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MCentridFS: a tool for identifying module biomarkers for multi-phenotypes from high-throughput data† Zhenshu Wen,a Wanwei Zhang,b Tao Zengb and Luonan Chen*bc Systematically identifying biomarkers, in particular, network biomarkers, from high-throughput data is an important and challenging task, and many methods for two-class comparison have been developed to exploit information of high-throughput data. However, as the high-throughput data with multi-phenotypes are available, there is a great need to develop effective multi-classification models. In this study, we proposed a novel approach, called MCentridFS (Multi-class Centroid Feature Selection), to systematically identify responsive modules or network biomarkers for classifying multi-phenotypes from high-throughput data. MCentridFS formulated the multi-classification model by network modules as a binary integer linear programming problem, which can be solved efficiently and effectively in an accurate manner. The approach is evaluated with respect to two diseases, i.e., multi-stages HCV-induced dysplasia and hepatocellular carcinoma and multi-tissues breast cancer, both of which demonstrated the high classification rate and the cross-validation rate of the approach. The computational results of the five-fold cross-validation of the two data show that MCentridFS outperforms the state-of-the-art multi-classification methods. We further verified the effectiveness of MCentridFS to characterize the multi-phenotype processes using module biomarkers by
Received 30th May 2014, Accepted 25th July 2014 DOI: 10.1039/c4mb00325j
two independent datasets. In addition, functional enrichment analysis revealed that the identified network modules are strongly related to the corresponding biological processes and pathways. All these results suggest that it can serve as a useful tool for module biomarker detection in multiple biological processes or multi-classification problems by exploring both big biological data and network information. The Matlab code
www.rsc.org/molecularbiosystems
for MCentridFS is freely available from http://www.sysbio.ac.cn/cb/chenlab/images/MCentridFS.rar.
Introduction As the high-throughput technologies, such as microarrays and the next generation sequencing technologies, mature and become prevalent in biological research, more and more datasets have been accumulated and available in the public databases, such as the NCBI Gene Expression Omnibus (GEO),1 the EBI ArrayExpress2 and the Stanford Microarray Database.3 As we know, the high-throughput data can simultaneously monitor thousands of genes and thus offer an unprecedented opportunity to fully characterize biological processes.4 However, how to extract the meaningful biomarkers from the huge amount of information is a significant challenge that scientists and clinicians often come across.5 a
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China Key Laboratory of Systems Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai 200031, China. E-mail: [email protected] c Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c4mb00325j b
2870 | Mol. BioSyst., 2014, 10, 2870--2875
Considerable efforts have been devoted to developing methods to identify individual gene biomarkers.6–8 However, it is well accepted that genes or proteins within a cell do not function alone but interact with each other to form networks or pathways so as to carry out biological functions.9–11 Therefore, pathway-based approaches have been developed to identify network biomarkers or even dynamical network biomarkers (DNBs) from a system perspective, which not only reliably characterize the diseases but also play a crucial role in revealing the essential biological mechanisms12–16 at the network level. However, most of the methods focusing on dissecting the biomarkers, are mainly for two-class samples, e.g., normal and disease samples, and just identify biomarkers one by one. Such limitations highlight the need to explore new approaches that can identify the network or module biomarkers simultaneously by classifying multiphenotypes.17,18 In this paper, we proposed a novel multi-classification model, called MCentridFS, to systematically identify network or module biomarkers from high-throughput data with multi-phenotypes. MCentridFS formulated the multi-classification model as a binary integer linear programming problem, which can be solved
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Paper Table 1
Molecular BioSystems Accuracy rates for HCC data and breast cancer data by MCentridFS
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Accuracy rate
Data
Classification accuracy rate using evaluated dataset (%)
Classification accuracy rate using independent dataset (%)
HCC data Breast cancer data
90.6719 87.8820
86.2530 91.7431
efficiently and effectively in an accurate manner. To evaluate the approach, we applied the approach to study two multi-class gene expression datasets, that is, multi-stage hepatocellular carcinoma (HCC)19 and multi-tissue breast cancer.20 The classification accuracy rates of our module biomarkers on the two datasets are 90.67% and 87.88%, respectively, and the five-fold cross-validation rates achieved are 84.07% and 82.83%, respectively. In addition, the classification accuracy rates on two independent datasets reach 86.25% and 91.74%, respectively (see Table 1). The results suggest that it can serve as a useful tool for module biomarker detection in multiple biological processes or multi-phenotypes by exploiting both large data and network information.
