document: Nonlinear adaptive distance metric learning for clustering A good distance metric is crucial for many data mining tasks . To learn a metric in the unsupervised setting , most metric learning algorithms project observed data to a low-dimensional manifold , where geometric relationships such as pairwise distances are preserved . It can be extended to the nonlinear case by applying the kernel trick , which embeds the data into a feature space by specifying the kernel function that computes the dot products between data points in the feature space . In this paper , we propose a novel unsupervised Nonlinear Adaptive Metric Learning algorithm , called NAML , which performs clustering and distance metric learning simultaneously . NAML firstmaps the data to a high-dimensional space through a kernel function ; then applies a linear projection to find a low-dimensional manifold where the separability of the data is maximized ; and finally performs clustering in the low-dimensional space . The performance of NAML depends on the selection of the kernel function and the projection . We show that the joint kernel learning , dimensionality reduction , and clustering can be formulated as a trace maximization problem , which can be solved via an iterative procedure in the EM framework . Experimental results demonstrated the efficacy of the proposed algorithm .
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