Bi-Level Multi-View fuzzy Clustering with Exponential Distance

TL;DR

This work addresses multi-view clustering by embedding an exponential distance through heat-kernel coefficients, enabling robust, kernel-informed soft clustering across heterogeneous views. It proposes two models: E-MVFCM, a centralized MVC with a shared membership across views and explicit heat-kernel forms, and EB-MVFCM, a bi-level extension that jointly learns feature weights and view weights. The optimization derives closed-form, iterative update rules for common memberships $\mu_{ik}^*$, view weights $v_h$, feature weights $w_j^h$, and per-view centers $A^h$, leveraging Lagrangian multipliers and the proper-time heat-kernel expansion. The methods aim to improve clustering performance on complex MV data, with the heat-kernel coefficient formulation facilitating principled, scalable inference; code for reproducibility is released on GitHub.

Abstract

In this study, we propose extension of fuzzy c-means (FCM) clustering in multi-view environments. First, we introduce an exponential multi-view FCM (E-MVFCM). E-MVFCM is a centralized MVC with consideration to heat-kernel coefficients (H-KC) and weight factors. Secondly, we propose an exponential bi-level multi-view fuzzy c-means clustering (EB-MVFCM). Different to E-MVFCM, EB-MVFCM does automatic computation of feature and weight factors simultaneously. Like E-MVFCM, EB-MVFCM present explicit forms of the H-KC to simplify the generation of the heat-kernel $\mathcal{K}(t)$ in powers of the proper time $t$ during the clustering process. All the features used in this study, including tools and functions of proposed algorithms will be made available at https://www.github.com/KristinaP09/EB-MVFCM.