A review on machine learning principles for multi-view biological data integration

Briefings in Bioinformatics

Volumn 19, Issue 2, 2018, Pages 325-340

  Li, Yifeng ^a   Wu, Fang Xiang ^b   Ngom, Alioune ^c  

^a NATIONAL RESEARCH COUNCIL CANADA   (Canada)

^b UNIVERSITY OF SASKATCHEWAN   (Canada)

^c UNIVERSITY OF WINDSOR   (Canada)

Author keywords

Data integration; Deep learning; Matrix factorization; Multi omics data; Multiple kernel learning; Network fusion; Random forest

Indexed keywords

DATA INTEGRATION; DEEP LEARNING; DEEP NEURAL NETWORK; KERNEL METHOD; MULTIOMICS; RANDOM FOREST; REVIEW; ANIMAL; BIOLOGICAL MODEL; GENE REGULATORY NETWORK; HUMAN; MACHINE LEARNING; PROCEDURES; SYSTEMS BIOLOGY;

ANIMALS; GENE REGULATORY NETWORKS; HUMANS; MACHINE LEARNING; MODELS, BIOLOGICAL; SYSTEMS BIOLOGY;

EID: 85049474548     PISSN: 14675463     EISSN: 14774054     Source Type: Journal    
DOI: 10.1093/bib/bbw113     Document Type: Review

References (171)

