Login Register Cart 0
Generic placeholder image

Current Bioinformatics

Editor-in-Chief

ISSN (Print): 1574-8936
ISSN (Online): 2212-392X

Back
Journal Home About Journal Editorial Board Journal Insight Current Issue Volumes/Issues
Subscribe
Research Article

Elastic Net Regularized Softmax Regression Methods for Multi-subtype Classification in Cancer

Author(s): Lin Zhang*, Yanling He, Haiting Song, Xuesong Wang, Nannan Lu, Lei Sun and Hui Liu*

Volume 15, Issue 3, 2020

Page: [212 - 224] Pages: 13

DOI: 10.2174/1574893613666181112141724

Price: $65

Abstract

Background: Various regularization methods have been proposed to improve the prediction accuracy in cancer diagnosis. Elastic net regularized logistic regression has been widely adopted for cancer classification and gene selection in genetics and molecular biology but is commonly applied to binary classification and regression. However, usually, the cancer subtypes can be more, and most likely cannot be decided precisely.

Objective: Besides the multi-class issue, the feature selection problem is also a critical problem for cancer subtype classification.

Methods: An Elastic Net Regularized Softmax Regression (ENRSR) for multi-classification is put forward to tackle the multiple classification issue. As an extension of elastic net regularized logistic regression, ENRSR enforces structure sparsity and ‘grouping effect’ for gene selection based on gene expression data, which may exhibit high correlation. The sparsity structure and ‘grouping effect’ help to select more propriate discriminable features for multi-classification.

Result: It is demonstrated that ENRSR gains more accurate and robust performance compared to the other 6 competing algorithms (K-means, Hierarchical Clustering, Expectation Maximization, Nonnegative Matrix Factorization, Support Vector Machine and Random Forest) in predicting cancer subtypes both on simulation data and real cancer gene expression data in terms of F measure.

Conclusion: Our proposed ENRSR method is a reliable regularized softmax regression for multisubtype classification.

Keywords: regularization, softmax regression, elastic net, multiple classification, gene selection, cancer.

