Low-Rank Preserving t-Linear Projection for Robust Image Feature Extraction

Logarithmic Learning Differential Convolutional Neural Network

Convolutional Neural Networks (CNNs) have revolutionized image classification through their innovative design and training methodologies in computer vision. Differential convolutional neural network with simultaneous multidimensional filter realization improved the performance of the convolutional neural network with calculation cost drawback. This paper introduces logarithmic learning integration into the differential Convolutional neural network to overcome the drawback by supplying faster error minimization and convergence. This task is done by incorporating LogRelu activation, a Logarithmic Cost Function, and unique logarithmic learning method. The effectiveness of the proposed approaches are evaluated by using various datasets and SGD/Adam optimizers. The first step is the adaptation of LogRelu activation function to convolutional and differential convolutional neural networks. The experiment results show that LogRelu integration to convolutional neural network and differential convolutional neural network yields performance improvements ranging from 1.61% to 5.44%. The same integration on ResNet-18, ResNet-34, and ResNet-50 enhances top-1 accuracy in the range of 3.07% and 9.96%. In addition to LogRelu activation function, a Logarithmic Cost Function with logarithmic learning method is also proposed and adapted to differential convolutional neural network. These improvements lead to a new differential convolutional neural network named as Logarithmic Differential Convolutional Neural Network (LDiffCNN), It consistently outperforms standard CNN by increasing the accuracy up to 3.02%. Notably, Logarithmic Differential Convolutional Neural Network demonstrates reduced training iterations up to 38% with faster convergence. The experimental results proved the efficiency of the proposed approach.

An Unsupervised Feature Extraction Approach Based on Self-Expression

Feature extraction algorithms lack good interpretability during the projection learning. To solve this problem, an unsupervised feature extraction algorithm, that is, block diagonal projection (BDP), based on self-expression is proposed. Specifically, if the original data are projected into a low-dimensional subspace by a feature extraction algorithm, although the data may be more compact, the new features obtained may not be as explanatory as the original sample features. Therefore, by imposing L2,1 norm constraint on the projection matrix, the projection matrix can be of row sparsity. On one hand, discriminative features can be selected to make the projection matrix to be more interpretable. On the other hand, irrelevant or redundant features can be suppressed. The proposed model integrates feature extraction and selection into one framework. In addition, since self-expression can well excavate the correlation between samples or sample features, the unsupervised feature extraction task can be better guided using this property between them. At the same time, the block diagonal representation regular term is introduced to directly pursue the block diagonal representation. Thus, the accuracy of pattern recognition tasks such as clustering and classification can be improved. Finally, the effectiveness of BDP in linear dimensionality reduction and classification is proved on various reference datasets. The experimental results show that this algorithm is superior to previous feature extraction counterparts.

Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery

Recently, transform-based tensor nuclear norm (TNN) minimization methods have received increasing attention for recovering third-order tensors in multi-dimensional imaging problems. The main idea of these methods is to perform the linear transform along the third mode of third-order tensors and then minimize the nuclear norm of frontal slices of the transformed tensor. The main aim of this paper is to propose a nonlinear multilayer neural network to learn a nonlinear transform by solely using the observed tensor in a self-supervised manner. The proposed network makes use of the low-rank representation of the transformed tensor and data-fitting between the observed tensor and the reconstructed tensor to learn the nonlinear transform. Extensive experimental results on different data and different tasks including tensor completion, background subtraction, robust tensor completion, and snapshot compressive imaging demonstrate the superior performance of the proposed method over state-of-the-art methods.