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

arXiv: https://arxiv.org/abs/2507.13417 · HTML: https://mlsanity.com/paper/2507.13417/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 3 of 3)

- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization](https://mlsanity.com/paper/2104.09003/) (2021)
- [Evidential relational clustering using medoids](https://mlsanity.com/paper/1507.04091/) (2015)

## Abstract (arXiv)

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.