Similarity Metric оf Categorical Distributions for Topic Modeling Problems with Akin Categories

Abstract

Estimating a level of similarity of two objects is a common problem in pattern recognition, clustering, and classification. Among these problems can be reviewer recommendation, similar text documents analysis, human pose detection in video, species distribution clustering, recommendation in internet-shops etc. In case of categorical attributes an object is described as a distribution of membership degrees over categories. Similarity metrics of such distributions are usually defined as a superposition of objects` similarities for each category. Most often it is a sum of similarities in separate categories. In addition to that each category is considered independently and in isolation the others. Some practical problems have categories that are akin. Therefore, it is expedient to consider objects` similarity not only directly, as a similarity between equivalent categories, but it is also necessary to consider an indirect similarity, cross-similarity through akin categories. It is such similarity metric of two categorical distributions that accounts for the kinship of different categories is proposed in this paper. The metric has two components. The first component is defined as Czekanowski metric. It defines a direct similarity of categorical distributions as a sum of intersection of distributions` membership degrees of two objects. After the intersection the remaining residuals are accounted for in the second component of the metric. The second metric`s component is defined as element-wise product of two matrices: matrix of residuals composition memberships of two categorical distributions and matrix of categories` paired kinship. It is assumed that kinship indices for each pair of categories are known. As a result, with a large number of categories the overall noisy contribution weakly akin categories is prominent. Therefore, it is proposed to filter the noise and account only for contribution strongly akin categories.