Towards Robust Nonlinear Subspace Clustering: A Kernel Learning Approach
This work addresses robustness in nonlinear subspace clustering for data analysis applications, representing a novel paradigm rather than an incremental improvement.
The paper tackles the problem of kernel-based subspace clustering by introducing DKLM, a data-driven method that learns the kernel from data to address limitations like predefined kernel influence and manifold preservation, resulting in improved clustering performance on synthetic and real-world datasets.
Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the influence of predefined kernels on model performance; (ii) the difficulty of preserving the original manifold structures in the nonlinear space; (iii) the dependency of spectral-type strategies on the ideal block diagonal structure of the affinity matrix. This paper presents DKLM, a novel paradigm for kernel-induced nonlinear subspace clustering. DKLM provides a data-driven approach that directly learns the kernel from the data's self-representation, ensuring adaptive weighting and satisfying the multiplicative triangle inequality constraint, which enhances the robustness of the learned kernel. By leveraging this learned kernel, DKLM preserves the local manifold structure of data in a nonlinear space while promoting the formation of an optimal block-diagonal affinity matrix. A thorough theoretical examination of DKLM reveals its relationship with existing clustering paradigms. Comprehensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed method.