« Previous Next »
Graphical Abstract

[1]
Nair VS, Maeda LS, Ioannidis JPA. Clinical outcome prediction by microRNAs in human cancer: a systematic review. J Natl Cancer Inst 2012; 104(7): 528-40.
[http://dx.doi.org/10.1093/jnci/djs027] [PMID: 22395642]
[2]
Wei JS, Greer BT, Westermann F, et al. Prediction of clinical outcome using gene expression profiling and artificial neural networks for patients with neuroblastoma. Cancer Res 2004; 64(19): 6883-91.
[http://dx.doi.org/10.1158/0008-5472.CAN-04-0695] [PMID: 15466177]
[3]
Zhang W, Wan YW, Allen GI, Pang K, Anderson ML, Liu Z. Molecular pathway identification using biological network-regularized logistic models. BMC Genomics 2013; 14(Suppl. 8): S7.
[http://dx.doi.org/10.1186/1471-2164-14-S8-S7] [PMID: 24564637]
[4]
Algamal ZY, Lee MH. Regularized logistic regression with adjusted adaptive elastic net for gene selection in high dimensional cancer classification. Comput Biol Med 2015; 67: 136-45.
[http://dx.doi.org/10.1016/j.compbiomed.2015.10.008] [PMID: 26520484]
[5]
Ma S, Huang J. Penalized feature selection and classification in bioinformatics. Brief Bioinform 2008; 9(5): 392-403.
[http://dx.doi.org/10.1093/bib/bbn027] [PMID: 18562478]
[6]
Kastrin A, Peterlin B. Rasch-based high-dimensionality data reduction and class prediction with applications to microarray gene expression data. Expert Syst Appl 2010; 37: 5178-85.
[http://dx.doi.org/10.1016/j.eswa.2009.12.074]
[7]
Chandra B, Gupta M. An efficient statistical feature selection approach for classification of gene expression data. J Biomed Inform 2011; 44(4): 529-35.
[http://dx.doi.org/10.1016/j.jbi.2011.01.001] [PMID: 21241823]
[8]
Kalina J. Classification methods for high-dimensional genetic data. Biocybern Biomed Eng 2014; 34: 10-8.
[http://dx.doi.org/10.1016/j.bbe.2013.09.007]
[9]
Lotfi E, Keshavarz A. Gene expression microarray classification using PCA-BEL. Comput Biol Med 2014; 54: 180-7.
[http://dx.doi.org/10.1016/j.compbiomed.2014.09.008] [PMID: 25282708]
[10]
Algamal ZY, Lee MH. Penalized logistic regression with the adaptive LASSO for gene selection in high-dimensional cancer classification. Expert Syst Appl 2015; 42: 9326-32.
[http://dx.doi.org/10.1016/j.eswa.2015.08.016]
[11]
Zheng CH, Chong YW, Wang HQ. Gene selection using independent variable group analysis for tumor classification. Neural Comput Appl 2011; 20: 161-70.
[http://dx.doi.org/10.1007/s00521-010-0513-2]
[12]
Zheng S, Liu W. An experimental comparison of gene selection by Lasso and Dantzig selector for cancer classification. Comput Biol Med 2011; 41(11): 1033-40.
[http://dx.doi.org/10.1016/j.compbiomed.2011.08.011] [PMID: 21955335]
[13]
Weston J, Mukherjee S, Chapelle O, Pontil M, Poggio T, Vapnik V. Feature selection for SVMs. Adv Neural Inf Process Syst 2001; 13: 668-74.
[14]
Chen Y, Lin C. Combining SVMs with various feature selection strategies. Studies in Fuzziness & Soft Computing 2006; 207: 315-24.
[http://dx.doi.org/10.1007/978-3-540-35488-8_13]
[15]
Tan M, Wang L, Tsang IW, Eds. Learning sparse svm for feature selection on very high dimensional datasets. Proceedings of the 27th international conference on machine learning. June 21-25; Haifa, Israel. Heidelberg: Springer-Verlag 2010.
[16]
Lazar C, Taminau J, Meganck S, et al. A survey on filter techniques for feature selection in gene expression microarray analysis. IEEE/ACM Trans Comput Biol Bioinformatics 2012; 9(4): 1106-19.
[http://dx.doi.org/10.1109/TCBB.2012.33] [PMID: 22350210]
[17]
Dudoit S, Fridlyand S, Speed TP. Comparison of discrimination methods for the classification of tumors using gene expression data. J Am Stat Assoc 2002; 97: 77-87.
[http://dx.doi.org/10.1198/016214502753479248]
[18]
Li T, Zhang C, Ogihara M. A comparative study of feature selection and multiclass classification methods for tissue classification based on gene expression. Bioinformatics 2004; 20(15): 2429-37.
[http://dx.doi.org/10.1093/bioinformatics/bth267] [PMID: 15087314]
[19]
Ding C, Peng H. Minimum redundancy feature selection from microarray gene expression data. J Bioinform Comput Biol 2005; 3(2): 185-205.
[http://dx.doi.org/10.1142/S0219720005001004] [PMID: 15852500]