Materials and methods Fig. 1 illustrates the schematic flowchart of MCentridFS. The details of the procedure are described in the following subsections and Results. Datasets We evaluated the approach on two different cancers, that is, HCC and breast cancer, the data for which were downloaded from NCBI GEO database with accession number GSE676419
and GSE10797,20 respectively. The HCC gene expression dataset contains 75 tissue samples including the normal stage and four neoplastic stages (very early HCC to metastatic tumors), while, there are totally 66 tissue samples including 5 normal stromal samples, 5 normal epithelial samples, 28 stromal samples of breast cancer and 28 epithelial samples of breast cancer. The preprocessing of probe level data was the same as that used in original ref. 19 and 20. If there are multiple probes corresponding to the same gene, we adopted the averaged intensity of these probes to represent the expression value of the gene. Construction of a comprehensive human PPI network and the differential PPI network We applied a voting method to construct an ensemble protein– protein interaction (PPI) network by integrating five curated human PPI databases, i.e., HPRD,21 BioGrid,22 IntAct,23 MINT24 and Reactome.25 Only interactions that are found in at least three of these databases were selected. The comprehensive PPI network contains 7001 nodes with 19 188 edges.16 We combined the constructed PPI network and the multi-phenotype gene expression data to obtain the differential PPI network. Specifically, we first applied the ANOVA method26 to identify genes that were differentially expressed on one or more of the K clusters (phenotypes) relative to the others (p-value o 0.05). Then if one (or two) node(s) of an edge in the PPI network is differentially expressed, we kept the edge in the final differential PPI network. In this way, the differential PPI network is defined.27 Identification of responsive modules for a multi-classification model by a binary integer linear programming model First, we exploit gene expression data and the PPI network to construct the differential PPI network (the process is described
Fig. 1 Schematic flowchart of MCentridFS. First, we exploited expression data and the PPI network to construct a differential PPI network, which is used to cluster network modules. Second, the activity matrix of modules is obtained by defining the activity of each module Mij. Through introducing indicative variable xi and designing a classifier, we formulate the identification of responsive modules as an integer linear programming problem. Finally, by solving it, among all modules we identify module biomarkers, which characterize multiple phenotypes.
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in the above subsection). Second, we decompose the differential PPI network into modules by the Markov Clustering (MCL) algorithm28 and only consider those n modules with more than 3 edges. Third, normalized gene expression data are employed to define the activity of module Mi in the case of sample Sj as P zkj gk 2Mi ffiffiffiffiffiffiffiffiffi ; Mij ¼ p jMi j where |Mi| means the number of nodes in the module Mi and Zkj corresponds to the normalized expression value of gene gk in sample Sj. In this way, we obtain the activity matrix with element Mij representing the activity of module Mi in the case of sample Sj. The indicative function is defined to indicate whether a module is selected or not as follows: ( 1; Mi is selected xi ¼ 0; otherwise
defined similarly. Through simple calculation,14,16 we can further express the conditions of the classifier as C(x1, x2, , xn)t r 0,
where C is a matrix function of Mij with each element Cij representing the j-th module’s contribution to the i-th condition of the classifier. t means the transpose of the vector x. Note that the above system of inequalities is linear for (x1, x2, , xn). The terms on the left side of eqn (1) represent the classification ability of modules, i.e., the more negative they are, the more clearly the modules are able to distinguish multi-class samples. We aim not only to classify the multi-class samples based on the designed classifier, but also to identify the minimal number of modules in this classification process. Therefore, by combining the two objectives, we formulate the module-identification problem as the following binary integer linear programming: min
x1 ;x2 ;;xn
Then, we design a classifier to select responsive modules for a three-classification model (see Fig. 2) as an example:
JS S1J22 JS S2J22 o 0, JS S1J22 JS S3J22 o 0, JS S2J22 JS S1J22 o 0,
JS S2J22 JS S3J22 o 0, JS S3J22 JS S1J22 o 0, JS S3J22 JS S2J22 o 0,
n X
xj þ l
j¼1
s X n X
Cij xj
i¼1 j¼1
s:t: C ðx1 ; x2 ; ; xn Þt 0; n X
for S A S1,
(2)
xi 1;
(3)
i¼1
for S A S1,
n X
for S A S2,
xi ¼ 0; 1;
for S A S2, for S A S3, for S A S3,
xi m;
i¼1
(1)
where S, Si, and S1 (i = 1, 2, 3) represent the sample, the i-th cluster samples, the Euclidean center of the i-th cluster samples, respectively. For K-classification model, the classifier can be
i 2 f1; 2; ; ng
