  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).
This paper presents an SVD-free lightweight approach to learning a nonlinear
dictionary using a randomized functional link called a 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. Sparse coefficients w.r.t an initial
random dictionary are derived by assuming Horseshoe prior are used as inputs
making it a lightweight network. Training the RVFL-based dictionary is free
from SVD computation as RVFL generates weights from the input to the output
layer analytically. 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 empirical evidence
of the method illustrated in image classification and reconstruction
applications shows that RVFLDL is scalable and provides a solution better than
those obtained using other nonlinear dictionary learning methods.