1. Zhou Z, Chawla N, Jin Y, et al. Big data opportunities and challenges: discussions from data analytics perspectives. IEEE Comput Intell Mag 2014;9(4):62–74.
2. The Cancer Genome Atlas Network. Comprehensive molecular portraits of human breast tumors. Nature 2012;490(7418):61–70.
3. The ENCODE Project Consortium. An integrated encyclopedia of DNA elements in the human genome. Nature 2012;489:57–74.
4. Roadmap Epigenomics Consortium, Kundaje A, Meuleman W, et al. Integrative analysis of 111 reference human epigenomes. Nature 2015;518:317–30.
5. The GTEx Consortium. The genotype-tissue expression (GTEx) project. Nature Genetics 2013;45(6):580–5.
6. Wheeler D, Srinivasan M, Egholm M, et al. The complete genome of an individual by massively parallel DNA sequencing. Nature 2008;452:872–6.
7. Johnson D, Mortazavi A, Myers R, et al. Genome-wide mapping of in vivo protein-DNA interactions. Science 2007;316(5830):447–55.
8. Boyle A, Davis S, Shulha H, et al. High-resolution mapping and characterization of open chromatin across the genome. Cell 2008;132:311–22.
9. Lister R, Pelizzola M, Dowen R, et al. Human DNA methylomes at base resolution show widespread epigenomic differences. Nature 2009;462:315–22.
10. Nagalakshmi U, Wang Z, Waern K, et al. The transcriptional landscape of the yeast genome defined by RNA sequencing. Science 2008;320(5881):1344–9.
11. Creighton C, Reid J, Gunaratne P. Expression profiling of microRNAs by deep sequencing. Brief Bioinform 2009;10(5):490–7.
12. Spurrier B, Ramalingam S, Nishizuka S. Reverse-phase protein lysate microarrays for cell signaling analysis. Nat Protoc 2008;3(11):1796–808.
13. Domon B, Aebersold R. Mass spectrometry and protein analysis. Science 2006;321(5771):212–7.
14. Dunn W, Erban A, Weber R, et al. Mass appeal: Metabolite identification in mass spectrometry-focused untargeted metabolomics. Metabolomics 2013;9:S44–66.
15. Xu R, Wunsch D. Clustering. New Jersey: Wiley-IEEE Press, 2008.
16. Ritchie M, Holzinger E, Li R, et al. Methods of integrating data to uncover genotype-phenotype interactions. Nat Rev Genet 2015;15:85–97.
17. Kristensen V, Lingjarde O, Russnes H, et al. Principles and methods of integrative genomic analyses in cancer. Nat Rev Cancer 2014;14:299–313.
18. Costello J, Heiser L, Georgii E, et al. A community effort to assess and improve drug sensitivity prediction algorithms. Nat Biotechnol 2014;32:1202–12.
19. Li Y, Chen C, Kaye A, et al. The identification of cis-regulatory elements: a review from a machine learning perspective. Biosystems 2015;138:6–17.
20. Nobel W, Support vector machine applications in computational biology. In: B Scholkopf, K Tsuda, JP Vert (eds), Kernel Methods in Computational Biology, Chap. 3. Cambridge, MA: MIT Press, 2004, 71–92.
21. Li Y, Ngom A. Data integration in machine learning. In: IEEE International Conference on Bioinformatics and Biomedicine, IEEE, IEEE Press, Piscataway, NJ, 2015, p. 1665–71.
22. Gligorijevic V, Przulj N. Methods for biological data integration: perspectives and challenges. J R Soc Interface 2015;12(112):20150571.
23. Ding J, Shi J, Wu F. SVM-RFE based feature selection for tandem mass spectrum quality assessment. Int J Data Min Bioinform 2011;5(1):73–88.
24. Cortes C, Vapnik V. Support vector networks. Mach Learn 1995;20:273–97.
25. Tibshirani R. Regression shrinkage and selection via the Lasso. J R Stat Soc Ser B 1996;58(1):267–88.
26. Zou H, Hastie T. Regularization and variable selection via the elastic net. J R Stat Soc Ser B 2005;67(2):301–20.
27. Yuan M, Lin Y. Model selection and estimation in regression with grouped variables. J R Stat Soc Ser B 2006;68(1):49–67.
28. Friedman J, Hastie T, Tibshirani R. Sparse inverse covariance estimation with the graphical lasso. Biostatistics 2008;9(3):432–41.
29. Friedman J, Hastie T, Tibshirani R. A note on the group lasso and a sparse group lasso. arXiv 2010:arXiv:1001.0736.
30. Jacob L, Obozinski G, Vert JP. Group Lasso with overlap and graph Lasso. In: International Conference on Machine Learning, ACM Press, New York, NY, 2009, p. 433–40.
