Adaptive distance metric learning for clustering

A good distance metric is crucial for unsupervised learning from high-dimensional data. To learn a metric without any constraint or class label information, most unsupervised metric learning algorithms appeal to projecting observed data onto a low-dimensional manifold, where geometric relationships such as local or global pairwise distances are preserved. However, the projection may not necessarily improve the separability of the data, which is the desirable outcome of clustering. In this paper, we propose a novel unsupervised Adaptive Metric Learning algorithm, called AML, which performs clustering and distance metric learning simultaneously. AML projects the data onto a low-dimensional manifold, where the separability of the data is maximized. We show that the joint clustering and distance metric learning can be formulated as a trace maximization problem, which can be solved via an iterative procedure in the EM framework. Experimental results on a collection of benchmark data sets demonstrated the effectiveness of the proposed algorithm.