Abstract
In the clinical practice, many diseases such as glioblastoma, leukemia, diabetes, and prostates have multiple subtypes. Classifying subtypes accurately using genomic data will provide individualized treatments to targetspecific disease subtypes. However, it is often difficult to obtain satisfactory classification accuracy using only one type of data, because the subtypes of a disease can exhibit similar patterns in one data type. Fortunately, multiple types of genomic data are often available due to the rapid development of genomic techniques. This raises the question on whether the classification performance can significantly be improved by combining multiple types of genomic data. In this article, we classified four subtypes of glioblastoma multiforme (GBM) with multiple types of genomewide data (e.g., mRNA and miRNA expression) from The Cancer Genome Atlas (TCGA) project. We proposed a multiclass compressed sensingbased detector (MCSD) for this study. The MCSD was trained with data from TCGA and then applied to subtype GBM patients using an independent testing data. We performed the classification on the same patient subjects with three data types, i.e., miRNA expression data, mRNA (or gene expression) data, and their combinations. The classification accuracy is 69.1% with the miRNA expression data, 52.7% with mRNA expression data, and 90.9% with the combination of both mRNA and miRNA expression data. In addition, some biomarkers identified by the integrated approaches have been confirmed with results from the published literatures. These results indicate that the combined analysis can significantly improve the accuracy of classifying GBM subtypes and identify potential biomarkers for disease diagnosis.
Introduction
Many diseases including cancers have multiple subtypes. For example, leukemia has four main categories: acute lymphoblastic leukemia (ALL), acute myelogenous leukemia, chronic lymphocytic leukemia, and chronic myelogenous leukemia. Each of these categories can be further divided into different subtypes [1]; for example, ALL can be further subtyped into six types [2]. Glioma has four subtypes, including oligodendroglioma, anaplastic oligodendroglioma, anaplastic astrocytoma, and glioblastoma multiforme (GBM) [3]. Prostate cancer has three major subtypes [4]. An accurate and effective classification of those subtypes based on genomic data will result in personalized treatments of the cancer in terms of a particular subtype. In this article, we are interested in the subtyping of GBM, which is a kind of glioma and is the most common form of malignant brain cancer in adults [5]. There is an increasing interest in classifying multiple subtypes of GBM based on its genomic measurements. Most of the existing works are based on gene expression data only. Benjamin et al. [6] classified two types of GBM in adults and found that the genes EGFR and TP53 were important in discriminating the two subtypes. Nutt et al. [7] built a knearest neighbor model with 20 features to classify 28 glioblastomas and 22 anaplastic oligodendrogliomas and found that the class distinctions were significantly associated with survival outcome (p = 0.05). Noushmehr et al. [8] separated a subset of samples in GBM from The Cancer Genome Atlas (TCGA) project, which displayed concerted hypermethylation at a large number of loci. The datasets we used to subtype GBM are also from TCGA. The subtypes of GBM samples in TCGA includes: proneural, neural, classical, and mesenchymal [9]. The GBM data we have tested include both miRNA expression and mRNA expression data. The miRNAs, also called microRNAs, are short noncoding RNA molecules that were recently found in all eukaryotic cells except fungi, algae, and marine plants. The human genome may contain over 1,000 miRNAs [10]. Aberrant expressions of miRNAs have been found to be related to many diseases, including cancers [11, 12]. They play an essential role in tissue differentiation during normal development and tumorigenesis [13].
In the last decade, the development of genomic techniques enables the availability of multiple data types on the same patient, such as mRNA or gene expression, SNP, miRNA expression, and copy number variation data. It is well recognized that a more comprehensive analysis result could be obtained based on integrating multiple types of genomic data than using an individual dataset. Soneson et al. [14] investigated the correlation between gene expression and copy number alterations using canonical correlation analysis for leukemia data. A webbased platform, called Magellan, was developed for the integrated analysis of DNA copy number and expression data in ovarian cancer [15], which found significant correlation between gene expression and patient survival. Troyanskaya et al. [16] developed a Bayesian framework to combine heterogeneous data sources to predict gene function with improved accuracy. A kernelbased statistical learning algorithm was also proposed in the combined analysis of multiple genomewide datasets [17]. In this article, we propose a novel classifier based on the compressed sensing (CS) theory that we have been working with.
