Local Metric Learning Based on Anchor Points for Multimedia Analysis

Distance metric learning has been shown to be an effective and efficient method which can lead to significant improvements in classification, clustering, and retrieval. Conventional metric learning methods which apply a global metric to capture the input features and their correlations are unsuitable for heterogeneous data, whose features vary according to different clusters. Thus, a number of local metric learning methods have been proposed to overcome this limitation. Unfortunately, most of them suffer from over-fitting or need the data set to be under a strong assumption, such as Gaussian distribution. To avoid over-fitting caused by learning local metric matrices separately in the previous researches, we propose a novel local metric learning method in which we learn a metric matrix for each pair of instances as linear combinations of basis metric matrices defined on different clusters of the input space without any assumption for data set. We get the parameters of the linear combinations by using the relationship between direct distance and anchor~distance between a pair of data points. Additionally, we design a novel expectation-maximization based optimization method to learn the linear combinations and basis metric matrices. Experimental results show that our method outperforms state-of-the-art methods on various data sets.