A Relevance-Based Learning Model of Fuzzy Similarity Measures

Abstract

Matching pairs of objects is a fundamental operation in data analysis. However, it requires to define a similarity measure between objects 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 derived from residual implication functions is proposed. Then a model allowing 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.

A unified view of class-selection with probabilistic classifiers

“…In particular, it has been shown in [26] that T-equivalences can be interpreted as similarity measures. In this context, let us consider the equivalence, or similarity, between p(θ (i) |x) and p(θ (i+1) |x).…”

New measures of similarity based on fuzzy implications

“…cludes well-known metrics like Hamming (or Manhattan), Euclidean and Tchebychev (or sup distance), but other metric measures can be included (see [17]). …”

“…For example, geometric measures like Minkowski metric are useful when a priori objective dimensions have to be measured, but they are not effective for other purposes like comparing faces, countries or personalities [31]. The main lack of geometric measures is they have to satisfy a metric axiomatic, which is difficult to fulfill [17,27].…”

“…In this paper we follow the fuzzy logic approach to define similarity, which can be found in [17,18] by using fuzzy implications, the logical bi-implication and aggregation operators. Also, in [4], by defining the fuzzy operators from the concept of algebra of residuated lattice.…”

“…In the literature, this kind of similarity measures are based on T-equalities [11,17]. A T-equality is a T-equivalence, and hence includes the axiom of Ttransitivity.…”