31. Azencott CA, Grimm D, Sugiyama M, et al. Efficient network-guided multi-locus association mapping with graph cuts. Bioinformatics 2012;29(ISMB/ECCB2013):i171–9.
32. Zhao P, Yu B. On model selection consistency of lasso. J Mach Learn Res 2006;7:2541–63.
33. Zou H. The adaptive LASSO and its oracle property. J Am Stat Assoc 2006;101:1418–29.
34. Meinshausen U, Buhlmann P. Stability selection. J R Stat Soc Ser B 2010;72(4):417–73.
35. Wu C, Ma S. A selective review of robust variable selection with applications in bioinformatics. Brief Bioinform 2015;16(5):873–83.
36. Pique-Regi R, Degner J, Pai A, et al. Accurate inference of transcription factor binding from DNA sequence and chromatin accessibility data. Genome Res 2011;21:447–55.
37. Pearl J, Probabilistic Reasoning in Intelligent Systems. San Mateo, CA: Morgan Kaufmann, 1988.
38. Chickering D, Learning Bayesian networks is NP-complete. In: D Frisher, HJ Lenz (eds.) Learning from Data: AI and Statistics V, Lecture Notes in Statistics, Chap. 12, Springer-Verlag New York, Inc, Secaucus, NJ, 1996, 121–30.
39. Elidan G, Nachman I, Friedman N. “Ideal Parent” structure learning for continuous variable Bayesian networks. J Mach Learn Res 2007;8:1799–833.
40. Davies S, Moore A. Mix-nets: Factored mixtures of Gaussians in Bayesian networks with mixed continuous and discrete variables. In: Proceedings of The Sixteenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers Inc, San Francisco, CA, 2000, p. 168–75.
41. Cheng J, Greiner R. Comparing Bayesian network classifiers. In: The Fifteenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers Inc, San Francisco, CA, 1999, p. 101–8.
42. Heckerman D, Geiger D, Chickering D. Learning Bayesian networks: the combination of knowledge and statistical data. Mach Learn 1995;20:197–243.
43. Langley P, Iba W, Thompson K. An analysis of Bayesian classifiers. In: The Tenth National Conference on Artificial Intelligence, AAAI Press, Menlo Park, CA, 1992, p. 223–8.
44. Friedman N, Geiger D, Goldszmith M. Bayesian Network Classifiers. Machine Learning 1997;29:103–30.
45. Chickering D, Meek C. Finding optimal Bayesian networks. In: The Eighteenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers Inc., San Francisco, CA, 2002, p. 94–102.
46. Heckerman D, A tutorial on learning with Bayesian networks. In: M Jordan (ed.) Learning in Graphical Models, Adaptive Computation and Machine Learning series, Chap. 11. Cambridge, MA: MIT, 1998, 301–54.
47. Breiman L, Friedman J, Stone C, et al. Classification and Regression Trees. Chapman and Hall/CRC, Boca Raton, FL, 1984.
48. Friedman J, Tibshirani R, Hastie T, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd edn. Springer-Verlag New York, Inc., Secaucus, NJ, 2009.
49. Opitz D, Maclin R. Popular ensemble methods: an empirical study. J Artif Intell Res 1999;11:169–98.
50. Sewell M. Ensemble Learning, Technical report, Department of Computer Science, University College London, 2011.
51. Breiman L. Bagging predictors. Machine Learning 1996;24:(3):123–140.
52. Kearns M, Thoughts on hypothesis boosting 1988.
53. Breiman L. Arcing classifiers. The Ann Stat 1998;26(3):801–49.
54. Gunduz N, Fokoue E. Robust classification of high dimension low sample size data. arXiv 2015:arXiv:1501.00592.
55. Biau G, Devroye L, Lugosi G. Consistency of random forests and other averaging classifiers. J Mach Learn Res 2008;9:2015–33.
56. Scornet E, Biau G, Vert JP. Consistency of random forests. Ann Stat 2015;43(4):1716–41.
57. Polikar R. Ensemble based systems in decision making. IEEE Circuits Syst Mag 2006;6(3):21–45.
58. Polikar R. Bootstrap inspired techniques in computational intelligence: Ensemble of classifiers, incremental learning, data fusion and missing features. IEEE Signal Proc Mag 2007;24(4):59–72.
59. Wozniak M, Grana M, Corchado E. A survey of multiple classifier systems as hybrid systems. Inf Fusion 2014;16:3–17.
60. Chen C, Liaw A, Breiman L. Using Random Forest to Learn Imbalanced Data. Technical report, Department of Statistics, University of California, Berkeley, 2004.