The CS technique enables compact storage and rapid transmission of large amounts of information. The technique can be used to extract significant statistical information from highdimensional datasets [18]. The CS technology has been proven to be a powerful tool in the signal processing and statistics fields. It demonstrates that a compressible signal can be recovered from far fewer samples than that needed by the Nyquist sampling theorem [19]. Our recent work used a CSbased detector (CSD) for subtyping leukemia with gene expression data [20]. The CSD achieved high classification accuracies, with 97.4% evaluated with crossvalidation and 94.3% evaluated with an independent dataset. The CSD showed better performance in subtyping two types of leukemia compared to some traditional classifiers such as the support vector machine (SVM), indicating the advantage of the CSD in analyzing highdimensional genomic data. In this article, we extended the CSD to multiple data types and proposed a detector called MCSD. In particular, we applied the MCSD to the subtyping of four types of GBM by combining miRNA expression and mRNA expression data. We present a novel combined analysis method based on the CS and demonstrate that the classification performance can significantly be improved in subtyping four types of GBM, with both miRNA expression and mRNA expression data.
Methods and materials
Data collection
The GBM data used in this study are publicly available from the website of TCGA [21]. The patients in the dataset can be classified into four subtypes, i.e., proneural, neural, classical, and mesenchymal [9]. The genomic data include miRNA expression (1,510 probes) and mRNA expression data (22,277 probes). We randomly divided the data (including 115 patients with both miRNA and mRNA expression data) into two sets: training and testing datasets. The total number of patients in the training dataset was 60 with 15 patients in each group. The testing dataset had 55 patients, with 17 proneural, 3 neural, 17 classical, and 18 mesenchymal subtypes (as listed in Table 1). The same number of patients in each subtype for training data was used for reducing the bias in the model building. Meanwhile, the numbers of patients in training and testing were approximately the same.
For multiple types of genomic data (e.g., miRNA expression data, mRNA expression data, etc.), we used x_{1i} to denote the data vector for the i th sample in data 1 (e.g., miRNA expression), x_{2i} to denote the data vector for the i th sample in data 2 (e.g., mRNA expression), and x_{ ni } to denote the data vector for the i th sample in data n. The combined data for the i th sample is ${x}_{i}={\left({x}_{1}\begin{array}{c}\hfill T\hfill \\ \hfill i\hfill \end{array},{x}_{2}\begin{array}{c}\hfill T\hfill \\ \hfill i\hfill \end{array},\dots ,{x}_{n}\begin{array}{c}\hfill T\hfill \\ \hfill i\hfill \end{array}\right)}^{T}$, which is arranged in a cascaded manner.
MCSD
Bayesian classifier
To classify a given observation y to one of n classes, we define the actual class (“ground truth”) to which it belongs as g; the class to which it is assigned (“decision”) as d. The n classes are defined as: π_{1,}π_{2},…,π_{ n }. Let U_{ πi } (y ,g) be the utility of assigning y, actually from π_{ g }, to π_{ i }. The “utility” is negative relevant to the Bayes Risk (BR) [22], which is the minimum classification error. Thus, we make: U = 1BR. The twoclass onedimensional BR (shaded area in Figure 1) can be calculated by
where y_{0} is the decision boundary, P_{1}P_{2} are the prior probabilities and P_{1}(y),P_{2}(y) are the conditional probability density functions of the two classes, respectively (shown in Figure 1).
