Fuzzy Comparison of Frequency Distributions

Abstract

Comparing empirical distributions is one of the fundamental tasks in data analysis. We start with a survey of existing statistical approaches to this problem. The current numeric methods are shown to suffer from several limitations, including restrictive assumptions about the underlying distributions and non-use of available domain knowledge. These limitations can be partially overcome via the time-consuming visual examination of frequency histograms by a human expert. In this paper, we present a fuzzy-based method for automating the process of comparing frequency histograms. Our approach builds upon a novel concept of automated perceptions, introduced in our previous work. We use the evolving approach of type-2 fuzzy logic for representing the domain knowledge of human experts. The proposed method provides an automated interpretation of the differences between histogram plots, based on a cognitive model of human perception. The perception-based approach to comparison of frequency histograms is demonstrated on several samples of real-world data.