Multi-layer convolutional transform learning algorithm based on proximal difference of convex method

GUO Yong-cheng; TANG Jian-hao; LI Zhen-ni; LÜ Jun

doi:10.7641/CTA.2022.11020

Abstract：Convolutional Transform Learning(CTL)combines the advantages of unsupervised learning and convolu-tional neural network,learning filters in an unsupervised way,which is a new sparse representation method.However,the existing single-layer CTL model is difficult to effectively extract the deep semantic information of input signals through only one layer of sparse coding.Further more,the l0-norm can enforce strong sparsity,but the l0-norm-constrained CTL is an NP-hard optimization problem.And the l1-norm-constrained CTL presents some drawbacks too,such as its inadequate sparsity and the overpenalization for large elements in the sparse vector.In order to solve these problems of the existing CTL model,This paper presents a multi-layer CTL model based on log regularizer(CTL-log):In order to extract the sparse features of input signals that are more discriminative and rich in semantics,the single-layer CTL model is extended by multiple layers.simultaneously,a log regularizer is used as sparse constraint of CTL model which can not only obtain accurate representations but also yield strong sparsity.Finally,we propose to employ the proximal difference of convex algorithm to efficiently address the nonconvex composite optimization,leading to a proximal difference of convex method based multi-layer convolutional transform learning algorithm.The experimental results demonstrate that the performance of the proposed CTL-log is better than the existing CTL model.And compared with the single-layer CTL-log,the multi-layer CTL-log has a comprehensive improvement in feature extraction,and the classification accuracy of SVM classifier is improved by about 2 percentage points.