where s is the number of the samples and m is the threshold to restrict the number of the modules. The first term in the objective function implies that we intend to minimize the number of modules, while the second term is used to characterize the classification ability of these modules, i.e., we intend to maximize the classification ability of these modules (or minimize C(x1, x2, , xn)t). l is a positive penalty parameter to control the trade-off between the number of modules and the classification ability of these modules. Algorithm for solving the binary integer linear programming problem Clearly, the formulated problem is NP-hard. We turn to relax the constraints from binary variables xi A {0, 1} to continuous variables xi A [0, 1]. With such a relaxation, we can adopt a linear programming algorithm to solve the problem in an efficient manner. The experimental results show that such relaxation is both efficient and effective, that is, we almost always obtain integral solutions although it is not theoretically ensured. Here, we describe a rule to determine how to choose l and m.29 Given l and m, we define the classification accuracy rate of the identified modules from the constraints C(x1, x2, , xk)t r 0 as follows: CA ¼
Fig. 2 An illustration of the schematic diagram of the classifier corresponding to a three-classification model.
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m0 ; m
where m and m0 are the number of samples to be classified, and the number of samples that are correctly classified, respectively. We choose the corresponding l and m when CA attains the maximum value, and the resulted modules are regarded as the
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putative responsive modules accordingly. Specifically, we test l and m by certain intervals and choose l and m corresponding to the maximum CA.
Table 2 Comparisons of five-fold cross-validation rates of MCentridFS with other state-of-the-art multi-classification methods
Results
Data
Decision trees (%)
kNN (%)
svm (%)
McentridFS (%)
Overview of module prediction
HCC data Breast cancer data
62.13 53.50
78.72 74.14
83.76 76.79
84.07 82.83
The flowchart to identify responsive modules for a multiclassification model is illustrated in Fig. 1. First, we exploited the high-throughput data with multi-phenotypes and constructed a PPI network to obtain the differential PPI network (see Materials and methods). Second, we obtained n modules, which contain more than three genes, by decomposing the differential PPI network through the Markov Clustering algorithm.28 Then, following the flowchart in Fig. 1, we finally identified p responsive modules from all n modules by adjusting l and m (see Materials and methods), which maximizes the classification accuracy rate CA in the binary integer linear programming problem.
rate, and the results are showed in Table 2. From Table 2, the results suggested that MCentridFS outperforms decision trees, kNN, and svm. Additionally, the high five-fold cross-validation classification rates of the four multi-classification methods indicated that the features (modules) identified by MCentridFS are efficient. All these results showed that MCentridFS can serve as a useful tool for module biomarker detection in multiple biological processes or multi-classification problems.
Application to HCC data The HCC dataset consists of 21 327 genes and 75 tissue samples, including 10 normal samples and four neoplastic stages (i.e., 13 cirrhotic liver tissue samples, 17 high-grade dysplastic liver tissue samples, 18 early HCC samples, and 17 very advanced HCC samples) of HCC samples. We applied the formulated multi-classification model to the HCC data and identified 12 modules from 267 modules to discriminate the five-class samples. To evaluate the quality of the identified modules in terms of distinguishing the five-class samples, we exploited the module activity matrix of modules (modules vs. samples) to check whether a sample belongs to its class of samples, and we found that these modules achieved a high classification accuracy rate CA = 90.67% (see Table 1). Application to breast cancer data We further evaluated the approach on a breast cancer dataset. There are totally 66 tissue samples and 22 277 probes in the breast cancer dataset. The 66 samples consist of 5 normal stromal samples, 5 normal epithelial samples, 28 stromal samples of breast cancer and 28 epithelial samples of breast cancer. We applied our multi-classification model to the breast cancer data, and identified 31 modules from 406 modules to discriminate the four-class samples. Also, we exploited these modules to evaluate the quality of the identified modules in terms of distinguishing the four-class samples, which achieved a high classification accuracy rate CA = 87.88% (see Table 1). Comparisons with the state-of-the art multi-classification methods We conducted the five-fold cross-validation of HCC and breast cancer data to evaluate the performance of MCentridFS and compare the results with other state-of-the-art multi-classification methods, such as decision trees,32 k-nearest neighbors (kNN),33 and support vector machines (svm).34 For each data and method, we performed five-fold cross-validation 100 times by exploiting 12 selected features and took the average accuracy
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Methods
