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 ($δ_j^h = \frac{\bar{x}_j^h}{(σ_j^h)^2}$) 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 ($θ^{h^{(t)}} = \frac{d_h^{(t)}}{n}$). 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.