61. Popovic D, Sifrim A, Davis J, et al. Problems with the nested granularity of feature domains in bioinformatics: the eXtasy case. BMC Bioinformatics 2015;16(Supp. 4):S2.
62. Pittman J, Huang E, Dressman H, et al. Integrated modeling of clinical and gene expression information for personalized prediction of disease outcomes. Proc Natl Acad Sci 2004;101(22):8431–6.
63. Drucker H, Burges C, Kaufman L, et al. Support vector regression machines. In: Advances in Neural Information Processing Systems. MIT Press, Cambridge, MA, 1996, 155–61.
64. von Luxburg U. A tutorial on spectral clustering. Stat Comput 2007;17(4):395–416.
65. Li Y, Ngom A. Sparse representation approaches for the classification of high-dimensional biological data. BMC Syst Biol 2013;7(Suppl 4):S6.
66. Gonen M, Alpaydin E. Multiple kernel learning algorithms. J Mach Learn Research 2011;12:2211–68.
67. Gonen M, Kaski S. Kernelized Bayesian matrix factorization. IEEE Trans Pattern Anal Mach Intell 2014;36:2047–60.
68. Wang J, Do HT, Woznica A, et al. Metric learning with multiple kernels. In: J Shawe-Taylor, R Zemel, P Bartlett, et al. (eds.) Advances in Neural Information Processing Systems 24. Curran Associates, Inc., Red Hook, NY, 2011, 1170–78.
69. Xing E, Jordan M, Russell S, et al. Distance metric learning with application to clustering with side-information. In: S Becker, S Thrun, K Obermayer (eds.) Advances in Neural Information Processing Systems 15. MIT Press, Cambridge, MA, 2003, 521–28.
70. Bellet A, Habrard A, Sebban M. A survey on metric learning for feature vectors and structured data. arXiv 2014. arXiv:1306.6709v4.
71. Kulis B. Metric learning: a survey. Found Trends Mach Learn 2012;5(4):287–364.
72. Li Y, Caron R, Ngom A. A decomposition method for large-scale sparse coding in representation learning. In: International Joint Conference on Neural Networks (IJCNN/WCCI), IEEE, IEEE Press, Piscataway, NJ, 2014, p. 3732–38.
73. Kim SJ, Magnani A, Boyd S. Optimal kernel selection in kernel Fisher discriminant analysis. In: International Conference on Machine Learning, ACM Press, New York, NY, 2006, p. 465–72.
74. Rakotomamonjy A, Bach F, Canu S, et al. SimpleMKL. J Mach Learn Res 2008;9:2491–521.
75. Zhang Y, Li A, Peng C, et al. Improve glioblastoma multiforme prognosis prediction by using feature selection and multiple kernel learning. IEEE/ACM Trans Comput Biol Bioinform 2016;DOI:10.1109/TCBB.2016.2551745.
76. Wang B, Mezlini A, Demir F, et al. Similarity network fusion for aggregating data types on a genomic scale. Nat Methods 2014;11(3):333–7.
77. Shen R, Olshen A, Ladanyi M. Integrative clustering of multiple genomic data types using a joint latent variable model with application to breast and lung cancer subtype analysis. Bioinformatics 2009;25(22):2906–12.
78. Marbach D, Costello J, Kuffner R, et al. Wisdom of crowds for robust gene network inference. Nat Methods 2012;9(8):796–804.
79. List M, Alcaraz N, Dissing-Hansen M, et al. KeyPathwayMinerWeb: online multi-omics network enrichment. Nucleic Acids Res 2016;44:W98–104. (Web Server):
80. Zitnik M, Zupan B. Gene network inference by fusing data from diverse distributions. Bioinformatics 2015;31:i230–9.
81. Chen B, Wang J, Li M, et al. Identifying disease genes by integrating multiple data sources. BMC Med Genomics 2014;7(Supp 2):S2.
82. Chen B, Wu F. Identifying protein complexes based on multiple topological structures in PPI networks. IEEE Trans Nanobiosci 2013;12(3):165–72.
83. Chen B, Wang J, Shang X, et al. Identifying individual-cancer-related genes by re-balancing the training samples. IEEE Trans Nanobiosci 2016;DOI:10.1109/ TNB.2016.2553119.
84. Chen B, Li M, Wang J, et al. A fast and high performance algorithm for identifying human disease genes. BMC Med Genomics 2015;8(Suppl 3):S2.
85. Chen B, Li M, Wang J, et al. Disease gene identification by using graph kernels and Markov random fields. Sci China Life Sci 2014;57(11):1052–63.
86. Ammad-ud-din M, Georgii E, Gonen M, et al. Integrative and personalized QSAR analysis in cancer by kernelized Bayesian matrix factorization. J Chem Inf Model 2014;54(8):2347–59.