Let us extend the BR to n classes and N dimensions. Then Equation (1) can be rewritten as
where P_{ j } is the prior probability of a given subject belonging to the class π_{ j }, j = 1,…,n; P_{ j }(y) is the conditional probability density function of the class π_{ j }, and Ω_{ i } is the Bayesian decision region for class π_{ i }[23].
For multiclass classification, an ideal detector should yield
where
where P(d = π_{ i }g = π_{ j }) denotes the probability of assigning a given observation y, actually belonging to π_{ j }, to π_{ i. }δ_{ ij } is the Kronecker’s delta.
According to the ideal observer decision theory [22], a decision is selected only if its expected utility is greater than the expected utility of any others. Thus, for any given observation y, we decide d = π_{ i } iff
From Equation (2) and the relationship of utility and BR, we know “utility” is a number that can be calculated. We denote that number as U_{ij} to express the utility of assigning a given observation y, actually belonging to π_{ j }, to π_{ i }. The inequality (4) can be written as
We apply Bayes’ rule
where P_{ y }(yg = π_{ k }), k = 1,…,n, is the probability density function for the signal observations. According to Inequality (5), we decide d = π_{ i } iff
That is known as maximum likelihood estimation. Specifically, the class label of the testing sample y is given by
If we assume π_{1}, π_{2},…,π_{ n } have the same prior probability, i.e., $P\left(g={\pi}_{k}\right)=\frac{1}{n}$. The detector (8) can be rewritten as
The calculation of the utility is shown in the Additional file 1.
Dimension reduction using CS
To reduce the dimension of original sample, we design a projection (sparse) matrix Φ , called compress matrix. The generation of the compress matrix can be formulated as a sparse representation problem as in Equation (10)
where $\mathit{Y}=\left\{{\mathit{y}}_{i}\right\}\in {\mathbb{R}}^{M\times c}$ is the projected sample, M is the dimension of the sample after the projection, y_{ i } is the i th column in the compressed signal, c is the total number of columns in the compressed signal, $\mathit{S}=\left\{{\mathit{s}}_{i}\right\}\in {\mathbb{R}}^{N\times c}$ is the original signal, and N is the dimension of the original signal and N >> M. The matrix $\mathit{\Phi}\in {\mathbb{R}}^{M\times N}$ is a sparse matrix, with most of the entries ‘0’s. The compress matrix Φ projects the original sample S to a much smaller dimensional signal Y. The original sample may contain redundancy; through this projection, the original sample can significantly be compressed and compactly represented, which usually lead to better classification performance. Suppose we have n groups, with c_{1} training samples in group 1, c_{2} training samples in group 2, and so forth, c_{ n } training samples in group n, and c = c_{1} + c_{2} + ··· + c_{ n } for $\mathit{S}=\left[{\mathit{s}}_{1,}{\mathit{s}}_{2},\dots ,{\mathit{s}}_{c}\right]\in {\mathbb{R}}^{N\times c}$ and $\mathit{Y}=\left[{\mathit{y}}_{1,}{\mathit{y}}_{2},\dots ,{\mathit{y}}_{c}\right]\in {\mathbb{R}}^{M\times c}$. The transpose of Equation (10) is
Let ${\left({\mathit{\Phi}}^{T}\right)}_{\mathrm{j}}\in {\mathbb{R}}^{N\times 1}$ denote the j th column of Φ^{T}, and ${\left({\mathit{Y}}^{T}\right)}_{\mathrm{j}}\in {\mathbb{R}}^{c\times 1}$ denote the j th column of Y^{T}, where j = 1, 2,…,M. Then Equation (11) can be rewritten as
The linear system given by (12) is an underdetermined system, which can be solved by using l1 norm minimization algorithm such as Homotopy method, or the least angle regression method [24]. The l1 norm optimization problem reads
subject to
where ‖(Φ^{T})_{ j }‖_{1} is the l1 norm of the vector (Φ^{T})_{ j }, i.e., the sum of the absolute values of entries in vector (Φ^{T})_{ j }. Obviously, the compress matrix Φ projects the original signal ${\mathit{s}}_{i}\in {\mathbb{R}}^{N\times 1}$ to a much smaller dimensional signal $\mathit{\Phi}{\mathit{s}}_{i}\in {\mathbb{R}}^{M\times 1}$. Instead of dealing with the original signal, we only use $\mathit{\Phi}{\mathit{s}}_{i}\in {\mathbb{R}}^{M\times 1}$ and $\mathit{\Phi}{\mathit{\Phi}}^{T}\in {\mathbb{R}}^{M\times M}$ in the subtyping procedure, leading to a fast classification.
