Online joint graph topology and dictionary learning for enhanced data representation

Abstract

Laplacian-Regularized Dictionary Learning (LRDL) demonstrates remarkable performance in capturing structured representations from data by leveraging underlying graph information. However, in real-world scenarios, the graph structure is typically unknown, posing a significant challenge for traditional DL methods. In this paper, we address this challenge by formulating and solving a joint problem of dictionary learning and graph structure estimation, aiming to enhance the interpretability and generalization error. To solve this problem, we employ the Proximal Alternating Linearized Minimization algorithm and its stochastic variant, yielding both batch and online optimization algorithms. Moreover, we introduce a novel graph learning algorithm based on alternating minimization specifically tailored for the graph learning sub-problem. We provide a detailed convergence analysis of the proposed algorithms, ensuring convergence to stationary points under mild assumptions. Experimental results on synthetic and real-world fMRI datasets validate the effectiveness of the proposed LRDL framework in discovering meaningful representations and graph structures from data.