87. Lan W, Wang J, Li M, et al. Predicting microRNA-disease associations based on microRNA and disease similarity. IEEE/ ACM Trans Comput Biol Bioinform 2016. DOI:10.1109/ TCBB.2016.2586190.
88. Li Y, Patra J. Genome-wide inferring gene-phenotype relationship by walking on the heterogeneous network. Bioinformatics 2010;26(9):1219–24.
89. Chen X, Liu MX, Yan GY. Drug-target interaction prediction by random walk on the heterogeneous network. Mol Biosyst 2012;8(7):1970–8.
90. Xuan P, Han K, Guo Y, et al. Prediction of potential disease-associated microRNAs based on random walk. Bioinformatics 2015;31(11):1805–15.
91. Liu Y, Zeng X, He Z, et al. Inferring microRNA-disease associations by random walk on a heterogeneous network with multiple data sources. IEEE/ACM Trans Comput Biol Bioinform 2016;DOI:10.1109/TCBB.2016.2550432.
92. Huang YF, Yeh HY, Soo VW. Inferring drug-disease associations from integration of chemical, genomic and phenotype data using network propagation. BMC Med Genomics 2013;6(Supp 3):S4.
93. Zitnik M, Zupan B. Data fusion by matrix factorization. IEEE Trans Pattern Anal Mach Intell 2015;37(1):41–53.
94. Zitnik M, Zupan B. Jumping across biomedical contexts using compressive data fusion. Bioinformatics 2016;32:i90–100.
95. Jolliffe I, Principal Component Analysis. Secaucus, NJ: Springer-Verlag New York. Inc., 2002.
96. Wall M, Rechtsteiner A, Rocha L, Singular value decomposition and principal component analysis. In: D Berrar, W Dubitzky, M Granzow (eds.) A Practical Approach to Microarray Data Analysis. Norwell, MA: Kluwer, 2003, 91–109.
97. Lawley D. The estimation of factor loadings by the method of maximum likelihood. Proc R Soc Edinb 1940;60:64–82.
98. West M. Bayesian factor regression models in the “large p, small n” paradigm. Bayesian Stat 2003;7:723–32.
99. Lee D, Seung S. Learning the parts of objects by nonnegative matrix factorization. Nature 1999;401:788–91.
100. Fertig E, Ding J, Favorov A, et al. CoGAPS: an R/C þþ package to identify patterns and biological process activity in transcriptomic data. Bioinformatics 2010;26(21):2792–3.
101. Li Y, Ngom A. The non-negative matrix factorization toolbox for biological data mining. BMC Source Code Biol Med 2013;8(1):10.
102. Li L, Wu L, Zhang H, et al. A fast multiplicative update algorithm for nonnegative matrix factorization and its convergence. IEEE Trans Neural Netw Learn Syst 2014;25(10):1855–63.
103. Kolda T, Bader B. Tensor decompositions and applications. SIAM Rev 2009;51(3):455–500.
104. Li Y, Ngom A. Non-negative matrix and tensor factorization based classification of clinical microarray gene expression data. In: IEEE International Conference on Bioinformatics and Biomedicine. IEEE, IEEE Press, Piscataway, NJ, 2010, p. 438–43.
105. Hinton G, Salakhutdinov R. Reducing the dimensionality of data with neural networks. Science 2006;313:504–7.
106. Hinton G. A practical guide to training restricted Boltzmann machines. Technical report., Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, 2010.
107. Li Y, Ngom A. Versatile sparse matrix factorization: theory and applications. Neurocomputing 2014;145:23–9.
108. Virtanen S, Klami A, Khan S, et al. Bayesian group factor analysis. In: Artificial Intelligence and Statistics Conference, La Palma, Canary Islands, 2012, p. 1269–77.
109. Klami A, Virtanen S, Leppaaho E, et al. Group factor analysis. IEEE Trans Neural Netw Learn Syst 2015;26(9):2136–47.
110. Klami A, Virtanen S, Kaski S. Bayesian cononical correlation analysis. J Mach Learn Res 2013;14:965–1003.
111. Bunte K, Leppaaho E, Saarinen I, et al. Sparse group factor analysis for biclustering of multiple data sources. Bioinformatics 2016;32(16):2457–63.
112. Hochreiter S, Bodenhofer U, Heusel M, et al. FABIA: Factor analysis for bicluster acquisition. Bioinformatics 2010;26(12):1520–7.
113. Liu J, Wang C, Gao J, et al. Multi-view clustering via joint nonnegative matrix factorization. In: SIAM International Conference on Data Mining, Austin, USA, 2013, p. 252–60.
114. Hidru D, Goldenberg A. EquiNMF: Graph regularized multi-view nonnegative matrix factorization. In: Workshop on Machine Learning in Computational Biology co-located with NIPS, Montreal, Canada, 2014, p. 1–9.
