<p>Existing (dis)similarity measures for mixed data often ignore data distribution and ordering information along numerical and categorical features, respectively, during distance computation. Additionally, combining numerical and categorical (dis)similarities is often done naively, failing to judiciously assign relative weights. This work introduces a unified dissimilarity measure for mixed data (EDMIX) that addresses these challenges. It employs an entropy-based measure (SEND) for numerical attributes which utilizes intra-attribute inhomogeneity efficiently. A Boltzmann’s entropy-based measure (EDMD) is adopted for categorical features, which effectively handles both nominal and ordinal attributes. Decay of attribute weight is analyzed to determine the threshold weights for numerical and categorical parts. Number of attributes whose weights are above the threshold value in each part decides the mixing proportion of the respective parts. Notably, EDMIX requires no input parameters and is adaptable to diversified mixed data. Experimental results highlight its superiority in terms of cluster quality, accuracy, discrimination ability, and execution time across diverse mixed datasets for clustering applications.</p>

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EDMIX: an entropy-based dissimilarity measure to cluster mixed data comprising of numerical–nominal–ordinal attributes

  • Amit Kumar Kar,
  • Amaresh Chandra Mishra,
  • Sraban Kumar Mohanty

摘要

Existing (dis)similarity measures for mixed data often ignore data distribution and ordering information along numerical and categorical features, respectively, during distance computation. Additionally, combining numerical and categorical (dis)similarities is often done naively, failing to judiciously assign relative weights. This work introduces a unified dissimilarity measure for mixed data (EDMIX) that addresses these challenges. It employs an entropy-based measure (SEND) for numerical attributes which utilizes intra-attribute inhomogeneity efficiently. A Boltzmann’s entropy-based measure (EDMD) is adopted for categorical features, which effectively handles both nominal and ordinal attributes. Decay of attribute weight is analyzed to determine the threshold weights for numerical and categorical parts. Number of attributes whose weights are above the threshold value in each part decides the mixing proportion of the respective parts. Notably, EDMIX requires no input parameters and is adaptable to diversified mixed data. Experimental results highlight its superiority in terms of cluster quality, accuracy, discrimination ability, and execution time across diverse mixed datasets for clustering applications.