Functional enrichment analysis of the identified modules We further analyzed the functional enrichment of the identified modules through a hypergeometric test using g:Profiler.35 The representative enriched GO terms in each module are presented in Tables S1 and S2 (ESI†) for HCC data and breast cancer data, respectively. From Tables S1 and S2 (ESI†), we found that, the identified modules are mainly enriched in the processes, which are highly correlated to the hallmarks of cancer and contribute to the major progression of cancer,36,37 such as the immune process, signaling pathways, cell communication, apoptosis, inflammatory process, etc. In addition, the specific processes, i.e., hepatic immune response, hepatitis B, and heparin binding, are also found in the progression of HCC. What’s more, the inflammatory process and immune response, which play an important role during the breast cancer progression,38 are also enriched in the identified modules. Validation of the identified modules using other independent datasets We further evaluated the effectiveness of the identified modules using gene expression data from other two independent datasets. For the HCC data, GSE50579,30 including 70 HCC samples and 10 normal samples, was used to verify the effectiveness of the 12 identified modules, and it achieved a 86.25% accuracy rate (see Table 1). Similarly, we obtained a 91.74% accuracy rate (see Table 1) for the breast cancer dataset GSE42568,31 which includes 104 breast cancer samples and 17 normal samples. These independent results provided additional evidence that the module-based biomarkers identified in this study could be used for disease analysis and prediction, and further suggested the effectiveness of MCentridFS.
Discussion and conclusion Our method is novel in several aspects compared to previous methods. First, in contrast to the conventional methods, our method is able to reveal responsive relations between module biomarkers and multiple phenotypes by integrating
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gene expression data and the PPI network. Second, technically, instead of those heuristic methods, which select biomarkers one by one, our method can identify module biomarkers in an accurate manner by formulating a binary integer linear programming problem, which can be solved efficiently and effectively, although the method requires more settings and parameters than some simple methods. Third, our method achieves high classification accuracy and a positive cross-validation rate for multi-class comparison by exploiting both high-throughput data and network information. In this paper, we focus on developing a computational approach, i.e., MCentridFS, to identify network or module biomarkers for classifying multi-phenotypes from high-throughput data, and the application of the approach to two datasets achieved promising classification accuracy rates (almost 90%) and cross-validation rates (84% and 82%), which demonstrates the effectiveness of MCentridFS. The results of the five-fold cross-validation classification rates of MCentridFS outperform other multi-classification methods, which also indicates that MCentridFS can serve as a useful tool for module biomarker detection in multiple biological processes or multi-classification problems. However, several important future topics remain to be studied. Our method may include more available information, such as copy number aberrations (CNA), and epigenomic data (e.g., DNA methylation data), into the multi-classification model,16 which should be studied further. Besides, we know that the five stages of the HCC data are progressive step by step, therefore, our multi-classification model may be improved to obtain more refined results to consider such an ordinal information. In addition, we may extend our framework to detect dynamical network biomarkers (DNBs) for early diagnosis of complex diseases,15 which can elucidate more details of cancer pathogenesis. Finally, our approach is useful to identify new oncogenes and cancer suppressor genes of various cancers by further analysis of the identified module biomarkers.16 In contrast to the traditional molecular biomarkers or node biomarkers, detecting edge biomarkers39,40 is also a hot topic. As a future work, our method can be extended to identify the edge biomarkers for classifying biological samples. In addition to the complex diseases analyzed in this manuscript, our method can be used to study phenotype evolutions of general dynamical biological processes in a similar manner.
Funding This research was supported by the foundation of Huaqiao University (No. 12BS223), and Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-PY119). The work was also supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB13040700), National Program on Key Basic Research Project (No. 2014CB910504), the National Natural Science Foundation of China (No. 61134013, 91029301, 91130033, 31200987), the Knowledge Innovation Program of CAS (No. KSCX2EW-R-01, 2013KIP218), and 863 project (No. 2012AA020406).
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Competing interests None.
Contributors ZSW wrote the paper, designed and performed the experiments, and analyzed the data. WWZ and TZ helped perform the experiments. TZ helped software preparation and publication. LNC conceived the experiments and contributed materials.
