A Relevance-Based Learning Model of Fuzzy Similarity Measures

Matching pairs of objects is a fundamental operation in data analysis. However, it requires the definition of a similarity measure between objects that are to be matched. The similarity measure may not be adapted to the various properties of each object. Consequently, designing a method to learn a measure of similarity between pairs of objects is an important generic problem in machine learning. In this paper, a general framework of fuzzy logical-based similarity measures based on T-equalities that are derived from residual implication functions is proposed. Then, a model that allows us to learn the parametric similarity measures is introduced. This is achieved by an online learning algorithm with an efficient implication-based loss function. Experiments on real datasets show that the learned measures are efficient at a wide range of scales and achieve better results than existing fuzzy similarity measures. Moreover, the learning algorithm is fast so that it can be used in real-world applications, where computation times are a key feature when one chooses an inference system.