Sparse Multiple Kernel Concept Factorization with Adaptive Orthogonal Factors

Concept factorization provides an interpretable route to clustering by expressing latent concepts as combinations of observed samples. Its development in multiple kernel settings, however, remains limited when one simultaneously requires kernel validity, low storage, and mathematically transparent optimization. This paper proposes a sparse multiple kernel concept factorization framework with adaptive orthogonal factors. The framework first constructs sparse positive semi-definite kernel matrices through localized neighborhood regression and then learns a shared nonnegative consensus representation together with kernel-specific orthogonal factors and adaptive kernel weights. The resulting block coordinate procedure contains two closed-form subproblems and one standard multiplicative update. The positive semi-definiteness of the sparse kernels is proved, the exact solutions of the orthogonality-constrained and weight-update blocks are derived, monotonic descent, lower boundedness, and the limiting behavior of the generated objective sequence are analyzed. The computational and storage complexity of the framework are also analyzed. Experiments on nine benchmark datasets, whose sample sizes range from 103 to 2.8×105, show that the proposed method remains competitive in clustering quality while retaining attractive runtime and memory behavior. The paper therefore offers a mathematically explicit and empirically verifiable treatment of sparse multiple kernel concept factorization.