On the Performance of Variable Selection and Classification via Rank-Based Classifier

Md Showaib Rahman Sarker, Michael Pokojovy and Sangjin Kim
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Md Showaib Rahman Sarker: Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA
Michael Pokojovy: Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA
Sangjin Kim: Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968, USA

Mathematics, 2019, vol. 7, issue 5, 1-16

Abstract: In high-dimensional gene expression data analysis, the accuracy and reliability of cancer classification and selection of important genes play a very crucial role. To identify these important genes and predict future outcomes (tumor vs. non-tumor), various methods have been proposed in the literature. But only few of them take into account correlation patterns and grouping effects among the genes. In this article, we propose a rank-based modification of the popular penalized logistic regression procedure based on a combination of ? 1 and ? 2 penalties capable of handling possible correlation among genes in different groups. While the ? 1 penalty maintains sparsity, the ? 2 penalty induces smoothness based on the information from the Laplacian matrix, which represents the correlation pattern among genes. We combined logistic regression with the BH-FDR (Benjamini and Hochberg false discovery rate) screening procedure and a newly developed rank-based selection method to come up with an optimal model retaining the important genes. Through simulation studies and real-world application to high-dimensional colon cancer gene expression data, we demonstrated that the proposed rank-based method outperforms such currently popular methods as lasso, adaptive lasso and elastic net when applied both to gene selection and classification.

Keywords: gene-expression data; ? 2 ridge; ? 1 lasso; adapative lasso; elastic net; BH-FDR; Laplacian matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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