A self-adaptive local metric learning method for classification

Abstract

Measuring distance among data point pairs is a necessary step among numerous counts of algorithms in machine learning, pattern recognition and data mining. In the local perspective, the emphasis of all existing supervised metric learning algorithms is to shrink similar data points and to separate dissimilar ones in the local neighborhoods. This provides learning more appropriate distance metric in dealing with the within-class multi modal data. In this article, a new supervised local metric learning method named Self-Adaptive Local Metric Learning Method (SA-LM2) has been proposed. The contribution of this method is in five aspects. First, in this method, learning an appropriate metric and defining the radius of local neighborhood are integrated in a joint formulation. Second, unlike the traditional approaches, SA-LM2 learns the parameter of local neighborhood automatically thorough its formulation. As a result, it is a parameter free method, where it does not require any parameters that would need to be tuned. Third, SA-LM2 is formulated as a SemiDefinite Program (SDP) with a global convergence guarantee. Fourth, this method does not need the similar set S, the focus here is on local areas’ data points and their separation from dissimilar ones. Finally, results of SA-LM2 are less influenced by noisy input data points than the other compared global and local algorithms. Results obtained from different experiments indicate the outperformance of this algorithm over its counterparts.