Abstract: The support vector machine(SVM) is one of the most concise and efficient classification methods in machine learning. Traditional SVMs mainly handle with binary classification problems by maximizing the smallest margins. However, the real-world data are much more complicated. On the one hand, the label set usually has more than two categories, so SVMs need to be generalized for solving multi-category problems reasonably. On the other hand, there may exist one special variable which should be singled out to preserve its effect on the final results from other variables such as age in bioscience field. We name such a special variable as targeted variable. In this work, in order to take both aspects mentioned above into consideration, targeted local angle-based multi-category support vector machine(TLAMSVM) is proposed. This new model not only solves multi-category problems but also pays special attention to targeted variable. Moreover, TLAMSVM solves multi-classification in the framework of angle-based method, which provides a better interpretation from the geometrical viewpoint, and it uses local smoothing method to pool the information of targeted variable. In order to validate the classification effect of TLAMSVM model, we apply it to both simulated and real data sets, respectively, and get the expected results in numerical experiments.

Key words: local smoothing, multi-category support vector machine, angle-based maximum margin classification framework