Abstract
Biomarker selection and cancer classification play an important role in knowledge discovery using genomic data. Successful identification of gene biomarkers and biological pathways can significantly improve the accuracy of diagnosis and help machine learning models have better performance on classification of different types of cancer. In this paper, we proposed a LogSum + L2 penalized logistic regression model, and furthermore used a coordinate decent algorithm to solve it. The results of simulations and real experiments indicate that the proposed method is highly competitive among several state-of-the-art methods. Our proposed model achieves the excellent performance in group feature selection and classification problems.
Highlights
Biomarker selection and cancer classification play an important role in knowledge discovery using genomic data
The results of simulations and real experiments indicate that the proposed method is highly competitive among several state-of-the-art methods
We proposed the LogSum + L2 penalized logistic regression model for feature group selection
Summary
In the cancer classification problem with high-dimensional and low-sample size data (p ≫ n),directly solving the logistic model (2) will make overfitting To solve this problem, we need add a regularization term to (2), the sparse logistic regression can be modelled as: p β = argmin l(β) +. The LEN penalty function is given as follows: P(β). Zou and Hastie have proposed the univariate s olution[21] for a LEN penalized regression coefficient as follows: βj = fLEN The univariate half thresholding operator for a L1/2 penalized linear regression coefficient is given as follows: βj = Half (wj, ) =. The univariate half thresholding operator for the HLR penalized linear regression coefficient is as follows: βj = HLR(wj,. We could rewrite the penalty function of the LogSum regularization as follows:.
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