Low-Rank Similarity Metric Learning in High Dimensions


  • Wei Liu IBM T. J. Watson Research Center
  • Cun Mu Columbia University
  • Rongrong Ji Xiamen University
  • Shiqian Ma The Chinese University of Hong Kong
  • John Smith IBM T. J. Watson Research Center
  • Shih-Fu Chang Columbia University




metric learning, similarity, 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 problem with reduced dimensionality. The latter step can be tackled efficiently through employing a linearized Alternating Direction Method of Multipliers. The efficacy of the proposed algorithm is demonstrated through experiments performed on four benchmark datasets with tens of thousands of dimensions.




How to Cite

Liu, W., Mu, C., Ji, R., Ma, S., Smith, J., & Chang, S.-F. (2015). Low-Rank Similarity Metric Learning in High Dimensions. Proceedings of the AAAI Conference on Artificial Intelligence, 29(1). https://doi.org/10.1609/aaai.v29i1.9639



Main Track: Novel Machine Learning Algorithms