- Open Access
Integrating fMRI and SNP data for biomarker identification for schizophrenia with a sparse representation based variable selection method
© Cao et al.; licensee BioMed Central Ltd. 2013
- Published: 11 November 2013
In recent years, both single-nucleotide polymorphism (SNP) array and functional magnetic resonance imaging (fMRI) have been widely used for the study of schizophrenia (SCZ). In addition, a few studies have been reported integrating both SNPs data and fMRI data for comprehensive analysis.
In this study, a novel sparse representation based variable selection (SRVS) method has been proposed and tested on a simulation data set to demonstrate its multi-resolution properties. Then the SRVS method was applied to an integrative analysis of two different SCZ data sets, a Single-nucleotide polymorphism (SNP) data set and a functional resonance imaging (fMRI) data set, including 92 cases and 116 controls. Biomarkers for the disease were identified and validated with a multivariate classification approach followed by a leave one out (LOO) cross-validation. Then we compared the results with that of a previously reported sparse representation based feature selection method.
Results showed that biomarkers from our proposed SRVS method gave significantly higher classification accuracy in discriminating SCZ patients from healthy controls than that of the previous reported sparse representation method. Furthermore, using biomarkers from both data sets led to better classification accuracy than using single type of biomarkers, which suggests the advantage of integrative analysis of different types of data.
The proposed SRVS algorithm is effective in identifying significant biomarkers for complicated disease as SCZ. Integrating different types of data (e.g. SNP and fMRI data) may identify complementary biomarkers benefitting the diagnosis accuracy of the disease.
- Sparse Representation
- fMRI Data
- High Classification Accuracy
- Restricted Isometry Property
- Sparse Model
Schizophrenia (SCZ) is one of the most disabling and emotionally devastating illnesses. The global median lifetime morbid risk for schizophrenia is 7.2/1,000 persons . Genetic factors play an important role in the development of schizophrenia. To date, over 1000 genes have been reported to associate with SCZ (http://www.szgene.org/default.asp) and many SNPs have been identified as biomarkers for the disease [2–4]. For example, Kordi-Tamandani et al. showed that that promoter methylation of the CTLA4 gene can increase the risk of SCZ disease . Shayevitz et al. confirmed the gene NOTCH4 as a candidate gene for schizophrenia with genome-wide association studies (GWAS) . Chen et al. stated that three SNPs spanning the MYO5B gene are significantly associated with SCZ: rs4939921, rs1557355 and rs4939924 . Besides genomic data, fMRI is another widely used data modality in SCZ studies . To date, many methods have been proposed to integrate multi-types of data in SCZ disease study [7–11]. For example, Chen et al. proposed parallel independent component analysis (paraICA) to identify genomic risk components associated with brain function abnormalities and detected significant biomarkers from both fMRI data and SNP data that are strongly correlated . Parallel ICA is an effective method for the joint analysis of multiple modalities including interconnections between them . Utilizing this method, Meda et al. detected three fMRI components significantly correlated with two distinct gene components in SCZ study . In this study, a novel sparse representation based variable selection (SRVS) method was proposed and applied to an integrative analysis of two types of data: fMRI and SNP, aiming to obtain comprehensive analysis.
Sparse representation including compressive sensing has been widely used in signal/image processing and computational mathematics [12–18]. Candes et al. showed that stable signal can be approximately recovered from incomplete and inaccurate measurements . Wright et al. proposed a sparse representation based clustering (SRC) for face recognition, demonstrating high classification accuracy . In our recent works [16–18], we developed novel classification and feature selection algorithms based on sparse representation theory. We applied those methods to gene expression data analysis , to chromosome image classification , and to joint analysis of different data modalities (e.g. SNP data and gene expression data) , and achieved improved classification accuracies as well as better feature selections.
In applications of sparse representation, The availability of a limited number of samples is an important issue (e.g., feature selection and signal recovery) . According to compressive sensing theory (e.g., the restricted isometry property (RIP) condition  for signal recovery), the number of available samples should not be less than the number of signals to be selected/recovered. However, the number of features/variables in genomic data (e.g. SNP data) or medical imaging data (e.g. fMRI data) are usually significantly big than the number of samples. In those cases, the traditional methods for compressive sampling cannot effectively analyse the data.
In a recent work, Li et al.  developed a voxel selection algorithm for fMRI data analysis. The method was based on sparse representation and is designed to get a sparse solution when sufficient samples exist. However, it may not handle the small sample problem described above.