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MCentridFS: a tool for identifying module biomarkers for multi-phenotypes from high-throughput data† Zhenshu Wen,a Wanwei Zhang,b Tao Zengb and Luonan Chen*bc Systematically identifying biomarkers, in particular, network biomarkers, from high-throughput data is an important and challenging task, and many methods for two-class comparison have been developed to exploit information of high-throughput data. However, as the high-throughput data with multi-phenotypes are available, there is a great need to develop effective multi-classification models. In this study, we proposed a novel approach, called MCentridFS (Multi-class Centroid Feature Selection), to systematically identify responsive modules or network biomarkers for classifying multi-phenotypes from high-throughput data. MCentridFS formulated the multi-classification model by network modules as a binary integer linear programming problem, which can be solved efficiently and effectively in an accurate manner. The approach is evaluated with respect to two diseases, i.e., multi-stages HCV-induced dysplasia and hepatocellular carcinoma and multi-tissues breast cancer, both of which demonstrated the high classification rate and the cross-validation rate of the approach. The computational results of the five-fold cross-validation of the two data show that MCentridFS outperforms the state-of-the-art multi-classification methods. We further verified the effectiveness of MCentridFS to characterize the multi-phenotype processes using module biomarkers by
Received 30th May 2014, Accepted 25th July 2014 DOI: 10.1039/c4mb00325j
two independent datasets. In addition, functional enrichment analysis revealed that the identified network modules are strongly related to the corresponding biological processes and pathways. All these results suggest that it can serve as a useful tool for module biomarker detection in multiple biological processes or multi-classification problems by exploring both big biological data and network information. The Matlab code
www.rsc.org/molecularbiosystems
for MCentridFS is freely available from http://www.sysbio.ac.cn/cb/chenlab/images/MCentridFS.rar.
Introduction As the high-throughput technologies, such as microarrays and the next generation sequencing technologies, mature and become prevalent in biological research, more and more datasets have been accumulated and available in the public databases, such as the NCBI Gene Expression Omnibus (GEO),1 the EBI ArrayExpress2 and the Stanford Microarray Database.3 As we know, the high-throughput data can simultaneously monitor thousands of genes and thus offer an unprecedented opportunity to fully characterize biological processes.4 However, how to extract the meaningful biomarkers from the huge amount of information is a significant challenge that scientists and clinicians often come across.5 a
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China Key Laboratory of Systems Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai 200031, China. E-mail: [email protected] c Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c4mb00325j b
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Considerable efforts have been devoted to developing methods to identify individual gene biomarkers.6–8 However, it is well accepted that genes or proteins within a cell do not function alone but interact with each other to form networks or pathways so as to carry out biological functions.9–11 Therefore, pathway-based approaches have been developed to identify network biomarkers or even dynamical network biomarkers (DNBs) from a system perspective, which not only reliably characterize the diseases but also play a crucial role in revealing the essential biological mechanisms12–16 at the network level. However, most of the methods focusing on dissecting the biomarkers, are mainly for two-class samples, e.g., normal and disease samples, and just identify biomarkers one by one. Such limitations highlight the need to explore new approaches that can identify the network or module biomarkers simultaneously by classifying multiphenotypes.17,18 In this paper, we proposed a novel multi-classification model, called MCentridFS, to systematically identify network or module biomarkers from high-throughput data with multi-phenotypes. MCentridFS formulated the multi-classification model as a binary integer linear programming problem, which can be solved
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Paper Table 1
Molecular BioSystems Accuracy rates for HCC data and breast cancer data by MCentridFS
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Accuracy rate
Data
Classification accuracy rate using evaluated dataset (%)
Classification accuracy rate using independent dataset (%)
HCC data Breast cancer data
90.6719 87.8820
86.2530 91.7431
efficiently and effectively in an accurate manner. To evaluate the approach, we applied the approach to study two multi-class gene expression datasets, that is, multi-stage hepatocellular carcinoma (HCC)19 and multi-tissue breast cancer.20 The classification accuracy rates of our module biomarkers on the two datasets are 90.67% and 87.88%, respectively, and the five-fold cross-validation rates achieved are 84.07% and 82.83%, respectively. In addition, the classification accuracy rates on two independent datasets reach 86.25% and 91.74%, respectively (see Table 1). The results suggest that it can serve as a useful tool for module biomarker detection in multiple biological processes or multi-phenotypes by exploiting both large data and network information.
