PADDLE: Proximal Algorithm for Dual Dictionaries LEarning

TL;DR

This paper introduces PADDLE, an algorithm that learns a dictionary and its dual for sparse coding, enabling direct coding without optimization, leading to efficient and effective image feature extraction.

Contribution

The paper proposes a novel proximal algorithm to jointly learn dictionaries and their duals, improving coding efficiency and classification performance.

Findings

Successfully recovers expected dictionaries on synthetic and real data.

Achieves state-of-the-art classification with less computational cost.

Demonstrates effectiveness of dual dictionaries in sparse coding.

Abstract

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new data. In order to overcome this drawback, we propose an algorithm aimed at learning both a dictionary and its dual: a linear mapping directly performing the coding. By leveraging on proximal methods, our algorithm jointly minimizes the reconstruction error of the dictionary and the coding error of its dual; the sparsity of the representation is induced by an $\ell_1$-based penalty on its coefficients. The results obtained on synthetic data and real images show that the algorithm is capable of recovering the expected dictionaries. Furthermore, on a benchmark dataset, we show that the image features obtained from the dual matrix yield state-of-the-art classification performance while being much less computational intensive.