Regression problem is currently a popular research topic in the field of machine learning. However, most existing research directly performs linear classification on the data after simple preprocessing, or performs classification after feature selection. It usually does not take into account the characteristics of the sample itself, especially for data that is linearly inseparable in original dimensional space and often produces unsatisfactory classification performance. Furthermore, the method of simply mapping the data into a kernel space using kernel trick before classification makes data classification more complex. It also results in unsatisfactory classification performance. In this paper, a simple yet effective semi-supervised Kernel discriminative Low-Rank Ridge Regression (KLRRR) model is proposed for data classification, which unifies kernel trick and discriminant subspace projection together. Specifically, the data is first mapped into kernel space to deal with the linear inseparability problem in original dimensional space, and then the projection matrix in the least square regression is decomposed into the product of two factor matrices to complete the joint discriminant subspace projection and regression. Experiments on 12 benchmark data sets show that the proposed KLRRR model greatly improves the classification performance in comparison with some state-of-the-arts.

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