RELIEF Algorithm and Similarity Learning for k-NN

In this paper, we study the links between RELIEF, a well-known feature re-weighting algorithm and SiLA, a similarity learning algorithm. On one hand, SiLA is interested in directly reducing the leave-one-out error or 0− 1 loss by reducing the number of mistakes on unseen examples. On the other hand, it has been shown that RELIEF could be seen as a distance learning algorithm in which a linear utility function with maximum margin was optimized. We first propose here a version of this algorithm for similarity learning, called RBS (for RELIEFBased Similarity learning). As RELIEF, and unlike SiLA, RBS does not try to optimize the leave-one-out error or 0 − 1 loss, and does not perform very well in practice, as we illustrate on several UCI collections. We thus introduce a stricter version of RBS, called sRBS, aiming at relying on a cost function closer to the 0 − 1 loss. Moreover, we also developed Positive, semidefinite (PSD) versions of RBS and sRBS algorithms, where the learned similarity matrix is projected onto the set of PSD matrices. Experiments conducted on several datasets illustrate the different behaviors of these algorithms for learning similarities for kNN classification. The results indicate in particular that the 0 − 1 loss is a more appropriate cost function than the one implicitly used by RELIEF. Furthermore, the projection onto the set of PSD matrices improves the results for RELIEF algorithm only.