Implicit Bernstein graph filtering for scalable multiple kernel clustering

Jiachen Zhang

doi:10.1016/j.neucom.2026.135320

Implicit Bernstein graph filtering for scalable multiple kernel clustering

2026-10-05

0

PRE

AI

DOI：10.1016/j.neucom.2026.135320

Original

Original request for help

Save

Abstract

En 中文

Unsupervised multiple kernel clustering (MKC) requires high-order graph spectral filtering across heterogeneous kernel graphs, but faces two fundamental obstacles: dense consensus operator materialization and unstable filter parameterization without label supervision. We propose implicit Bernstein graph filtering (IBGF), which treats each kernel-induced graph as a fixed spectral operator and realizes multi-graph filtering through sparse recursive Laplacian-vector products on a shared low-rank embedding, never explicitly constructing the dense consensus operator. Graph filters are parameterized by Bernstein polynomial bases on Laplacians whose spectra are scaled to [0,1] . Under the nonnegative unit-norm coefficient representation guaranteed by the Perron–Frobenius structure of the coefficient update, the resulting spectral responses are nonnegative and bounded, while the graph-specific coefficient updates remain compact. We further establish a bandwise spectral-energy result showing that low-frequency preservation amplifies cluster-smooth structures relative to perturbations, and prove ascent-preserving embedding updates and objective convergence. After sparse graph construction, the alternating optimization has near-linear per-iteration complexity for fixed small graph and filter parameters. We explicitly distinguish this iterative complexity from the potentially quadratic cost of forming full source kernels from raw features. Experiments on nine benchmark datasets demonstrate a favorable trade-off between clustering quality and computational efficiency. Code is at https://github.com/zjc-web/IBGF .

Keywords:

Graph spectral filtering

Multiple kernel clustering

Bernstein polynomials

Operator realization

Kernel-induced graphs

Implicit Bernstein graph filtering for scalable multiple kernel clustering

Abstract

Journal

Organization

Cited Papers