Learning discriminative low-rank representation for image classification

Low-rank representation (LRR) has attracted much attention recently due to its efficacy in a rich variety of real world applications. Recently, the non-convex regularization has become widely used in the rank minimization problem. In this paper, we propose a discriminative low-rank representation with Schatten-p norm (DLRR-SPN) to learn a robust and discriminative affinity matrix for image recognition. To this end, we first impose the Schatten-p norm regularization on the representation matrix to learn the global structure of data. Moreover, the adaptive distance penalty is used to preserve the local neighbor relationship of data. The objective function is formulated as a Schatten-p norm minimization problem, which can be solved via alternating direction method of multipliers (ADMM). To enhance the separation ability of the discriminative affinity matrix for semi-supervised recognition problem, the angular information of the principal directions of the low-rank representation is further exploited. Finally, an effective semi-supervised classifier is utilized on the learned affinity matrix for final prediction. Extensive experimental results on image recognition demonstrate the effectiveness of the proposed method and its superiority in performance over the related state-of-the-art methods.

The conventional studies on different types of remote sensing (RS) images classifications are conducted separately. Thanks to the powerful potential of deep learning to automatically learn features from data, exploring a unified method is possible. Moreover, recent research shows that sparse and low-rank representations can convey valuable information for patterns classification. Therefore, this paper presents a two-stream heterogeneous RS images unified interpretation network (HRSIUI-Net). One stream is to transfer the pre-trained fully convolutional network to learn deep multi-scale spatial features of RS data. The other stream is to employ a subspace learning based on graph embedding to learn the sparse and low-rank subspace representations of high-dimensional features. And then, two streams of learned subspace features are integrated for classification combined with an SVM. The experimental results on two typical RS data indicate that HRSIUI-Net can achieve competitive performance.

Feature extraction (FE) methods based on low-rank representation (LRR) have become important topics in hyperspectral images (HSIs) data analysis. In this paper, a supervised FE method for HSIs data based on LRR with the ability to preserve the local pairwise constraints information (LRLPC) is proposed. LRLPC does not change the data dimensionality and only employs a technique to enrich the original feature space (OFS) and to obtain enriched feature space, which results in features richer than OFS. To overcome the problem of LRR in lacking the local structure information (LSI) of data, a local discriminative regularization term is imposed on the fitness function of LRR to keep the LSI of data. For nonlinear structure of data, LRLPC is extended to kernel LRLPC (KLRLPC) using kernel trick. Utilization of existing information in the pairwise constraints is useful for limited labeled samples situations as a common problem in HSI data analysis. The obtained experimental results using two well-known HSI data sets confirm the effectiveness of LRLPC and KLRLPC for dimension reduction and classification of HSIs.

With the development of cross-modal image fusion in multi-sensor systems, current fusion technologies have made significant progress in feature extraction, facilitating more effective image analysis. However, insufficient fusion information may degrade the correlation between the source and fused images, often resulting in the omission of critical features from the original modalities. Therefore, in order to preserve as much information as possible, especially for the complete extraction of effective feature information in source images, this paper proposes a new cross-modal image fusion method based on low-rank representation and convolutional sparse learning named LRCFuse. Firstly, the learned low-rank representation (LLRR) blocks are employed to perform dimensionality reduction on the source images while simultaneously extracting their low-rank and sparse feature components. Nevertheless, considering that the low-rank representation has insufficient modeling ability for different modal images, we introduce common feature preservation module (CFPM) blocks based on convolutional sparse coding. By leveraging the CFPM module, LRCFuse recovers common features from both source images to mitigate the loss caused by the imperfect assumptions of low-rank representation. Based on this, a multi-level optimization strategy incorporating pixel loss, shallow-level loss, mid-level loss, deep-level loss, and sobel loss is proposed to hierarchically learn and refine diverse image features. Quantitative and qualitative evaluations are conducted across various datasets, revealing that LRCFuse can effectively detect targets infrared salient targets, preserve additional details in visible images, and achieve better fusion results for subsequent downstream tasks.