In this study, a novel sparse representation based variable selection (SRVS) algorithm was proposed to select relevant biomarkers from big data sets having small sample sizes. The analysis was obtained by using a window based approach, whose size determines the resolution of the variable selection. We first tested the SRVS algorithm on a simulated data set (size of 100 × 1e6, with 50 cases and 50 controls), demonstrating the multi-resolution characteristic of the method. Then the algorithm was applied to an integrative analysis of two real data sets: a SNP data set (size of 208 × 759075) and a fMRI data set (size of 208 × 153594). Using the proposed SRVS algorithm, biomarkers for SCZ were identified and validated.
fMRI and SNP data collection
A total of 208 subjects, after signing informed consent, were recruited in the study, including 96 SCZ cases (age: 34 ± 11, 74 males) and 112 healthy controls (age: 32 ± 11, 68 males). Both SNP and fMRI data were collected from each of those 208 subjects. The healthy controls have no history of psychiatric disorders and were free of any medical. SCZ cases met the DSM-IV diagnostic criteria for schizophrenia. After pre-processing, 153594 fMRI voxels and 759075 SNP loci were obtained for the following biomarker selections. Please refer to  for detailed description of data collection and pre-processing.
Generalized sparse model
where is the phenotype vector of the subjects; matrix and represent data sets of different modalities having normalized column vectors (e.g., ); ; , and are the weight factors for and respectively. The measurement error . We aim to reconstruct the unknown sparse vector based on and , where , , and .
It can be proven that when , the matrix has the difficulty to satisfy the restricted isometry property (RIP) condition  for signal recovery. In this work, and . Thus . To overcome this problem, we propose the SRVS algorithm described as follows.
where represents norm; . The SRVS Algorithm given below is used to solve the minimization problem and select the phenotype relevant column vectors out of .
Spare representation base variable selection (SRVS) algorithm (http://hongbaocao.weebly.com/software-for-download.html)
1. Initialize ;
2. For the th step, randomly select from ; Mark the indexes of the columns in as ;
4. Update with : ; where and denote the th entries in and respectively;
5. If , update ; go to Step 2.
6. Set . The non-zero entries in correspond to the columns in to be selected.
It can be proven that, by using the SRVS algorithm, one can identify the significant variables with high probabilities. In addition, the SRVS algorithm can be shown convergent for any given and , generating an effective solution for the sparse model specified by Eq. (2). In the following section, we discuss the sparsity control issue to determine the number of variables to be selected.
Sparsity control using
Further sparsity control using
To validate the variable selected using our proposed SRVS algorithm, we compared our selected SNPs and fMRI voxels with that of previous studies. In addition, we used the selected SNPs and fMRI voxels to identify SCZ patients from healthy controls with the sparse representation based classifier (SRC) . Then a leave one out (LOO) cross-validation approach was carried out to evaluate the identification accuracy. We compared the classification results with that of Li et al.'s method . Furthermore, we compared the results of using variables selected from one type of data and that of both types of data. We also studied the influences of selecting different number of variables.
We applied our SRVS method with the sparse model given by Eq. (1) to an integrative analysis of SNP and fMRI data sets. The results were compared with that of Li et al.'s method under different weighting factors. We also discussed the sparsity control issues using and .
Variable selection with different weight factors
In each of the 16 trials given by Figure 3, we selected the top 200 biomarkers by our proposed SRVS method and by Li et al.'s method . As shown in Figure 3, the weight factor has similar effects on the variable selection of the two methods. It was interesting to see that even though the number of SNPs was much larger than that of fMRI voxels (759075 vs. 153594), similar number of variables were selected from both data sets when weight factor for SNP data set was around 0.5 (0.46 for SRVS method with norms, and 0.47 for Li et al.'s method). This suggests that the two data sets may contain similar information for the SCZ case/control study.
Comparison with Li et al.'s method
The comparison with the reported first 45 SCZ genes (http://www.szgene.org/default.asp). The Index is the order of the specific gene in the top 45 reported genes list.
Li et al.'s method
To further compare the two methods at different sparsity level, we studied more top variables in each of the 16 trials. To reach this purpose, we set and for SRVS method. For Li's method , the number of subjects selected in each run was one tenth of total number of subjects; and we set the threshold = 0.01(please refer to  for the meaning of ). As a consequence, 500 to 800 variables (SNPs and fMRI voxels) were selected in each trial. In this case, our proposed method selected 20 reported genes. For Li et al.'s method, 14 reported genes were located, and 11 of the top 45 genes were identified by both methods . However, the genes identified by the two methods have <10% overlaps. For the top 50 genes selected by the two methods, there was only one gene, CSMD1, was identified by both methods. We listed the top 50 genes and the corresponding SNPs chosen by the two methods in Additional file 2.
