Adaptive Consensus Kernel Clustering for Manifold-Structured Data

초록

Clustering is an essential task in unsupervised learning, but it remains challenging when data lie on non-linear manifolds with non-uniform sampling densities. Traditional methods such as k-means and fixed-bandwidth spectral clustering can struggle to capture complex geometric structures and are sensitive to bandwidth or hyperparameter choices. This paper presents Adaptive Consensus Kernel Clustering (ACKC), a method that constructs multiple locally adaptive affinity matrices at different neighborhood scales and combines them through a consensus process. Our theoretical analysis shows that ACKC reliably recovers manifold cluster structures under mild Lipschitz and bounded-curvature assumptions, achieving sample complexity of the order of log (1 / d) / ?2. Extensive experiments on synthetic and real-world datasets, including Gaussian mixtures, high-dimensional sparse data, Swiss roll, spirals, and S-curve manifolds, demonstrate that ACKC outperforms both k-means and fixed-bandwidth spectral clustering, exhibiting increased robustness to hyperparameter choices and improved recovery of non-linear manifolds. We also provide empirical evidence for the spectral gap properties that explain ACKC's performance advantages and illustrate that our method remains stable in parameter variations, and noise levels.