Soft-ECM: An extension of Evidential C-Means for complex data

TL;DR

Soft-ECM extends Evidential C-Means to effectively cluster complex data types like mixed and time series data using semi-metrics, overcoming limitations of existing belief function-based clustering methods.

Contribution

It introduces Soft-ECM, a novel algorithm that adapts ECM for complex data by utilizing semi-metrics, enabling clustering of non-Euclidean and mixed data types.

Findings

Soft-ECM achieves comparable results to fuzzy clustering on numerical data.

It effectively handles mixed data types.

Demonstrates benefits with semi-metrics like DTW for time series.

Abstract

Clustering based on belief functions has been gaining increasing attention in the machine learning community due to its ability to effectively represent uncertainty and/or imprecision. However, none of the existing algorithms can be applied to complex data, such as mixed data (numerical and categorical) or non-tabular data like time series. Indeed, these types of data are, in general, not represented in a Euclidean space and the aforementioned algorithms make use of the properties of such spaces, in particular for the construction of barycenters. In this paper, we reformulate the Evidential C-Means (ECM) problem for clustering complex data. We propose a new algorithm, Soft-ECM, which consistently positions the centroids of imprecise clusters requiring only a semi-metric. Our experiments show that Soft-ECM present results comparable to conventional fuzzy clustering approaches on numerical data, and we demonstrate its ability to handle mixed data and its benefits when combining fuzzy clustering with semi-metrics such as DTW for time series data.