Metric learning from relative comparisons by minimizing squared residual

Eric Yi Liu, Zhishan Guo, Xiang Zhang, Vladimir Jojic, Wei Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

41 Scopus citations


Recent studies [1]-[5] 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.

Original languageEnglish (US)
Title of host publicationProceedings - 12th IEEE International Conference on Data Mining, ICDM 2012
Number of pages6
StatePublished - Dec 1 2012
Event12th IEEE International Conference on Data Mining, ICDM 2012 - Brussels, Belgium
Duration: Dec 10 2012Dec 13 2012


Other12th IEEE International Conference on Data Mining, ICDM 2012

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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