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.

本文介绍了一种基于 RVFL 的非线性字典学习算法，该算法学习将非线性稀疏系数映射到密集的输入特征的字典。实验证明，该方法在图像分类和重建应用中的表现与其他非线性字典学习方法相当，并且具有可伸缩性，提供比其他非线性字典学习方法更好的解决方案。

基于 RVFL 的非线性字典学习的一种无 SVD 方法

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

In the paradigm of multi-task learning, mul- tiple related prediction tasks
are learned jointly, sharing information across the tasks. We propose a
framework for multi-task learn- ing that enables one to selectively share the
information across the tasks. We assume that each task parameter vector is a
linear combi- nation of a finite number of underlying basis tasks. The
coefficients of the linear combina- tion are sparse in nature and the overlap
in the sparsity patterns of two tasks controls the amount of sharing across
these. Our model is based on on the assumption that task pa- rameters within a
group lie in a low dimen- sional subspace but allows the tasks in differ- ent
groups to overlap with each other in one or more bases. Experimental results on
four datasets show that our approach outperforms competing methods.

提出一种基于稀疏系数和低维子空间的多任务学习框架，能够选择性地在相关任务间共享信息，实验结果显示该方法优于竞争方法。