Analysis discriminative convolutional graph dictionary learning for generalized signal classification

Abstract

Analysis discriminative dictionary learning (ADDL) techniques have been studied for addressing image classification problems. However, existing ADDL methods ignore the structural dependency within the signals and cannot fit the general class of signals with irregular structures, including spherical images and 3D objects. In this paper, we propose a novel analysis discriminative convolutional graph dictionary learning method that fully exploits the structural dependency for signal classification, especially for irregular graph signals. The proposed method integrates the graph embedding information to analysis convolutional dictionary learning to derive a set of class-specific convolutional graph sub-dictionaries for extracting consistent class-specific features. An analytical decorrelation term is introduced as regularization to constrain the linear classifier for each class and improve the discrimination ability of dictionary-based sparse representation. Furthermore, we develop an efficient alternating update algorithm to solve the formulated non-convex minimization problem that simultaneously achieves sparse representation using ISTA and optimizes the convolutional graph dictionary and classifiers in an analytic manner. To our best knowledge, this paper is the first attempt to achieve analysis dictionary learning for generalized classification of signals with regular and irregular structures. Experimental results show that the proposed method outperforms state-of-the-art discriminative dictionary learning methods by 0.26% to 2.68% in classification accuracy for both regular and irregular signal classification. Notably, it is comparable to recent deep learning models with up to about 1% accuracy loss in irregular signal classification.