Label Consistent Generalized Adaptive Weighted Recursive Least Squares Dictionary Learning

The Generalized Adaptive Weighted Recursive Least Squares (GAWRLS) dictionary learning method has shown potential for unsupervised dictionary learning. This paper advances GAWRLS by incorporating classification error as an additional cost to enable supervised learning tasks and introduces the Label Consistency for online supervised dictionary learning in classification tasks. The new method is denoted as Label Consistent Generalized Adaptive Weighted Recursive Least Squares Dictionary Learning (LC-GAWRLS). By incorporating both sparse representation error and classification error into the cost function, LC-GAWRLS enables simultaneous learning of the dictionary and classifier parameters. Particularly, to ensure label consistency, the proposed algorithm introduces a correction weight to adaptively regulate the impact of each training data during the model update, enhancing robustness against variations in training data compared to previous dictionary learning methods. Simulation results on real datasets demonstrate that LC-GAWRLS achieves higher classification accuracy compared to existing state-of-the-art supervised dictionary learning methods, particularly in scenarios with limited training samples per class.