Learning Distance Functions using Equivalence Relations

We address the problem of learning distance metrics using side-information in the form of groups of "similar" points. We propose to use the RCA algorithm, which is a simple and efficient algorithm for learning a full ranked Mahalanobis metric (Shental et al., 2002). We first show that RCA obtains the solution to an interesting optimization problem, founded on an information theoretic basis. If the Mahalanobis matrix is allowed to be singular, we show that Fisher's linear discriminant followed by RCA is the optimal dimensionality reduction algorithm under the same criterion. We then show how this optimization problem is related to the criterion optimized by another recent algorithm for metric learning (Xing et al., 2002), which uses the same kind of side information. We empirically demonstrate that learning a distance metric using the RCA algorithm significantly improves clustering performance, similarly to the alternative algorithm. Since the RCA algorithm is much more ...

• Type: Conference
• Year: 2003
• Where: ICML
• Authors: Aharon Bar-Hillel, Tomer Hertz, Noam Shental, Daphna Weinshall
• Keywords: Dimensionality Reduction Algorithm, Efficient Algorithm, ICML 2003, Machine Learning, RCA Algorithm