Topology preserving dictionary learning for pattern classification

In recent years, dictionary learning (DL) has shown significant potential in various classification tasks. However, most of previous works aim to learn a synthesis dictionary. The other major category of DL-analysis dictionary learning has not been fully exploited yet. This paper proposes a novel DL method, named Topology Preserving Dictionary Learning (TPDL). First, we propose a triplet-constraint-based topology preserving loss function to capture the underlying local topological structures of data in a supervised manner. Second, a sparse-label-matrix-based function is integrated into the basic analysis model to improve discriminative ability. Third, Huber M-estimator is employed as a robust metric to handle the errors (e.g., outliers and noise) that possibly exist in data. Then, an alternating optimization algorithm is developed based on half-quadratic minimization and alternate search strategy. Closed-form solutions in each alternating optimization stage speed up the minimization process. Experiments on four commonly used datasets show that our proposed TPDL achieves competitive performance in contrast to state-of-the-art DL methods.