Main brain regions of selected voxels using SRVS method
Selected voxels number
Middle Frontal Gyrus
Middle Temporal Gyrus
Superior Temporal Gyrus
Medial Frontal Gyrus
Superior Frontal Gyrus
From Figure 6 (a) we showed that the highest classification accuracy was achieved at the weight factor , where around equal sized SNPs and fMRI voxels were selected by the SRVS method. At the two ends (), the classification accuracies were relatively lower. This suggests that using biomarkers from both types of data may lead to better identification accuracy.
In this study, we introduced a novel sparse representation based variable selection (SRVS) method, and applied it to an integrative analysis of SNP data and fMRI data. In the case of medical imaging data (e.g. fMRI data) or genomic data (e.g. SNP data), the number of samples tend to be much less than the number of variables (e.g. fMRI voxles; SNP loci). As a consequence, many of those variables are correlated and cannot be identified by traditional sparse signal recovery methods. The proposed SRVS method can identify significant variables with high probability, regardless of the coherence conditions required for exact signal recovery in compressive sensing. For example, significant fMRI voxels functionally correlated (within neighbour brain regions) were identified simultaneously by using our proposed SRVS algorithms (see Figure 5 (a)). This manifests the capability of out proposed SRVS method in handling big data set with small sample sizes.
In addition, the proposed SRVS method can be generalized to integrate multiple data modalities for joint analysis and achieve comprehensive diagnosis. As can be seen from Figure 6 (a), the highest classification accuracy was achieved using approximately equal sized variables from both data sets, suggesting that using biomarkers from both types of data may lead to higher diagnosis accuracy.
Another advantage of the SRVS method is its multiple detection resolutions. By choosing different values of widow length one can select different number of variables at different significance level. Furthermore, the error term can be used for further sparsity control of the solution , selecting the most important variables. This multi-resolution characteristic of SRVS provides a flexible variable selection approach for big data sets.
When compared to the previous SCZ studies, our method effectively identified more reported SCZ genes than Li et al.'s method. Furthermore, most of the brain regions identified using our proposed SRVS method are previously reported as SCZ associated brain regions. When using the selected variable to identify SCZ patients from controls, our method generated significantly higher classification ratio than Li et al.'s method (Figure 5 (b), ). Those results demonstrated the effectiveness of our method.
Our proposed SRVS is effective in variable selection for complex disease as SCZ. The biomarkers selected generate better identification accuracy than that of Li et al.'s method. When combining information from fMRI data and SNP data for integrative analysis, higher identification accuracy can be achieved, demonstrating the advantage of the combined analysis.
This work is partially supported by the NIH and NSF.
This work is based on "Bio marker identification for diagnosis of schizophrenia with integrated analysis of fMRI and SNPs ", by Hongbao Cao which appeared in Bioinformatics and Biomedicine (BIBM), 2012 IEEE International Conference on. © 2012 IEEE .
The publication costs for this article were funded by the corresponding author.
This article has been published as part of BMC Medical Genomics Volume 6 Supplement 3, 2013: Selected articles from the IEEE International Conference on Bioinformatics and Biomedicine 2012: Medical Genomics. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcmedgenomics/supplements/6/S3.
