Metric Learning from Relative Comparisons By Minimizing Squared Residual
Recent studies - have suggested using constraints in the form of relative distance comparisons to represent domain knowledge: d(a, b) < d(c, d) where d(·) is the distance function and a, b, c, d are data objects. Such constraints are readily available in many problems where pairwise constraints are not natural to obtain. In this paper we consider the problem of learning a Mahalanobis distance metric from supervision in the form of relative distance comparisons. We propose a simple, yet effective, algorithm that minimizes a convex objective function corresponding to the sum of squared residuals of constraints. We also extend our model and algorithm to promote sparsity in the learned metric matrix. Experimental results suggest that our method consistently outperforms existing methods in terms of clustering accuracy. Furthermore, the sparsity extension leads to more stable estimation when the dimension is high and only a small amount of supervision is given.
E. Y. Liu et al., "Metric Learning from Relative Comparisons By Minimizing Squared Residual," Proceedings of the 12th IEEE International Conference on Data Mining, ICDM (2012, Brussels, Belgium), pp. 978-983, Institute of Electrical and Electronics Engineers (IEEE), Dec 2012.
The definitive version is available at http://dx.doi.org/10.1109/ICDM.2012.38
12th IEEE International Conference on Data Mining, ICDM (2012: Dec. 10-13, Brussels, Belgium)
Keywords and Phrases
Clustering Accuracy; Convex Objectives; Data Objects; Distance Functions; Domain Knowledge; Mahalanobis Distances; Mahalanobis Metric; Metric Learning; Metric Matrix; Model And Algorithms; Pairwise Constraints; Relative Comparisons; Relative Distances
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Article - Conference proceedings
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