[20]
Lee JW, Lee JB, Park M, Song SH. An extensive evaluation of recent classification tools applied to microarray data. Comput Stat Data Anal 2005; 48: 869-85.
[http://dx.doi.org/10.1016/j.csda.2004.03.017]
[21]
Monari G, Dreyfus G. Withdrawing an example from the training set: an analytic estimation of its effect on a nonlinear parameterized model. Neurocomputing Letters 2000; 35: 195-201.
[http://dx.doi.org/10.1016/S0925-2312(00)00325-8]
[22]
Rivals I, Personnaz L. MLPs (mono-layer polynomials and multi-layer perceptrons) for nonlinear modeling. J Mach Learn Res 2003; 3: 1383-98.
[23]
Guyon I, Elisseff A. An Introduction to variable and feature selection. J Mach Learn Res 2003; 3: 1157-82.
[24]
Zou H, Hastie T. Regularization and variable selection via the elastic net. J R Stat Soc Series B Stat Methodol 2005; 67: 301-20.
[http://dx.doi.org/10.1111/j.1467-9868.2005.00503.x]
[25]
De Mol C, De Vito E, Rosasco L. Elastic-net regularization in learning theory. J Complexity 2009; 25: 201-30.
[http://dx.doi.org/10.1016/j.jco.2009.01.002]
[26]
Ogutu JO, Schulz-Streeck T, Piepho H-P, Eds. Genomic selection using regularized linear regression models: ridge regression, lasso, elastic net and their extensions.Proceedings of the 15th European workshop on QTL mapping and marker assisted selection (QTLMAS) May 19-20. Rennes, France 2011.
[http://dx.doi.org/10.1186/1753-6561-6-S2-S10]
[27]
Winham S, Wang C, Motsinger-Reif AA. A comparison of multifactor dimensionality reduction and L1-penalized regression to identify gene-gene interactions in genetic association studies. Stat Appl Genet Mol Biol 2011; 10: 4.
[http://dx.doi.org/10.2202/1544-6115.1613] [PMID: 21291414]
[28]
Nan XF, Wang N, Gong P, Zhang CY, Chen YX, Wilkins D. Biomarker discovery using 1-norm regularization for multiclass earthworm microarray gene expression data. Neurocomputing 2012; 92: 36-43.
[http://dx.doi.org/10.1016/j.neucom.2011.09.035]
[29]
Barretina J, Caponigro G, Stransky N, et al. The Cancer Cell Line Encyclopedia enables predictive modelling of anticancer drug sensitivity. Nature 2012; 483(7391): 603-7.
[http://dx.doi.org/10.1038/nature11003] [PMID: 22460905]
[30]
Peng HY, Fu YL, Liu JS, Fang X, Jiang CF. Optimal gene subset selection using the modified SFFS algorithm for tumor classification. Neural Comput Appl 2013; 23: 1531-8.
[http://dx.doi.org/10.1007/s00521-012-1148-2]
[31]
Kamkar I, Gupta SK, Phung D, Venkatesh S. Stable feature selection for clinical prediction: exploiting ICD tree structure using Tree-Lasso. J Biomed Inform 2015; 53: 277-90.
[http://dx.doi.org/10.1016/j.jbi.2014.11.013] [PMID: 25500636]
[32]
Hoerl AE, Kennard RW. Ridge regression biased estimation for non-orthogonal problems. Technometrics 1970; 8: 27-51.
[33]
Tibshirani R. Regression shrinkage and selection via the lasso. J R Stat Soc Series B Stat Methodol 1996; 58: 267-88.
[34]
Liu Z, Jiang F, Tian G, et al. Sparse logistic regression with Lp penalty for biomarker identification. Stat Appl Genet Mol Biol 2007. 6e6
[http://dx.doi.org/10.2202/1544-6115.1248] [PMID: 17402921]
[35]
Li JT, Jia YM, Zhao ZH. Partly adaptive elastic net and its application to microarray classification. Neural Comput Appl 2013; 22: 1193-200.
[http://dx.doi.org/10.1007/s00521-012-0885-6]
[36]
Mitov V, Claassen M. A fused elastic net logistic regression model for multi-task binary classification. arXiv preprint arXiv:13127750 [Internet] 2013 Available from:. https://arxiv.org/abs/1312.7750
[37]
Zhao C, Deshwar AG, Morris Q. Relapsing-remitting multiple sclerosis classification using elastic net logistic regression on gene expression data. Syst Biomed 2013; 1: 247-53.
[http://dx.doi.org/10.4161/sysb.26131]
[38]
Kim M, Banerjee S, Park SM, Pathak J, Eds. Improving risk prediction for depression via Elastic Net regression-Results from Korea National Health Insurance Services Data. AMIA Annual Symposium Proceedings. Nov 4-8; Chicago, USA. Washington, D.C.: American Medical Informatics Association 2016.
[39]
Liu W, Li Q. An efficient elastic net with regression coefficients method for variable selection of spectrum data. PLoS One 2017; 12(2) e0171122
