Learning Dynamic Similarity Metric Based on Relative Distance Information and Estimates of Its Retrieval Error

Abstract

We analyze a learning method of weight of attributes in a similarity function for case retrieval by using relative distance information from a user. The relative distance information represents whether a training case is more similar to one case in the case base than to another case in the case base. We give an analysis in a PAC (probably approximately correct)-learning for the method. By using the method, we can efficiently learn weight such that the probability that the error rate of similar case retrieval by using the learned weight is more than ε is at most δ. The sample size of training cases to achieve the above is polynomially bounded in the number of attributes n, the size of case base, ε^<-l> and δ^<-l>, and the running time is polynomially bounded in the size of training cases. We also show experimental results on the sample size and the error rate for similar case retrieval under the assumption of uniform probability distribution over cases. The results indicate that the sample size is approximately 2n/ε on average.