An SVD-free Approach to Nonlinear Dictionary Learning based on RVFL
G. Madhuri Atul Negi
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.