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Kernel Entropy Component Analysis with Nongreedy L1-Norm Maximization.

ABSTRACT: Kernel entropy component analysis (KECA) is a newly proposed dimensionality reduction (DR) method, which has showed superiority in many pattern analysis issues previously solved by principal component analysis (PCA). The optimized KECA (OKECA) is a state-of-the-art variant of KECA and can return projections retaining more expressive power than KECA. However, OKECA is sensitive to outliers and accused of its high computational complexities due to its inherent properties of L2-norm. To handle these two problems, we develop a new extension to KECA, namely, KECA-L1, for DR or feature extraction. KECA-L1 aims to find a more robust kernel decomposition matrix such that the extracted features retain information potential as much as possible, which is measured by L1-norm. Accordingly, we design a nongreedy iterative algorithm which has much faster convergence than OKECA's. Moreover, a general semisupervised classifier is developed for KECA-based methods and employed into the data classification. Extensive experiments on data classification and software defect prediction demonstrate that our new method is superior to most existing KECA- and PCA-based approaches. Code has been also made publicly available.

SUBMITTER: Ji H

PROVIDER: S-EPMC6204191 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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Kernel Entropy Component Analysis with Nongreedy L1-Norm Maximization.

Ji Haijin H Huang Song S

Computational intelligence and neuroscience 20181014

Kernel entropy component analysis (KECA) is a newly proposed dimensionality reduction (DR) method, which has showed superiority in many pattern analysis issues previously solved by principal component analysis (PCA). The optimized KECA (OKECA) is a state-of-the-art variant of KECA and can return projections retaining more expressive power than KECA. However, OKECA is sensitive to outliers and accused of its high computational complexities due to its inherent properties of L2-norm. To handle thes ...[more]

PMID: 30405708

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Project description:BackgroundThis paper introduces the notion of optimizing different norms in the dual problem of support vector machines with multiple kernels. The selection of norms yields different extensions of multiple kernel learning (MKL) such as L(infinity), L1, and L2 MKL. In particular, L2 MKL is a novel method that leads to non-sparse optimal kernel coefficients, which is different from the sparse kernel coefficients optimized by the existing L(infinity) MKL method. In real biomedical applications, L2 MKL may have more advantages over sparse integration method for thoroughly combining complementary information in heterogeneous data sources.ResultsWe provide a theoretical analysis of the relationship between the L2 optimization of kernels in the dual problem with the L2 coefficient regularization in the primal problem. Understanding the dual L2 problem grants a unified view on MKL and enables us to extend the L2 method to a wide range of machine learning problems. We implement L2 MKL for ranking and classification problems and compare its performance with the sparse L(infinity) and the averaging L1 MKL methods. The experiments are carried out on six real biomedical data sets and two large scale UCI data sets. L2 MKL yields better performance on most of the benchmark data sets. In particular, we propose a novel L2 MKL least squares support vector machine (LSSVM) algorithm, which is shown to be an efficient and promising classifier for large scale data sets processing.ConclusionsThis paper extends the statistical framework of genomic data fusion based on MKL. Allowing non-sparse weights on the data sources is an attractive option in settings where we believe most data sources to be relevant to the problem at hand and want to avoid a "winner-takes-all" effect seen in L(infinity) MKL, which can be detrimental to the performance in prospective studies. The notion of optimizing L2 kernels can be straightforwardly extended to ranking, classification, regression, and clustering algorithms. To tackle the computational burden of MKL, this paper proposes several novel LSSVM based MKL algorithms. Systematic comparison on real data sets shows that LSSVM MKL has comparable performance as the conventional SVM MKL algorithms. Moreover, large scale numerical experiments indicate that when cast as semi-infinite programming, LSSVM MKL can be solved more efficiently than SVM MKL.AvailabilityThe MATLAB code of algorithms implemented in this paper is downloadable from http://homes.esat.kuleuven.be/~sistawww/bioi/syu/l2lssvm.html.

Dataset Information

Kernel Entropy Component Analysis with Nongreedy L1-Norm Maximization.

Publications

Kernel Entropy Component Analysis with Nongreedy L1-Norm Maximization.

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