Low-Rank Similarity Metric Learning in High Dimensions

Metric learning has become a widespreadly used tool in machine learning. To reduce expensive costs brought in by increasing dimensionality, low-rank metric learning arises as it can be more economical in storage and computation. However, existing low-rank metric learning algorithms usually adopt nonconvex objectives, and are hence sensitive to the choice of a heuristic low-rank basis. In this paper, we propose a novel low-rank metric learning algorithm to yield bilinear similarity functions. This algorithm scales linearly with input dimensionality in both space and time, therefore applicable to high-dimensional data domains. A convex objective free of heuristics is formulated by leveraging trace norm regularization to promote low-rankness. Crucially, we prove that all globally optimal metric solutions must retain a certain low-rank structure, which enables our algorithm to decompose the high-dimensional learning task into two steps: an SVD-based projection and a metric learning proble...

• Type: Journal
• Year: 2015
• Where: AAAI
• Authors: Wei Liu, Cun Mu, Rongrong Ji, Shiqian Ma, John R. Smith, Shih-Fu Chang
• Keywords: AAAI 2015, Intelligent Agents