Dictionary learning under global sparsity constraint

TL;DR

This paper introduces a novel dictionary learning method that applies a global sparsity constraint to better capture complex data structures, outperforming existing methods in reconstruction and structure revealing.

Contribution

The proposed method uniquely enforces a global sparsity constraint across the entire dataset, enhancing dictionary adaptability and representation quality.

Findings

Outperforms existing methods in dictionary recovery

Achieves better data reconstruction accuracy

Effectively reveals salient data structures

Abstract

A new method is proposed in this paper to learn overcomplete dictionary from training data samples. Differing from the current methods that enforce similar sparsity constraint on each of the input samples, the proposed method attempts to impose global sparsity constraint on the entire data set. This enables the proposed method to fittingly assign the atoms of the dictionary to represent various samples and optimally adapt to the complicated structures underlying the entire data set. By virtue of the sparse coding and sparse PCA techniques, a simple algorithm is designed for the implementation of the method. The efficiency and the convergence of the proposed algorithm are also theoretically analyzed. Based on the experimental results implemented on a series of signal and image data sets, it is apparent that our method performs better than the current dictionary learning methods in original dictionary recovering, input data reconstructing, and salient data structure revealing.