Determination of feature vector
We need to select significant features to represent the original data before we classify the data. For each sample, we extracted five feature characteristics [20]: the mean and the standard deviation of each group’s standard deviation (MeanStd, StdStd), the standard deviation of the means of all the groups (StdMean), and the mean and standard deviation of Pearson’s linear correlation coefficient (MeanCorr, StdCorr) between the samples and their class label vector. Therefore, for the i th sample, we have a fivedimensional feature vector as follows:
where i = 1,2,…,N, and N is the number of samples. Each element in the vector V_{ i } has been normalized by its overall maximum value so that its value is between 0 and 1, i.e., V_{ i } ∈ [0, 1]. A number of M informative features were selected by setting the threshold values of V_{ i }. If a feature is informative or significant, we expect that the values from different patients within the same subtype are similar while the differences among different subtypes are relatively large. In addition, it is easy to understand that, if the correlation between the feature vector and the class label is high, the feature vector can serve as a significant biomarker to distinguish the subtypes. According to the above analysis, matrix Y in Equation (10) is built by those features with low MeanStd, StdStd, StdCorr while high StdMean, MeanCorr, which are significant for the classification.
Classifier based on CS
In this particular study of subtyping four types of GBM with miRNA expression and mRNA expression data, we make a hypothesis that the data follow a normal distribution. In other words, the probability density function for the data is
where $\widehat{\mathit{y}}\in {\mathbb{R}}^{N}$ is a given observation; $\mathit{s}\in {\mathbb{R}}^{N}$ is the mean of a sample; and σ is the standard deviation of the data.
After compressing the original sample, the probability density function (Equation 14) is still Gaussian but with different mean and standard deviation given by [18]
where $\widehat{\mathit{y}}\in {\mathbb{R}}^{M}$ is a compressed observation; $\mathit{s}\in {\mathbb{R}}^{N}$ is a known signal and Φ is the compress matrix. The MCSD used in this study is constructed by substituting Equation (15) into Equation (9) for maximum likelihood estimation.
The classification algorithm is described as below.

1.
Inputs: training dataset and testing dataset

2.
Normalize the rows of the training and the testing datasets to the range of [0,1]

3.
Select informative features according to the feature selection criteria

4.
Calculate compress matrix $\mathit{\Phi}\in {\mathbb{R}}^{M\times N}$ by the training dataset by Equation (14)

5.
Identify the class of the compressed testing data by Equation (9), where the probability density function is given by Equation (15).
There are many other classifiers such as SVM that can be used. But our purpose here is to show that dimension reduction with the CS can improve subsequent classification and the often used Bayesian classifier is chosen.
Results
We subtyped four types of GBM with multiple genomic data types (e.g., miRNA expression, mRNA expression, and their combinations) from TCGA. The MCSD was first trained by the training data with known class labels, and was then employed to detect subtypes in another independent testing dataset. The classification accuracy by the MCSD was compared with that without using MCSD. The classification performance between using the combined data types and using a single type of data was also compared.
