Biased p-norm support vector machine for PU learning

• We propose a new version of support vector machine named biased p-norm support vector machine (BPSVM). BPSVM can realize classification and feature selection simultaneously for PU learning problem.
• To realize feature selection, we prove the lower bounds of the optimal solution of BPSVM theoretically. The lower bounds can be used to identify which element should be eliminated.
• We test our BPSVM on text classification data set and phosphoralytion sites prediction sites and the numerical results show the effectiveness of our methods.

In this paper, we propose a new version of support vector machine named biased p-norm support vector machine (BPSVM) involved in learning from positive and unlabeled examples. Compared with the previous works, BPSVM can not only improve the performance of classification but also select relevant features automatically based on estimating theoretically the lower bounds for the nonzero components in the solution to the corresponding optimization problem. Preliminary, numerical results show that our BPSVM is effective in both classification and features selection.