Learning to Construct the Learning Space for Scalable Multiple Kernel Clustering

Standard complete multiple kernel clustering (MKC) is infeasible for large-scale data, requiring \(O(n^2)\) storage and \(O(n^3)\) decomposition of \(V\) \(n \times n\) kernel matrices. Scalable MKC methods approximate kernel $K_v$ as $K{H}_v{H}_v^{\top }$ ($K{H}_v\in {\mathbb{R}}^{n\times m}$, $m\ll n$), reducing storage to $O(nm)$ and decomposition to $O(m^3)$. However, existing methods freeze $K{H}_v{H}_v^{\top }$, so as view weights ${\gamma }_v$ update, the combined kernel ${\sum }_v{\gamma }_v^2{K}_v$ diverges from the frozen approximation, degrading clustering performance. To address this limitation, we propose a Learning to Construct the Learning Space for Scalable Multiple Kernel Clustering (LCLS-SMKC) method, which is a space-plasticity method that jointly optimizes the space-shaping parameters and the consensus embedding. Specifically, multi-scale leverage scores select diverse landmarks to cover the kernel space, yielding a more accurate per-view approximation $K{H}_v$. Subsequently, A self-learning dual-mode switch modulates the kernel space to be adaptive to view disparity rather than frozen. For small disparity, an enlarged-disparity space is selected to retain cross-view diversity. For large disparity, a purified space suppresses noise via adaptive joint feature denoising, embedding alignment, and view consistency mining. Furthermore, the dimensionality variation coefficient is embedded into kernel-space parameters, and an error-driven feedback loop updates these space parameters to minimize approximation error to enable adaptive learning. Finally, theoretical analysis establishes guarantees on approximation error, Lyapunov stability, linear convergence, and generalization, while experiments on six diverse datasets confirm consistent superiority over state-of-the-art scalable MKC methods in performance.