115. Zhang S, Liu C, Li W, et al. Discovery of multi-dimensional modules by integrative analysis of cancer genomic data. Nucleic Acids Res 2012;40(19):9379–91.
116. Yang Z, Michailidis G. A non-negative matrix factorization methods for detecting modules in heterogeneous omics multi-modal data. Bioinformatics 2016;32(1):1–8.
117. Hellton K, Thoresen M. Integrative clustering of high-dimensional data with joint and individual clusters. Biostatistics 2016;17(3):537–48.
118. Lock E, Hoadley K, JS, et al. Joint and individual variation explained (JIVE) for integrated analysis of multiple data types. Ann Appl Stat 2013;7:1:523–42.
119. Wold H, Nonlinear estimation by iterative least square procedures. In: F David (ed.) Research Papers in Statistics. New York: John Wiley and Sons Inc., 1966, 411–44.
120. Biancolillo A, Liland K, Mage I, et al. Variable selection in multi-block regression. Chemometr Intell Lab Syst 2016;165:89–101.
121. Trygg J, Wold S. Orthogonal projections to latent structures (O-PLS). J Chemometr 2002;16:119–28.
122. Trygg J. O2-PLS for qualitative and quantitative analysis in multivariate calibration. J Chemometr 2002;16:283–93.
123. Trygg J, Wold S. O2-PLS, a two-block (X-Y) latent variable regression (LVR) method with an integral OSC filter. J Chemometr 2003;17:53–64.
124. Bylesjo M, Eriksson D, Kusano M, et al. Data integration in plant biology: the O2PLS method for combined modeling of transcript and metabolite data. Plant J 2007;52:1181–91.
125. Lofstedt T, Trygg J. OnPLS- A novel multiblock method for the modelling of predictive and orthogonal variation. J Chemometr 2011;25:441–55.
126. Lofstedt T, Hanafi M, Mazerolles G, et al. OnPLS path modelling. Chemometr Intell Lab Syst 2012;118:139–49.
127. Srivastava V, Obudulu O, Bygdell J, et al. OnPLS integration of transcriptomic, proteomic and metabolomic data shows multi-level oxidative stress responses in the cambium of transgenic hipI- superoxide dismutase Populus plants. BMC Genomics 2013;14:893.
128. Rantalainen M, Bylesjo M, Cloarec O, et al. Kernel-based orthogonal projections to latent structures (K-OPLS). J Chemometr 2007;21:376–85.
129. Omberg L, Golub G, Alter O. A tensor higher-order singular value decomposition for integrative analysis of DNA microarray data from different studies. Proc Natl Acad Sci USA 2007;104(47):18371–6.
130. Cichocki A, Zdunek R, Phan A, et al. Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. West Sussex: John Wiley & Sons, 2009.
131. Smilde A, Mage I, Naes T, et al. Common and distinct components in data fusion. ArXiv 2016. arXiv:1607.02328.
132. Wang Z, Yuan W, Montana G. Sparse multi-view matrix factorization: a multivariate approach to multiple tissue comparisons. Bioinformatics 2015;31(19):3163–71.
133. Hubert M, Branden K. Robust methods for partial least squares regression. J Cheometr 2003;17:537–49.
134. Huang J, Nie F, Huang H, et al. Robust manifold nonnegative matrix factorization. ACM Trans Knowl Discov Data 2014;8(3):Article No. 11.
135. Huang H, Ding C. Robust tensor factorization using R1 norm. In: IEEE Conference on Computer Vision and Pattern Recognition, IEEE Press, Piscataway, NJ, 2008, p. 1–8.
136. Luttinen J, Ilin A. Transformations in variational Bayesian factor analysis to speed up learning. Neurocomputing 2010;73:1093–102.
137. Cemgil A. Bayesian inference for nonnegative matrix factorization models. Computat Intell Neurosci 2009;2009:785152.
138. LeCun Y, Bengio Y, Hinton G. Deep learning. Nature 2015;521:436–44.
139. Hinton G, Osindero S, Teh Y. A fast learning algorithm for deep belief nets. Neural Comput 2006;18:1527–54.
140. Salakhutdinov R, Hinton G. Deep Boltzmann machine. In: International Conference on Artificial Intelligence and Statistics, Volume 5 of JMLR: W&CP, Microtome Publishing, Brookline, MA, 2009, p. 448–455.
141. LeCun Y, Bengio Y, Convolutional networks for images, speech, and time series. In: M Arbib (ed.) The Handbook of Brain Theory and Neural Networks. Cambridge, MA: MIT Press, 1995, 255–8.
