### 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 |
---|---|

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

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*Proceedings - 12th IEEE International Conference on Data Mining, ICDM 2012.*, 6413822, pp. 978-983, 12th IEEE International Conference on Data Mining, ICDM 2012, Brussels, Belgium, 12/10/12. https://doi.org/10.1109/ICDM.2012.38

**Metric learning from relative comparisons by minimizing squared residual.** / Liu, Eric Yi; Guo, Zhishan; Zhang, Xiang; Jojic, Vladimir; Wang, Wei.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Metric learning from relative comparisons by minimizing squared residual

AU - Liu, Eric Yi

AU - Guo, Zhishan

AU - Zhang, Xiang

AU - Jojic, Vladimir

AU - Wang, Wei

PY - 2012/12/1

Y1 - 2012/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84874034396&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874034396&partnerID=8YFLogxK

U2 - 10.1109/ICDM.2012.38

DO - 10.1109/ICDM.2012.38

M3 - Conference contribution

AN - SCOPUS:84874034396

SN - 9780769549057

SP - 978

EP - 983

BT - Proceedings - 12th IEEE International Conference on Data Mining, ICDM 2012

ER -