Parameter-free entropy-regularized multi-view clustering with hierarchical feature selection

Multi-view clustering faces critical challenges in automatically discovering patterns across heterogeneous data while managing high-dimensional features and eliminating irrelevant information. Traditional approaches suffer from manual parameter tuning and lack principled cross-view integration mechanisms. This work introduces two complementary algorithms: AMVFCM-U and AAMVFCM-U, providing a unified parameter-free framework. Our approach replaces fuzzification parameters with entropy regularization terms that enforce adaptive cross-view consensus. The core innovation employs signal-to-noise ratio based regularization ($\delta_j^h = \frac{\bar{x}_j^h}{(\sigma_j^h)^2}$) for principled feature weighting with convergence guarantees, coupled with dual-level entropy terms that automatically balance view and feature contributions. AAMVFCM-U extends this with hierarchical dimensionality reduction operating at feature and view levels through adaptive thresholding ($\theta^{h^{(t)}} = \frac{d_h^{(t)}}{n}$). Evaluation across five diverse benchmarks demonstrates superiority over 15 state-of-the-art methods. AAMVFCM-U achieves up to 97% computational efficiency gains, reduces dimensionality to 0.45% of original size, and automatically identifies critical view combinations for optimal pattern discovery.

Bi-Level Multi-View fuzzy Clustering with Exponential Distance

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.

Rectified Gaussian kernel multi-view k-means clustering

In this paper, we show two new variants of multi-view k-means (MVKM) algorithms to address multi-view data. The general idea is to outline the distance between $h$-th view data points $x_i^h$ and $h$-th view cluster centers $a_k^h$ in a different manner of centroid-based approach. Unlike other methods, our proposed methods learn the multi-view data by calculating the similarity using Euclidean norm in the space of Gaussian-kernel, namely as multi-view k-means with exponent distance (MVKM-ED). By simultaneously aligning the stabilizer parameter $p$ and kernel coefficients $\beta^h$, the compression of Gaussian-kernel based weighted distance in Euclidean norm reduce the sensitivity of MVKM-ED. To this end, this paper designated as Gaussian-kernel multi-view k-means (GKMVKM) clustering algorithm. Numerical evaluation of five real-world multi-view data demonstrates the robustness and efficiency of our proposed MVKM-ED and GKMVKM approaches.