Table 2 shows the comparison of the GBM classification accuracy for the testing dataset, with and without the compress matrix used in our algorithm (see Section “Methods and materials”). The results were obtained on three types of data, i.e., miRNA expression data, mRNA expression data, and their combinations. The classification accuracy is defined as the ratio between the number of correctly labeled samples and the number of total samples. The result calculated by the noncompressed detector had a classification accuracy of 41.8% with miRNA expression data. However, when we used the MCSD to classify the four subtypes, the accuracy of classifying the testing dataset was 69.1%, with 54 selected informative features out of 1,510 features. When we tested the classifiers on the mRNA expression data, the result calculated by the noncompressed detector was 32.7%. However, the classification result with the MCSD was 52.7%, which employed a subset of the features, 432 out of 22,277 features.
We also tested if the classification performance of the MCSD was better than noncompressed detector in the combined analysis of both miRNA expression and mRNA expression data as shown in Table 2. The subtyping accuracy by the noncompressed detector was 32.7%. The classification accuracy by the MCSD showed a significant improvement over the noncompressed detector. The accuracy was 90.9% (121 informative features selected or 145 informative features selected). The 121 features selected are shown in Additional file 2 with the probes and the corresponding symbols.
Figure 2 demonstrates the classification accuracy when different numbers of informative features were employed. The combined analysis of the two types of genomewide data was always able to achieve a significant higher subtyping accuracy than any single data type analysis when the same number of informative features were used (with a subset of features less than 450), indicating the advantages of the combined analysis. Figure 2 also shows that the classification accuracy was low when only a few features were used, indicating that the subset was too small to represent the characteristics of the entire dataset. When we increased the number of features used in the MCSD, the classification accuracy went up. The accuracy of classifying the testing dataset reached the highest value, 69.1, 52.7, and 90.9% on the miRNA expression, mRNA expression, and their combinations, respectively. However, more features may also add redundancy and thus cause the decrease of the classification accuracy. Therefore, we conclude that the use of fewer but significant features will achieve better classification accuracy.
Figure 3a displays the normalized levels of the 121 selected features (118 mRNAs and 3 miRNAs) from both miRNA expression and mRNA expression data for the combined analysis, with the highest classification accuracy of 90.9%. If using the mRNA and miRNA data separately, they only give the accuracy as 49.1 and 47.3%, respectively. The samples with arrows were misclassified to the subtypes pointed by the arrows (e.g., the 17th sample that belongs to proneural was misclassified to classical). Each column represents a patient/sample and each row represents a feature (a probe from miRNA expression or mRNA expression data). The four subtypes of GBM are proneural, neural, classical, and mesenchymal. Each feature was normalized by the largest value in each row. It can be found that the misclassification only happens among the subtypes of proneural, neural, and classical. The number of misclassified samples in each subtype is one sample in proneural, two samples in neural, two samples in classical, and zero samples in mesenchymal. The expression levels in the subtype mesenchymal exhibit a significant difference from other three subtypes as shown in Figure 3a. Figure 3b displays the same selected features in the training dataset.
Conclusion and discussion
In this study, we applied the proposed MCSD to subtype four types of GBM: proneural, neural, classical, and mesenchymal with multiple genetic data from TCGA. High classification accuracy was achieved by using CSbased technique (i.e., MCSD) along with the combination of multiple datasets. The results from combining two types of genomic data were compared with those from single type of data. Moreover, the performance of the classification with and without MCSD technique had also been compared. The comparisons showed that the CSbased combined analysis of multiple types of genetic data could significantly improve the accuracy of detecting GBM subtypes.
Combining different types of genomic data allows us to interpret the information in the datasets comprehensively. The information from miRNA and mRNA are complementary to each other; so a combined analysis can give a better result than single data type analysis. miRNAs are a recently discovered class of small noncoding RNAs that regulate gene expression [25], which can be combined with mRNA data for better disease subtyping. However, if no dimension reduction with CS was applied, we found from Table 2 that the classification accuracy from combined analysis was comparable to that from the single mRNA expression because of the redundancy added. The classification performance was significantly improved after we used CS method, indicating that CS may reduce redundancy [26] in the combined datasets and thus improve the classification accuracy.
