM-II+GASVM preserves the interactions among the genes that result in the best classification accuracy by using only two genes of Lung data set and only six genes of MLL data set. These genes among thousand of genes may be excellent candidate for medical investigations.
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Data
Set
Lung
MLL
Method
Table 3. A list of informative genes in the best gene subsets.
Gene Description
Name Number
2, 6, 7, 8, 9, 10 34320_at
2, 6, 7, 8, 9, 10 41286_at
1, 2, 6, 9
1, 2, 6, 9
1, 2, 6, 9
36873_at
AL050224
X77753
D16532
40520_g_at Y00638
38462_at U64028
6
6
9
1, 2, 9
1, 2, 9
1, 2
6
31340_at
1116_at
34950_at
1356_at
32262_at
Y12779
M28170
40489_at D31840
32392_s_at M57951
AB018303
U18321
AL049669
PTRF: polymerase I and transcript release factor
TACSTD2: tumor-associated calcium signal transducer 2
Human gene for very low density lipoprotein receptor, 5'flanking
Human mRNA for leukocyte common antigen (T200)
Human NADH:ubiquinone oxidoreductase subunit B13 mRNA, complete cds
H.sapiens mRNA for enamelysin
Human cell surface protein CD19 (CD19) gene, complete cds
Human DRPLA mRNA for ORF, complete cds
Human bilirubin UDP-glucuronosyltransferase isozyme 2 mRNA, complete cds
Homo sapiens mRNA for KIAA0760 protein, partial cds
Human ionizing radiation resistance conferring protein mRNA, complete cds
Human gene from PAC 612B18, chromosome 1
Table 4. Benchmark of the GASVM-II+GASVM with GASVMs, GASVM-II, and SVM.
Lung Data Set (Average; The Best) MLL Data Set (Average; The Best)
#Final Selected
Genes
Accuracy (%) #Final Selected
LOOCV Test Genes
Accuracy (%)
LOOCV Test
GASVM-II+GASVM
( Proposed Approach)
(2.1 ± 0.32;
2)
(100 ± 0;
100)
(94.16 ± 6.85;
98.66)
(6.5 ± 0.71;
6)
(100 ± 0;
100)
(92 ± 8.20;
100)
GASVM-II
GASVM (multi-objective)
GASVM (single-objective)
SVM classifier
(10 ± 0;
10)
(4,418.5 ± 50.19;
4,433)
(6,267.8 ± 56.34;
6,342)
(12,533 ± 0;
12,533)
(100 ± 0;
100)
(75.31 ± 0.99;
78.13)
(75 ± 0;
75)
(65.63 ± 0;
65.63)
(59.33 ± 29.32;
97.32)
(85.84 ± 3.97;
93.29)
(84.77 ± 2.53;
87.92)
(85.91 ± 0;
85.91)
(30 ± 0;
30)
(4,465.2 ± 18.34;
4,437)
(6,298.8 ± 51.51;
6,224)
(12,582 ± 0;
12,582)
(100 ± 0;
100)
(94.74 ± 0;
94.74)
(94.74 ± 0;
94.74)
(92.98 ± 0;
92.98)
(84.67 ± 6.33;
93.33)
(90 ± 3.51;
93.33)
(87.33 ± 2.11;
86.67)
(86.67 ± 0;
86.67)
Note: The best result shown in shaded cells.
Table 5. Benchmark of the GASVM-II+GASVM with previous works.
Author [Reference]
#Final Selected
Genes
Lung Data Set
Accuracy (%)
MLL Data Set
#Final Selected
LOOCV Test Genes
Accuracy (%)
LOOCV Test
Our work
Shah and Kusiak [10]
Gordon et al. [4]
Wang [2]
Li et al. [5]
Yang et al. [6]
Wang et al. [12]
Armstrong et al. [11]
-
-
-
-
-
2
8
4
100
100
-
99.45
-
-
-
-
98.66
98.66
97.32
-
97.99
-
-
-
-
-
56
6
-
-
39
100
100
-
-
98.61
-
97.2
100
95
100
-
-
-
100
-
-
-
Note: The best result shown in shaded cells. ‘–‘ means that result is not available.
Biologists can save much time since they can directly refer to the genes that have higher possibility to be useful for cancer diagnosis and drug target.
The benchmark of the proposed approach comparing with GASVM-II, GASVMs (singleobjective and multi-objective), and SVM are summarised in Table 4. The LOOCV accuracy, test accuracy, and number of selected genes are written in the parenthesis; the first and second parts are average result and showcased the best result, respectively. In the table, the GASVM-II+GASVM has outperformed
GASVM-II, GASVMs, and SVM in terms of LOOCV accuracy, test accuracy, and number of selected genes on average result and the best result. Generally,
GASVM-II was better than GASVMs and SVM on both data sets. A smaller size gene subset that is produced by the GASVM-II+GASVM results in higher classification accuracy. Hence, it may provide more insights into the molecular classification and diagnosis of cancers. This suggests that gene selection using the proposed approach is needed for cancer classification of microarray data.
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Table 5 displays benchmark of the best results of this work and previous related works on both data sets.
The best result of the proposed approach was obtained from the best subset in Table 2. Based on LOOCV and test accuracies of Lung data set, it was noted that the best results (100% LOOCV accuracy and 98.66% test accuracy) from this work were equal to the best result from current previous work [10]. However, this work only uses two genes to achieve the accuracies, whereas eight genes were used in the work of Shah and Kusiak
[10]. Hence, GASVM-II+GASVM outperformed the previous works. The first original work [4] achieved only 97.32% test accuracy by using 4 genes, while
97.99% of further previous work [5].
Similarly there was an increase in LOOCV (100%) and test accuracies (100%) for MLL data set as compared to the previous works [2][5][6][11][12].
Moreover, the number of selected genes was also lower than the previous works. Li et al. [5] work also achieved 100% test accuracy, but they did not provide the result for the LOOCV accuracy and the number of selected genes. Generally, this work has also outperformed the related previous works on MLL data set.
In this paper, an approach (GASVM-II+GASVM) using two hybrid methods is designed, developed, and analysed for gene selection and classification on two microrray data sets. This research found many combinations of gene subsets that were not equal number of genes have produced the different classification accuracy. This finding suggests that there are many irrelevant and noisy genes in microarray data and some of them act negatively on the acquired accuracy by the relevant genes. In addition, the performances of the GASVM-II+GASVM were superior to the GASVM-II, GASVMs, SVM, and other related previous works. This is due to the fact that
GASVM-II and GASVM are used into the two stages of the proposed approach. Focusing attention on a smaller subset of genes is useful not only because it produces good classification accuracy, but also since informative genes in this subset may provide insights into the mechanisms responsible for the cancer itself.
These informative genes that were identified by the
GASVM-II+GASVM are useful for cancer diagnosis.
Even though the proposed approach has classified tumours with higher accuracy, it is still cannot completely avoid over-fitting problem. Therefore, a hybrid of particle swarm optimisation technique and support vector machine (PSOSVM) is recently developed for gene selection and classification. In future research, an improved PSOSVM would be considered to solve the over-fitting problem.
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