142. Graves A, Jaitly N. Towards end-to-end speech recognition with recurrent neural networks. In: International Conference on Machine Learning (ICML), JMLR: W&CP volume 32, Curran Associates, Inc., Red Hook, NY, 2014, p. 1764–72.
143. Li Y, Chen C, Wasserman W. Deep feature selection: theory and application to identify enhancers and promoters. J Comput Biol 2016;23(5):322–36.
144. Srivastava N, Salakhutdinov R. Multimodal learning with deep Boltzmann machines. J Mach Learn Res 2014;15:2949–80.
145. Liang M, Li Z, Chen T, et al. Integrative data analysis of multi-platform cancer data with a multimodal deep learning approach. IEEE/ACM Trans Comput Biol Bioinform 2015;12(4):928–37.
146. Bengio IGY, Courville A. Deep Learning, 2016. Book in preparation for MIT Press, Cambridge, MA. http://www.deeplearningbook.org
147. Hornik K. Approximation capabilities of multilayer feedforward networks. Neural Netw 1991;4(2):251–7.
148. Farago A, Lugosi G. Strong universal consistency of neural network classifiers. IEEE Trans Inf Theory 1993;39(4):1146–51.
149. Liano K. Robust error measure for supervised neural network learning with outliers. IEEE Trans Neural Netw 1996;7(1):246–50.
150. Seltzer M, Yu D, Wang Y. An investigation of deep neural networks for noise robust speech recognition. In: International Conference on Acoustics, Speech, and Signal Processing, 2013, p. 7398–492.
151. de-la Calle-Silos F, Gallardo-Antoln A, Pelaez-Moreno C. Deep maxout networks applied to noise-robust speech recognition, chap. In: Advances in Speech and Language Technologies for Iberian Languages. Springer-Verlag, Berlin Heidelberg, 2014, 109–18.
152. Srivastava N, Hinton G, Krizhevsky A, et al. Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 2014;15:1929–58.
153. Wu Y, Zhang S, Benjio Y, et al. On multiplicative integration with recurrent neural networks. ArXiv 2016. arXiv:1606.06630.
154. Woods A, Wormwood K, Wetie A, et al. Autism spectrum disorder: An omics perspective. Proteomics 2015;9(1-2):159–68.
155. Friedman J, Hastie T, Tibshirani R. Regularization paths for generalized linear models via coordinate descent. J Stat Softw 2010;33:1–22.
156. Pedregosa F, Varoquaux G, Gramfort A, et al. Scikit-learn: machine learning in Python. J Mach Learn Res 2011;12:2825–30.
157. Meier L, van de Geer S, Buhlmann P. The group lasso for logistic regression. J R Stat SocSer B 2008;70(1):53–71.
158. Mairal J, Bach F, Ponce J. Sparse modeling for image and vision processing. Found Trends Comput Graph Vision 2014;8(2-3):85–283.
159. Scutari M. Learning Bayesian networks with the bnlearn R package. J Stat Softw 2010;35(3):1–22.
160. Liaw A, Wiener M. Classification and regression by randomForest. R News 2002;2(3):18–22.
161. Strazar M, Curk T. Learning the kernel matrix via predictive low-rank approximation. arXiv 2016. arXiv:1601.04366.
162. Xu X, Tsang I, Xu D. Soft margin multiple kernel learning. IEEE Trans Neural Netw Learn Syst 2013;24(5):749–61.
163. Varma M, Babu B. More generality in efficient multiple kernel learning. In: International Conference on Machine Learning, 2009, p. 1065–72.
164. Mevik BH, Wehrens R. The pls package: Principal component and partial least squares regression in R. J Stat Softw 2007;18(2):1–23.
165. Chung D, Keles S. Sparse partial least squares classification for high dimensional data. Stat Appl Genet Mol Bioinform 2010;9(1):17.
166. Bouhaddani S, Houwing-Duistermaat J, Jongbloed G, et al. Evaluation of O2PLS in omics data integration. BMC Bioinformatics 2016;17(Suppl 2):S11.
167. Bylesjo M, Rantalainen M, Nicholson J, et al. K-OPLS package: Kernel-based orthogonal projections to latent structures for prediction and interpretation in feature space. BMC Bioinformatics 2008;9:106.
168. Bader BW, Kolda TG, et al. Matlab Tensor Toolbox Version 2.6. Available online 2015.
169. Andersson C, Bro R. The N-way toolbox for MATLAB. Chemometr Intell Lab Syst 2000;52(1):1–4.
170. Rasmussen M, Bro RA. tutorial on the LASSO approach to sparse modelling. Chemometr Intell Lab Syst 2012;119:21–31.
171. Acar E, Papalexakis E, Gurdeniz G, et al. Structure-revealing data fusion. BMC Bioinformatics 2014;15:239.