- McGrath J, Saha S, Chant D, Welham J: Schizophrenia: a concise overview of incidence, prevalence, and mortality. Epidemiol Rev. 2008, 30: 67-76. 10.1093/epirev/mxn001.View ArticlePubMedGoogle Scholar
- Kordi-Tamandani DM, Vaziri S, Dahmardeh N, Torkamanzehi A: Evaluation of polymorphism, hypermethylation and expression pattern of CTLA4 gene in a sample of Iranian patients with schizophrenia. Mol Biol Rep. 2013, 40: 5123-5128. 10.1007/s11033-013-2614-3.View ArticlePubMedGoogle Scholar
- Shayevitz C, Cohen OS, Faraone SV, Glatt SJ: A re-review of the association between the NOTCH4 locus and schizophrenia. Am J Med Genet B Neuropsychiatr Genet. 2012, 159B (5): 477-83. 10.1002/ajmg.b.32050.View ArticlePubMedGoogle Scholar
- Chen Y, Tian L, Zhang F, Liu C, Lu T, Ruan Y, Wang L, Yan H, Yan J, Liu Q, Zhang H, Ma W, Yang J, Li K, Lv L, Zhang D, Yue W: Myosin Vb gene is associated with schizophrenia in Chinese Han population. Psychiatry Res. 2013, 207: 13-8. 10.1016/j.psychres.2013.02.026.View ArticlePubMedGoogle Scholar
- Meda SA, Bhattarai M, Morris NA, Astur RS, Calhoun VD, Mathalon DH, Kiehl KA, Pearlson GD: An fMRI study of working memory in first-degree unaffected relatives of schizophrenia patients. Schizophr Res. 2008, 104: 85-95. 10.1016/j.schres.2008.06.013.PubMed CentralView ArticlePubMedGoogle Scholar
- Szycik GR, Münte TF, Dillo W, Mohammadi B, Samii A, Emrich HM, Dietrich DE: Audiovisual integration of speech is disturbed in schizophrenia: an fMRI study. Schizophr Res. 2009, 110: 111-118. 10.1016/j.schres.2009.03.003.View ArticlePubMedGoogle Scholar
- Chen J, Calhoun VD, Pearlson GD, Ehrlich S, Turner JA, Ho BC, Wassink TH, Michael AM, Liu J: Multifaceted genomic risk for brain function in schizophrenia. NeuroImage. 2012, 61: 866-875. 10.1016/j.neuroimage.2012.03.022.PubMed CentralView ArticlePubMedGoogle Scholar
- Liu J, Ghassemi MM, Michael AM, Boutte D, Wells W, Perrone-Bizzozero N, Macciardi F, Mathalon DH, Ford JM, Potkin SG, Turner JA, Calhoun VD: An ICA with reference approach in identification of genetic variation and associated brain networks. Frontiers in Human Neuroscience. 2012, 6: 1-10.Google Scholar
- Yang H, Liu J, Sui J, Pearlson G, Calhoun VD: A Hybrid Machine Learning Method for Fusing fMRI and Genetic Data to Classify Schizophrenia. Frontiers in Human Neuroscience. 2010, 4: 1-9.View ArticleGoogle Scholar
- Meda SA, Jagannathan K, Gelernter J, Calhoun VD, Liu J, Stevens MC, Pearlson GD: A pilot multivariate parallel ICA study to investigate differential linkage between neural networks and genetic profiles in schizophrenia. NeuroImage. 2010, 53: 1007-1015. 10.1016/j.neuroimage.2009.11.052.PubMed CentralView ArticlePubMedGoogle Scholar
- Liu J, Pearlson G, Windemuth A, Ruano G, Perrone-Bizzozero NI, Calhoun V: Combining fMRI and SNP data to investigate connections between brain function and genetics using parallel ICA. Hum Brain Mapp. 2009, 30: 241-255. 10.1002/hbm.20508.PubMed CentralView ArticlePubMedGoogle Scholar
- Gribonval R, Nielsen M: Sparse decompositions in unions of bases. IEEE Trans Inf Theory. 2003, 49: 3320-3325. 10.1109/TIT.2003.820031.View ArticleGoogle Scholar
- Tropp JA, Gilbert AC, Muthukrishnan S, Strauss MJ: Improved sparse approximation over quasi-incoherent dictionaries. Proc 2003 IEEE Int Conf Image Process, Barcelona, Spain. 2003, 1: 137-140.Google Scholar
- Candes E, Romberg J, Tao T: Stable signal recovery from incomplete and inaccurate measurements. Comm On Pure and Applied Math. 2006, 59: 1207-1223. 10.1002/cpa.20124.View ArticleGoogle Scholar
- Wright J, Yang AY, Ganesh A, Sastry SS, Ma Y: Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach. 2009, 31: 210-227.View ArticleGoogle Scholar
- Tang W, Cao H, Duan J, Wang YP: A compressed sensing based approach for subtyping of leukemia from gene expression data. J Bioinform Comput Biol. 2011, 9: 631-645. 10.1142/S0219720011005689.PubMed CentralView ArticlePubMedGoogle Scholar