Materials and methods Fig. 1 illustrates the schematic flowchart of MCentridFS. The details of the procedure are described in the following subsections and Results. Datasets We evaluated the approach on two different cancers, that is, HCC and breast cancer, the data for which were downloaded from NCBI GEO database with accession number GSE676419
and GSE10797,20 respectively. The HCC gene expression dataset contains 75 tissue samples including the normal stage and four neoplastic stages (very early HCC to metastatic tumors), while, there are totally 66 tissue samples including 5 normal stromal samples, 5 normal epithelial samples, 28 stromal samples of breast cancer and 28 epithelial samples of breast cancer. The preprocessing of probe level data was the same as that used in original ref. 19 and 20. If there are multiple probes corresponding to the same gene, we adopted the averaged intensity of these probes to represent the expression value of the gene. Construction of a comprehensive human PPI network and the differential PPI network We applied a voting method to construct an ensemble protein– protein interaction (PPI) network by integrating five curated human PPI databases, i.e., HPRD,21 BioGrid,22 IntAct,23 MINT24 and Reactome.25 Only interactions that are found in at least three of these databases were selected. The comprehensive PPI network contains 7001 nodes with 19 188 edges.16 We combined the constructed PPI network and the multi-phenotype gene expression data to obtain the differential PPI network. Specifically, we first applied the ANOVA method26 to identify genes that were differentially expressed on one or more of the K clusters (phenotypes) relative to the others (p-value o 0.05). Then if one (or two) node(s) of an edge in the PPI network is differentially expressed, we kept the edge in the final differential PPI network. In this way, the differential PPI network is defined.27 Identification of responsive modules for a multi-classification model by a binary integer linear programming model First, we exploit gene expression data and the PPI network to construct the differential PPI network (the process is described
Fig. 1 Schematic flowchart of MCentridFS. First, we exploited expression data and the PPI network to construct a differential PPI network, which is used to cluster network modules. Second, the activity matrix of modules is obtained by defining the activity of each module Mij. Through introducing indicative variable xi and designing a classifier, we formulate the identification of responsive modules as an integer linear programming problem. Finally, by solving it, among all modules we identify module biomarkers, which characterize multiple phenotypes.
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Paper
in the above subsection). Second, we decompose the differential PPI network into modules by the Markov Clustering (MCL) algorithm28 and only consider those n modules with more than 3 edges. Third, normalized gene expression data are employed to define the activity of module Mi in the case of sample Sj as P zkj gk 2Mi ffiffiffiffiffiffiffiffiffi ; Mij ¼ p jMi j where |Mi| means the number of nodes in the module Mi and Zkj corresponds to the normalized expression value of gene gk in sample Sj. In this way, we obtain the activity matrix with element Mij representing the activity of module Mi in the case of sample Sj. The indicative function is defined to indicate whether a module is selected or not as follows: ( 1; Mi is selected xi ¼ 0; otherwise
defined similarly. Through simple calculation,14,16 we can further express the conditions of the classifier as C(x1, x2, , xn)t r 0,
where C is a matrix function of Mij with each element Cij representing the j-th module’s contribution to the i-th condition of the classifier. t means the transpose of the vector x. Note that the above system of inequalities is linear for (x1, x2, , xn). The terms on the left side of eqn (1) represent the classification ability of modules, i.e., the more negative they are, the more clearly the modules are able to distinguish multi-class samples. We aim not only to classify the multi-class samples based on the designed classifier, but also to identify the minimal number of modules in this classification process. Therefore, by combining the two objectives, we formulate the module-identification problem as the following binary integer linear programming: min
x1 ;x2 ;;xn
Then, we design a classifier to select responsive modules for a three-classification model (see Fig. 2) as an example:
JS S1J22 JS S2J22 o 0, JS S1J22 JS S3J22 o 0, JS S2J22 JS S1J22 o 0,
JS S2J22 JS S3J22 o 0, JS S3J22 JS S1J22 o 0, JS S3J22 JS S2J22 o 0,
n X
xj þ l
j¼1
s X n X
Cij xj
i¼1 j¼1
s:t: C ðx1 ; x2 ; ; xn Þt 0; n X
for S A S1,
(2)
xi 1;
(3)
i¼1
for S A S1,
n X
for S A S2,
xi ¼ 0; 1;
for S A S2, for S A S3, for S A S3,
xi m;
i¼1
(1)
where S, Si, and S1 (i = 1, 2, 3) represent the sample, the i-th cluster samples, the Euclidean center of the i-th cluster samples, respectively. For K-classification model, the classifier can be
i 2 f1; 2; ; ng
