Non-integer norm regularized logistic regression

In the task of learning from gene expression profiling using microarray techniques, microarray gene expression data is usually highly contaminated by various noises and contain the overwhelming number of genes relative to the number of available samples. Hence, finding efficient and discriminative genes is crucial to cancer classification. However, the problem is NP-complete and brings out a great challenge for machine learning and statistic techniques. In this paper, a class of sparse q-norm regularization terms (0 <; q ≤ 2) are considered for the developing sparse classifiers for determining discriminative genes, and classification algorithm of conjugate gradient q-norm regularization Logistic regression is proposed. This approach was tried on synthetic datasets and bladder, lymphoma and colon benchmark data sets. It obtained encouraging results on those data sets as compared with L1-norm and L2-norm Logistic regression.