An SVD-free Approach to Nonlinear Dictionary Learning based on RVFL

This paper presents a novel nonlinear dictionary learning algorithm leveraging the theory of a feed-forward neural network called Random Vector Functional Link (RVFL). The proposed RVFL-based nonlinear Dictionary Learning (RVFLDL) learns a dictionary as a sparse-to-dense feature map from nonlinear sparse coefficients to the dense input features. Kernel-based nonlinear dictionary learning methods operate in a feature space obtained by an implicit feature map, and they are not independent of computationally expensive operations like Singular Value Decomposition (SVD). Training the RVFL-based dictionary is free from SVD computation as RVFL generates weights from the input to the output layer analytically. Sparsity-inducing Horse-shoe prior is assumed on the coefficients to generate a sparse coefficient matrix w.r.t an initial random dictionary. Higher-order dependencies between the input sparse coefficients and the dictionary atoms are incorporated into the training process by nonlinearly transforming the sparse coefficients and adding them as enhanced features. Thus the method projects sparse coefficients to a higher dimensional space while inducing nonlinearities into the dictionary. For classification using RVFL-net, a classifier matrix is learned as a transform that maps nonlinear sparse coefficients to the labels. The performance of the method illustrated in image classification and reconstruction applications is comparable to that of other nonlinear dictionary learning methods. Experiments show that RVFLDL is scalable and provides a solution better than those obtained using other nonlinear dictionary learning methods.