Document Classification via Nonlinear Metric Learning

Learning a proper distance metric is an important problem in document classification, because the similarities of samples in many problems are usually measured by distance metric. In this paper, we address the nonlinear metric leaning problem with applying in the document classification. First, we propose a new representation about nonlinear metric by using a linear combination of some basic kernels. Second, we give a linear metric learning method by a triplet constraint and k-nearest neighbors, and then we develop it to a nonlinear method based on multiple kernel by above nonlinear metric. Further, the corresponding problem can be rewritten as an unconstrained optimization problem on positive definite matrices groups. At last, to ensure the learned distance matrix must be a positive definite matrix, we provide an improved intrinsic steepest descent algorithm with adaptive step-size to solve this unconstrained optimization. The experimental results show that our proposed method is effective on some document classification problems.