where s is the number of the samples and m is the threshold to restrict the number of the modules. The first term in the objective function implies that we intend to minimize the number of modules, while the second term is used to characterize the classification ability of these modules, i.e., we intend to maximize the classification ability of these modules (or minimize C(x1, x2, , xn)t). l is a positive penalty parameter to control the trade-off between the number of modules and the classification ability of these modules. Algorithm for solving the binary integer linear programming problem Clearly, the formulated problem is NP-hard. We turn to relax the constraints from binary variables xi A {0, 1} to continuous variables xi A [0, 1]. With such a relaxation, we can adopt a linear programming algorithm to solve the problem in an efficient manner. The experimental results show that such relaxation is both efficient and effective, that is, we almost always obtain integral solutions although it is not theoretically ensured. Here, we describe a rule to determine how to choose l and m.29 Given l and m, we define the classification accuracy rate of the identified modules from the constraints C(x1, x2, , xk)t r 0 as follows: CA ¼
Fig. 2 An illustration of the schematic diagram of the classifier corresponding to a three-classification model.
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m0 ; m
where m and m0 are the number of samples to be classified, and the number of samples that are correctly classified, respectively. We choose the corresponding l and m when CA attains the maximum value, and the resulted modules are regarded as the
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putative responsive modules accordingly. Specifically, we test l and m by certain intervals and choose l and m corresponding to the maximum CA.
Table 2 Comparisons of five-fold cross-validation rates of MCentridFS with other state-of-the-art multi-classification methods
Results
Data
Decision trees (%)
kNN (%)
svm (%)
McentridFS (%)
Overview of module prediction
HCC data Breast cancer data
62.13 53.50
78.72 74.14
83.76 76.79
84.07 82.83
The flowchart to identify responsive modules for a multiclassification model is illustrated in Fig. 1. First, we exploited the high-throughput data with multi-phenotypes and constructed a PPI network to obtain the differential PPI network (see Materials and methods). Second, we obtained n modules, which contain more than three genes, by decomposing the differential PPI network through the Markov Clustering algorithm.28 Then, following the flowchart in Fig. 1, we finally identified p responsive modules from all n modules by adjusting l and m (see Materials and methods), which maximizes the classification accuracy rate CA in the binary integer linear programming problem.
rate, and the results are showed in Table 2. From Table 2, the results suggested that MCentridFS outperforms decision trees, kNN, and svm. Additionally, the high five-fold cross-validation classification rates of the four multi-classification methods indicated that the features (modules) identified by MCentridFS are efficient. All these results showed that MCentridFS can serve as a useful tool for module biomarker detection in multiple biological processes or multi-classification problems.
Application to HCC data The HCC dataset consists of 21 327 genes and 75 tissue samples, including 10 normal samples and four neoplastic stages (i.e., 13 cirrhotic liver tissue samples, 17 high-grade dysplastic liver tissue samples, 18 early HCC samples, and 17 very advanced HCC samples) of HCC samples. We applied the formulated multi-classification model to the HCC data and identified 12 modules from 267 modules to discriminate the five-class samples. To evaluate the quality of the identified modules in terms of distinguishing the five-class samples, we exploited the module activity matrix of modules (modules vs. samples) to check whether a sample belongs to its class of samples, and we found that these modules achieved a high classification accuracy rate CA = 90.67% (see Table 1). Application to breast cancer data We further evaluated the approach on a breast cancer dataset. There are totally 66 tissue samples and 22 277 probes in the breast cancer dataset. The 66 samples consist of 5 normal stromal samples, 5 normal epithelial samples, 28 stromal samples of breast cancer and 28 epithelial samples of breast cancer. We applied our multi-classification model to the breast cancer data, and identified 31 modules from 406 modules to discriminate the four-class samples. Also, we exploited these modules to evaluate the quality of the identified modules in terms of distinguishing the four-class samples, which achieved a high classification accuracy rate CA = 87.88% (see Table 1). Comparisons with the state-of-the art multi-classification methods We conducted the five-fold cross-validation of HCC and breast cancer data to evaluate the performance of MCentridFS and compare the results with other state-of-the-art multi-classification methods, such as decision trees,32 k-nearest neighbors (kNN),33 and support vector machines (svm).34 For each data and method, we performed five-fold cross-validation 100 times by exploiting 12 selected features and took the average accuracy
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Methods
