Analysis of a similarity measure for non-overlapped data

A similarity measure is a measure evaluating the degree of similarity between two fuzzy data sets and has become an essential tool in many applications including data mining, pattern recognition, and clustering. In this paper, we propose a similarity measure capable of handling non-overlapped data as well as overlapped data and analyze its characteristics on data distributions. We first design the similarity measure based on a distance measure and apply it to overlapped data distributions. From the calculations for example data distributions, we find that, though the similarity calculation is effective, the designed similarity measure cannot distinguish two non-overlapped data distributions, thus resulting in the same value for both data sets. To obtain discriminative similarity values for non-overlapped data, we consider two approaches. The first one is to use a conventional similarity measure after preprocessing non-overlapped data. The second one is to take into account neighbor data information in designing the similarity measure, where we consider the relation to specific data and residual data information. Two artificial patterns of non-overlapped data are analyzed in an illustrative example. The calculation results demonstrate that the proposed similarity measures can discriminate non-overlapped data.