- Cao H, Duan J, Lin D, Wang YP: Sparse Representation Based Clustering for Integrated Analysis of Gene Copy Number Variation and Gene Expression Data. IJCA. 2012, 19: 131-138.Google Scholar
- Cao H, Deng HW, Li M, Wang YP: Classification of multicolor fluorescence in situ hybridization (M-FISH) images with sparse representation. IEEE Trans Nanobioscience. 2012, 11: 111-118.PubMed CentralView ArticlePubMedGoogle Scholar
- Donoho DL, Elad M, Temlyakov VN: Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Transactions on Information Theory. 2006, 52: 6-18.View ArticleGoogle Scholar
- Cai T, Wang L: Orthogonal Matching Pursuit for Sparse Signal Recovery. IEEE Trans on Inf Theory. 2011, 57: 1-26.View ArticleGoogle Scholar
- Li Y, Namburi P, Yu Z, Guan C, Feng J, Gu Z: Voxel selection in FMRI data analysis based on sparse representation. IEEE Trans Biomed Eng. 2009, 56: 2439-2451.View ArticlePubMedGoogle Scholar
- Cao H, Duan J, Lin D, Calhoun V, Wang YP: Bio marker identification for diagnosis of schizophrenia with integrated analysis of fMRI and SNPs. Bioinformatics and Biomedicine (BIBM), 2012 IEEE International Conference on: 4-7 October 2012. 2012, 1-6. 10.1109/BIBM.2012.6392674.View ArticleGoogle Scholar
- Li YQ, Cichocki A, Amari S: Analysis of sparse representation and blind source separation. Neural Comput. 2004, 16: 1193-1234. 10.1162/089976604773717586.View ArticlePubMedGoogle Scholar
- Davenport M, Duarte M, Hegde C, Baraniuk R: Introduction to compressive sensing. Connexions Web site. 2011, Apr 10, [http://cnx.org/content/m37172/1.7/]Google Scholar
- Donoho DL, Tsaig Y: Fast Solution of L1-Norm Minimization Problems When the Solution May Be Sparse. IEEE Trans on Information Theory. 2008, 54: 4789-4812.View ArticleGoogle Scholar
- Davis G, Mallat S, Avellaneda M: Greedy adaptive approximation. J Constr Approx. 1997, 13: 57-98. 10.1007/BF02678430.View ArticleGoogle Scholar
- Tropp JA: Greed is good: Algorithmic results for sparse approximation. IEEE Trans Inf Theory. 2004, 50: 2231-2242. 10.1109/TIT.2004.834793.View ArticleGoogle Scholar
- Tropp JA: Just relax: Convex programming methods for identifying sparse signals. IEEE Trans Inf Theory. 2006, 51: 1030-1051.View ArticleGoogle Scholar
- Barron A, Cohen A, Dahmen W, DeVore R: Approximation and learning by greedy algorithms. Ann Statist. 2008, 36: 64-94. 10.1214/009053607000000631.View ArticleGoogle Scholar
- Duan J, Soussen C, Brie D, Idier J, Wang YP: On LARS/homotopy equivalence conditions for over-determined LASSO. IEEE Signal Processing Letters. 2012, 19: 894-897.View ArticleGoogle Scholar
- Fisher RA, Yates F: Statistical tables for biological, agricultural and medical research. 1948, OCLC 14222135London: Oliver & Boyd, 26-27. 3Google Scholar
- Lee H, Lee DS, Kang H, Kim BN, Chung MK: Sparse brain network recovery under compressed sensing. IEEE TMI. 2011, 30: 1154-1165.Google Scholar
- Pascual-Leone A, Manoach DS, Birnbaum R: Goff DC Motor cortical excitability in schizophrenia. Biol Psychiatry. 2002, 52: 24-31. 10.1016/S0006-3223(02)01317-3.View ArticlePubMedGoogle Scholar
- Kumari V, Gray JA, Honey GD, Soni W, Bullmore ET, Williams SC, Ng VW, Vythelingum GN, Simmons A, Suckling J, Corr PJ, Sharma T: Procedural learning in schizophrenia: a functional magnetic resonance imaging investigation. Schizophrenia Research. 2002, 57: 97-107. 10.1016/S0920-9964(01)00270-5.View ArticlePubMedGoogle Scholar
- Onitsuka T, Shenton ME, Salisbury DF, Dickey CC, Kasai K, Toner SK, Frumin M, Kikinis R, Jolesz FA, McCarley RW: Middle and inferior temporal gyrus gray matter volume abnormalities in chronic schizophrenia: an MRI study. Am J Psychiatry. 2004, 161: 1603-11. 10.1176/appi.ajp.161.9.1603.PubMed CentralView ArticlePubMedGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.