[http://dx.doi.org/10.1371/journal.pone.0171122] [PMID: 28152003]
[40]
Gonzales GB, De Saeger S. Elastic net regularized regression for time-series analysis of plasma metabolome stability under sub-optimal freezing condition. Sci Rep 2018; 8(1): 3659.
[http://dx.doi.org/10.1038/s41598-018-21851-7] [PMID: 29483546]
[41]
Liang Y, Liu C, Luan XZ, et al. Sparse logistic regression with a L1/2 penalty for gene selection in cancer classification. BMC Bioinformatics 2013; 14: 198.
[http://dx.doi.org/10.1186/1471-2105-14-198] [PMID: 23777239]
[42]
Gourevitch B, Le Bouquin-Jeannes R. K-means clustering method for auditory evoked potentials selection. Med Biol Eng Comput 2003; 41(4): 397-402.
[http://dx.doi.org/10.1007/BF02348081] [PMID: 12892361]
[43]
Kaneko H, Suzuki SS, Okada J, Akamatsu M. Multineuronal spike classification based on multisite electrode recording, whole-waveform analysis, and hierarchical clustering. IEEE Trans Biomed Eng 1999; 46(3): 280-90.
[http://dx.doi.org/10.1109/10.748981] [PMID: 10097463]
[44]
Slatkin M, Excoffier L. Testing for linkage disequilibrium in genotypic data using the Expectation-Maximization algorithm. Heredity 1996; 76(Pt 4): 377-83.
[http://dx.doi.org/10.1038/hdy.1996.55] [PMID: 8626222]
[45]
Sajda P, Du S, Brown TR, et al. Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain. IEEE Trans Med Imaging 2004; 23(12): 1453-65.
[http://dx.doi.org/10.1109/TMI.2004.834626] [PMID: 15575404]
[46]
Cortes C, Vapnik V. Support-vector networks. Mach Learn 1995; 20: 273-370.
[http://dx.doi.org/10.1007/BF00994018]
[47]
Díaz-Uriarte R, Alvarez de Andrés S. Gene selection and classification of microarray data using random forest. BMC Bioinformatics 2006; 7: 3.
[http://dx.doi.org/10.1186/1471-2105-7-3] [PMID: 16398926]
[48]
Combettes PL, Wajs VR. Signal recovery by proximal forward-backward splitting. Multiscale Model Simul 2005; 4: 1168-200.
[http://dx.doi.org/10.1137/050626090]
[49]
Friedman J, Hastie T, Höfling H, Tibshirani R. Pathwise coordinate optimization. Ann Appl Stat 2007; 1: 302-32.
[http://dx.doi.org/10.1214/07-AOAS131]
[50]
D W. E B; R Rf. Action recognition from arbitrary views using 3D exemplar. Proceedings of IEEE International Conference on Computer Vision. 1-7.
[51]
Chen C, Peng J, Sun SR, Peng CW, Li Y, Pang DW. Tapping the potential of quantum dots for personalized oncology: current status and future perspectives. Nanomedicine (Lond) 2012; 7(3): 411-28.
[http://dx.doi.org/10.2217/nnm.12.9] [PMID: 22385199]
[52]
Goldhirsch A, Winer EP, Coates AS, et al. Panel members. Personalizing the treatment of women with early breast cancer: highlights of the St Gallen International Expert Consensus on the Primary Therapy of Early Breast Cancer 2013. Ann Oncol 2013; 24(9): 2206-23.
[http://dx.doi.org/10.1093/annonc/mdt303] [PMID: 23917950]
[53]
Chen C, Yuan JP, Wei W, et al. Subtype classification for prediction of prognosis of breast cancer from a biomarker panel: correlations and indications. Int J Nanomedicine 2014; 9: 1039-48.
[http://dx.doi.org/10.2147/IJN.S58270] [PMID: 24591826]
[54]
Chow KH, Factor RE, Ullman KS. The nuclear envelope environment and its cancer connections. Nat Rev Cancer 2012; 12(3): 196-209.
[http://dx.doi.org/10.1038/nrc3219] [PMID: 22337151]
[55]
Carpenter RL, Lo HW. Regulation of Apoptosis by HER2 in Breast Cancer. J Carcinog Mutagen 2013; 2013(Suppl. 7): 300.
[PMID: 27088047]
[56]
Huang W, Sherman BT, Lempicki RA. Systematic and integrative analysis of large gene lists using DAVID bioinformatics resources. Nat Protoc 2009; 4(1): 44-57.
[http://dx.doi.org/10.1038/nprot.2008.211] [PMID: 19131956]
[57]
Kafri M, Metzl-Raz E, Jona G, Barkai N. The Cost of Protein Production. Cell Rep 2016; 14(1): 22-31.
[http://dx.doi.org/10.1016/j.celrep.2015.12.015] [PMID: 26725116]
[58]
Mukhopadhyay A, Bandyopadhyay S, Maulik U. Multi-class clustering of cancer subtypes through SVM based ensemble of pareto-optimal solutions for gene marker identification. PLoS One 2010; 5(11) e13803
[http://dx.doi.org/10.1371/journal.pone.0013803] [PMID: 21103052]

Rights & Permissions Print Cite
Article Metrics
8
© 2024 Bentham Science Publishers | Privacy Policy