We consider the problem of learning classifiers from samples which have additional features that are absent due to noise or corruption of measurement. The common approach for handling missing features in discriminative models is first to complete their unknown values, and then a standard classification algorithm is employed over the completed data. In this paper, an algorithm which aims to maximize the margin of each sample in its own relevant subspace is proposed. We show how incomplete data can be classified directly without completing any missing features in a large-margin learning framework. Moreover, according to the theory of optimal kernel function, we proposed an optimal kernel function which is a convex composition of a set of linear kernel function to measure the similarity between additional features of each two samples. Based on the geometric interpretation of the margin, we formulate an objective function to maximize the margin of each sample in its own relevant subspace. In this formulation, we make use of the structural parameters trained from existing features and optimize the structural parameters trained from additional features only. A two-step iterative procedure for solving the objective function is proposed. By avoiding the pre-processing phase in which the data is completed, our algorithm could offer considerable computational saving. We demonstrate our results on a large number of standard benchmarks from UCI and the results show that our algorithm can achieve better or comparable classification accuracy compared to the existing algorithms.
['Xinwang Liu', 'Jianping Yin', 'En Zhu', 'Guomin Zhang', 'Yubin Zhan', 'Miaomiao Li']
A Large Margin Classifier with Additional Features