A Multivariate Fuzzy Weighted K-Modes Algorithm with Probabilistic Distance for Categorical Data

Abstract

Data clustering is a data mining approach that assigns similar data to the same group. Traditionally, cluster similarity considers all attributes equally, but in real-world applications, some attributes may be more important than others. Therefore, this study proposes an algorithm that utilizes multivariate fuzzy weighting to demonstrate the varying importance of each attribute, using a Gini impurity measure for weight assignment. Additionally, the proposed algorithm implements probabilistic distance to reduce sensitivity to noise. Probabilistic distance offers more detailed information and better interpretation than Hamming distance, which ignores attribute positions. Probabilistic distance utilizes information about the attribute?s position within and between clusters. This enhances clustering performance by creating clusters with more similar attributes. Therefore, the proposed Multivariate Fuzzy Weighted K-Modes with Probabilistic Distance for Categorical Data (MFWKM-PD) algorithm, based on the multivariate fuzzy K-modes algorithm, not only considers detailed membership calculations but also considers the varying contributions of attributes and their positions in distance calculation. This study evaluated the proposed MFWKM-PD using several benchmark datasets. The experiments validated that the proposed MFWKM-PD shows promising results compared to other algorithms in terms of accuracy, NMI, and ARI.