Informative features/biomarkers selected in this study have also been validated to be associated with GBM and have been reported in the literatures. In the combined data analysis, the 121 features/probes selected (shown in Additional file 2), the 3 miRNA expression probes and 118 mRNA expression probes are listed. Two of the selected miRNAs probes that represent the same miRNA, “hsamiR9” (sequence “TCATACAGCTAGATAACCAA”), have been validated to have stemness potential and chemoresistance to GBM cells [27–29], and known to be specifically expressed during brain neurogenesis. In the listed mRNA expression probes, the four probes of “CD44” and the three probes of “ASCL1” are selected. Both of the genes have been validated as biomarkers in subtyping GBM in multiple genomic studies [9, 30–32]. It demonstrates the significance of “CD44” and “ASCL1” in discriminating different subtypes of GBM. The three probes from “THBS1” are also selected in the 121 probes list. “THBS1” is a subunit of a disulfidelinked homotrimeric protein. This protein has been shown to play roles in platelet aggregation, angiogenesis, and tumorigenesis [33]. “THBS1” is also a major activator of “TGFB1” and the “TGFB1” expression is associated with GBM [34]. Moreover, it has been found that “TbRII”, a receptor of “TGFB1”, has a strong relationship with human malignant glioblastoma cells [35]. There are biomarkers listed in Additional file 2 that have not been reported yet. However, they may be potential biomarkers for GBM, deserving further study.
We also performed Gene Ontology (GO) analyses to determine that these genes were enriched in specific GO terms (biological processes). The GO term “antigen processing” and presentation “lymphocyte mediated immunity” (p = 1.78 × 10^{–6}), and several GO terms related to wounding healing [e.g. “response to wounding” (p = 1.26 × 10^{–8}); “wound healing” (p = 2.44 × 10^{–6})], and cell adhesion [e.g. “biological adhesion” (p = 6.53 × 10^{–7}); “cell adhesion” (p = 6.41 × 10^{–7})] showed highly significant enrichment for our selected genes. These results were expected. Taking “lymphocyte mediated immunity”related GO categories as an example, lymphocytemediated cellular responses play a critical role in the body’s ability to generate an antitumor immune response, and activation status of lymphocytes is an important determinant of sensitivity to tumormediated apoptosis [36]. In addition, according to previous studies, the miRNAs we identified are related to glioblastoma. For example, it was found that “hasmiR9” inhibit differentiation of glioblastoma stem cells, and the calmodulinbinding transcription activator 1 (CAMTA1) as “hasmiR9” target is a tumor suppressor in glioblastoma [37].
To test the stability of the classification results, the samples in training and testing were randomly rearranged ten more times. The number of samples from each subtype in training and testing was maintained the same as in the description in the section “Data collection”. The overall classification rate has an average value of 87.1% with a standard deviation of 4.5%, indicating that the results are rather robust.
In summary, we have developed a CSbased technique for combining multiple genomic data to subtype glioblastoma more accurately. The biomarkers identified with our approaches have also been validated or reported in some existing literatures, indicating that the integrated approach can provide comprehensive information for better disease diagnosis.
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Acknowledgments
This study was supported by the NIH grant R21 LM010042, NSF Advances in Biological informatics (ABI) grant and The Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning. The authors deeply appreciate the anonymous referees for their valuable suggestions.
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Additional file 1: U for the MCSD.(DOC 55 KB)
List of 121 selected features.
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Tang, W., Duan, J., Zhang, JG. et al. Subtyping glioblastoma by combining miRNA and mRNA expression data using compressed sensingbased approach. J Bioinform Sys Biology 2013, 2 (2013). https://doi.org/10.1186/1687415320132
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Keywords
 Glioblastoma
 Data integration
 Compressed sensing
 Classification
 mRNA
 miRNA