Sparse Projection Matrix Approximation and Its Applications

This letter introduces a sparse regularized projection matrix approximation (SPMA) model to recover cluster structures from affinity matrices. The model is formulated as a projection approximation problem with an entry-wise sparsity penalty to encourage sparse solutions. We propose two algorithms to solve this problem: one involves direct optimization on the Stiefel manifold using the Cayley transformation, while the other employs the Alternating Direction Method of Multipliers (ADMM). Numerical experiments on synthetic and real-world datasets demonstrate that our regularized projection matrix approximation approach significantly outperforms state-of-the-art methods in clustering accuracy and performance.