Functional enrichment analysis of the identified modules We further analyzed the functional enrichment of the identified modules through a hypergeometric test using g:Profiler.35 The representative enriched GO terms in each module are presented in Tables S1 and S2 (ESI†) for HCC data and breast cancer data, respectively. From Tables S1 and S2 (ESI†), we found that, the identified modules are mainly enriched in the processes, which are highly correlated to the hallmarks of cancer and contribute to the major progression of cancer,36,37 such as the immune process, signaling pathways, cell communication, apoptosis, inflammatory process, etc. In addition, the specific processes, i.e., hepatic immune response, hepatitis B, and heparin binding, are also found in the progression of HCC. What’s more, the inflammatory process and immune response, which play an important role during the breast cancer progression,38 are also enriched in the identified modules. Validation of the identified modules using other independent datasets We further evaluated the effectiveness of the identified modules using gene expression data from other two independent datasets. For the HCC data, GSE50579,30 including 70 HCC samples and 10 normal samples, was used to verify the effectiveness of the 12 identified modules, and it achieved a 86.25% accuracy rate (see Table 1). Similarly, we obtained a 91.74% accuracy rate (see Table 1) for the breast cancer dataset GSE42568,31 which includes 104 breast cancer samples and 17 normal samples. These independent results provided additional evidence that the module-based biomarkers identified in this study could be used for disease analysis and prediction, and further suggested the effectiveness of MCentridFS.
Discussion and conclusion Our method is novel in several aspects compared to previous methods. First, in contrast to the conventional methods, our method is able to reveal responsive relations between module biomarkers and multiple phenotypes by integrating
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gene expression data and the PPI network. Second, technically, instead of those heuristic methods, which select biomarkers one by one, our method can identify module biomarkers in an accurate manner by formulating a binary integer linear programming problem, which can be solved efficiently and effectively, although the method requires more settings and parameters than some simple methods. Third, our method achieves high classification accuracy and a positive cross-validation rate for multi-class comparison by exploiting both high-throughput data and network information. In this paper, we focus on developing a computational approach, i.e., MCentridFS, to identify network or module biomarkers for classifying multi-phenotypes from high-throughput data, and the application of the approach to two datasets achieved promising classification accuracy rates (almost 90%) and cross-validation rates (84% and 82%), which demonstrates the effectiveness of MCentridFS. The results of the five-fold cross-validation classification rates of MCentridFS outperform other multi-classification methods, which also indicates that MCentridFS can serve as a useful tool for module biomarker detection in multiple biological processes or multi-classification problems. However, several important future topics remain to be studied. Our method may include more available information, such as copy number aberrations (CNA), and epigenomic data (e.g., DNA methylation data), into the multi-classification model,16 which should be studied further. Besides, we know that the five stages of the HCC data are progressive step by step, therefore, our multi-classification model may be improved to obtain more refined results to consider such an ordinal information. In addition, we may extend our framework to detect dynamical network biomarkers (DNBs) for early diagnosis of complex diseases,15 which can elucidate more details of cancer pathogenesis. Finally, our approach is useful to identify new oncogenes and cancer suppressor genes of various cancers by further analysis of the identified module biomarkers.16 In contrast to the traditional molecular biomarkers or node biomarkers, detecting edge biomarkers39,40 is also a hot topic. As a future work, our method can be extended to identify the edge biomarkers for classifying biological samples. In addition to the complex diseases analyzed in this manuscript, our method can be used to study phenotype evolutions of general dynamical biological processes in a similar manner.
Funding This research was supported by the foundation of Huaqiao University (No. 12BS223), and Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-PY119). The work was also supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB13040700), National Program on Key Basic Research Project (No. 2014CB910504), the National Natural Science Foundation of China (No. 61134013, 91029301, 91130033, 31200987), the Knowledge Innovation Program of CAS (No. KSCX2EW-R-01, 2013KIP218), and 863 project (No. 2012AA020406).
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Competing interests None.
Contributors ZSW wrote the paper, designed and performed the experiments, and analyzed the data. WWZ and TZ helped perform the experiments. TZ helped software preparation and publication. LNC conceived the experiments and contributed materials.
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