Joint Feature Selection with Low-rank Dictionary Learning

Feature selection is one of the well known dimensionality reduction methods that efficiently describes the input data by removing irrelevant variables and reduces the effects of noise to provide good prediction results. In this paper, we propose a feature selection method by integrating dictionary learning and low-rank matrix approximation and apply it to image classification. The objective function finds a subset of features by preserving the reconstructive relationship of the data. This is achieved by minimizing the withinclass reconstruction residual and simultaneously maximizing the between-class reconstruction residual. Simultaneously, the l2,1-norm minimization on projection matrix is applied to jointly select the most relevant and discriminative features. The combination of low-rank approximation and Fisher discrimination dictionary learning, leads in more compactness within the same class and dissimilarity between different classes. As a result, even a simple classifier like KNN would perform surprisingly well and classify data accurately. Our proposed method is extensively evaluated on different benchmark image datasets and shows superior performance over several feature selection methods. The experimental results together with the theoretical analysis validate the effectiveness of our method for feature selection, and its efficacy for image classification.