Generalized adaptive weighted recursive least squares dictionary learning

•We generalize the recursive least squares dictionary learning algorithm.•Our algorithm GAW-RLS introduces a correction weight for the arrival data.•Controls the relative consistency between arrival data and existing dictionary.•This improves the convergence of algorithm, MSE of sparse representation.•This makes the algorithm more robust in dealing with outliers in the training data.

Recursive least squares (RLS) dictionary learning algorithm is one of the well-known dictionary update approaches which continuously update the dictionary per arrival of new training data. In RLS algorithm a forgetting factor is added to control the memory and the effect of the previous data in the dictionary update stage. In this paper, we generalize the RLS algorithm by introducing an additional correction weight for the arrival data. This additional correction weight adaptively controls the relative consistency between the arrival data and the existing dictionary estimate. Consequently, we show that the conventional RLS is a special case of our method. Synthetic data, with and without containing outliers, are used to train both methods. Experimental results verify that adding the correction weight in our proposed method improves the recovery of original dictionary and MSE of sparse representation for both types of training data. The improvement increases as the percentage of outliers increase.