### Abstract

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 language | English (US) |
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Title of host publication | Proceedings - 12th IEEE International Conference on Data Mining, ICDM 2012 |

Pages | 978-983 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2012 |

Event | 12th IEEE International Conference on Data Mining, ICDM 2012 - Brussels, Belgium Duration: Dec 10 2012 → Dec 13 2012 |

### Other

Other | 12th IEEE International Conference on Data Mining, ICDM 2012 |
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Country | Belgium |

City | Brussels |

Period | 12/10/12 → 12/13/12 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

## Cite this

*Proceedings - 12th IEEE International Conference on Data Mining, ICDM 2012*(pp. 978-983). [6413822] https://doi.org/10.1109/ICDM.2012.38