Gene Shaving using influence function of a kernel method

Identifying significant subsets of the genes, gene shaving is an essential and challenging issue for biomedical research for a huge number of genes and the complex nature of biological networks,. Since positive definite kernel based methods on genomic information can improve the prediction of diseases, in this paper we proposed a new method, "kernel gene shaving (kernel canonical correlation analysis (kernel CCA) based gene shaving). This problem is addressed using the influence function of the kernel CCA. To investigate the performance of the proposed method in a comparison of three popular gene selection methods (T-test, SAM and LIMMA), we were used extensive simulated and real microarray gene expression datasets. The performance measures AUC was computed for each of the methods. The achievement of the proposed method has improved than the three well-known gene selection methods. In real data analysis, the proposed method identified a subsets of $210$ genes out of $2000$ genes. The network of these genes has significantly more interactions than expected, which indicates that they may function in a concerted effort on colon cancer.Comment: 14 pages, 6 figures, submitted to ICCIT2018, Banglades

Gene-Gene association for Imaging Genetics Data using Robust Kernel Canonical Correlation Analysis

In genome-wide interaction studies, to detect gene-gene interactions, most methods are divided into two folds: single nucleotide polymorphisms (SNP) based and gene-based methods. Basically, the methods based on the gene are more effective than the methods based on a single SNP. Recent years, while the kernel canonical correlation analysis (Classical kernel CCA) based U statistic (KCCU) has proposed to detect the nonlinear relationship between genes. To estimate the variance in KCCU, they have used resampling based methods which are highly computationally intensive. In addition, classical kernel CCA is not robust to contaminated data. We, therefore, first discuss robust kernel mean element, the robust kernel covariance, and cross-covariance operators. Second, we propose a method based on influence function to estimate the variance of the KCCU. Third, we propose a nonparametric robust KCCU method based on robust kernel CCA, which is designed for contaminated data and less sensitive to noise than classical kernel CCA. Finally, we investigate the proposed methods to synthesized data and imaging genetic data set. Based on gene ontology and pathway analysis, the synthesized and genetics analysis demonstrate that the proposed robust method shows the superior performance of the state-of-the-art methods.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0556

Robust Kernel (Cross-) Covariance Operators in Reproducing Kernel Hilbert Space toward Kernel Methods

To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel cross-covariance operator (kernel CCO). They are sensitive to contaminated data, even when using bounded positive definite kernels. First, we propose robust kernel covariance operator (robust kernel CO) and robust kernel crosscovariance operator (robust kernel CCO) based on a generalized loss function instead of the quadratic loss function. Second, we propose influence function of classical kernel canonical correlation analysis (classical kernel CCA). Third, using this influence function, we propose a visualization method to detect influential observations from two sets of data. Finally, we propose a method based on robust kernel CO and robust kernel CCO, called robust kernel CCA, which is designed for contaminated data and less sensitive to noise than classical kernel CCA. The principles we describe also apply to many kernel methods which must deal with the issue of kernel CO or kernel CCO. Experiments on synthesized and imaging genetics analysis demonstrate that the proposed visualization and robust kernel CCA can be applied effectively to both ideal data and contaminated data. The robust methods show the superior performance over the state-of-the-art methods