weiaaai15

Wei Liu, Cun Mu, Rongrong Ji, Shiqian Ma, John R. Smith, Shih-Fu Chang. Low-Rank Similarity Metric Learning in High Dimensions. In AAAI Conference on Artificial Intelligence (AAAI), Austin, Texas, USA, 2015.

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Abstract

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

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Wei Liu
Rongrong Ji
John_R. Smith
Shih-Fu Chang

BibTex Reference

@InProceedings{weiaaai15,
   Author = {Liu, Wei and Mu, Cun and Ji, Rongrong and Ma, Shiqian and Smith, John R. and Chang, Shih-Fu},
   Title = {Low-Rank Similarity Metric Learning in High Dimensions},
   BookTitle = {AAAI Conference on Artificial Intelligence (AAAI)},
   Address = {Austin, Texas, USA},
   Year = {2015}
}

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