This paper presents a novel method for anomaly detection in hyperspectral image(HSI) based on low-rank representation. In the observed HSI, the anomalies can be separated from the background. Since each pixel in the background can be approximately represented by a background dictionary, and the representation coefficients of the background pixels are correlative, a low-rank representation model is used to model the background part. Besides, to gain robust representation coefficient, the sum-to-one constraint is added. The advantage of the proposed low-rank representation sum-to-one (LRRSTO) method is that it makes use of the global correlation of the background and strength the robustness of the representation. Experiments results have been conducted using both simulated and real data sets. These experiments indicated that our algorithm achieves very promising performance.

Discriminative feature extraction based on sparse and low-rank representation

Sparse coding is a popular technique for achieving compact data representation and has been used in many applications. However, the instability issue often causes degeneration in practice and thus attracts a lot of studies. While the traditional graph sparse coding preserves the neighborhood structure of the data, this study integrates the low-rank representation(LRR) to fix the inconsistency of sparse coding by holding the subspace structures of the high-dimensional observations. The proposed method is dubbed low-rank graph regularized sparse coding (LogSC), which learns sparse codes and low-rank representations jointly rather than the traditional two-step approach. Since the two data representations share a dictionary matrix, the resulted sparse representation on this dictionary could be benefited from LRR. We solved the optimization problem of LogSC by using the linearized alternating direction method with adaptive penalty. Experimental results show the proposed method is discriminative in feature learning and robust to various noises. This work provides a one-step approach to integrating graph embedding in representation learning.

Feature extraction based on Low-rank affinity matrix for biological recognition

Improved sparse representation with low-rank representation for robust face recognition

Improving generalization of double low-rank representation using Schatten-p norm

Discriminative low-rank preserving projection for dimensionality reduction

Intelligence modeling interpretable for incipient fault diagnosis of batch process represents a serious challenge. For the multivariate, nonlinear, and high-dimensionality characteristics of process data, existing fault diagnosis solutions are easily concealed by noise while neglect the low amplitude and noise interference of the incipient faults. In this paper, an intelligent incipient fault diagnosis model based on deep time series feature extraction network is proposed, which integrates denoising autoencoder (DAE), layer normalization and dropout layer added LSTM (LD-LSTM), and stacked autoencoder (SAE) to obtain the efficient features. DAE is applied to restore the data and eliminate noise interference. LD-LSTM is utilized to extract time series features, in which the layer normalization and the dropout layer are added between the layers of the LSTM to solve the problems of slow model convergence and over-fitting. SAE performs the feature extraction to obtain deep time series features and learns more efficient expressions. The softmax function is applied to achieve the incipient fault diagnosis based on the deep time series features. A case study on a fed-batch penicillin fermentation process suggests that the proposed method can obtain an accuracy rate of 98.97%, which has increased an average of 20% than the traditional shallow machine learning. The accuracy of fault recognition and comparative experiments demonstrate the effectiveness and feasibility of this model, and provide a solution for the application of intelligent fault diagnosis in batch industries.

Video-based human pose recovery is usually conducted by retrieving relevant poses using image features. In the retrieving process, the mapping between 2D images and 3D poses is assumed to be linear in most of the traditional methods. However, their relationships are inherently non-linear, which limits recovery performance of these methods. In this paper, we propose a novel pose recovery method using non-linear mapping with multi-layered deep neural network. It is based on feature extraction with multimodal fusion and back-propagation deep learning. In multimodal fusion, we construct hypergraph Laplacian with low-rank representation. In this way, we obtain a unified feature description by standard eigen-decomposition of the hypergraph Laplacian matrix. In back-propagation deep learning, we learn a non-linear mapping from 2D images to 3D poses with parameter fine-tuning. The experimental results on three data sets show that the recovery error has been reduced by 20%-25%, which demonstrates the effectiveness of the proposed method.

Recently, radiometric identification has attracted much attention. Previous research works considered feature extraction and classification separately, which resulted in that the extracted RF fingerprint features may not be good features and not be suitable for a designated classifier. In this letter, a novel radiometric identification method is proposed to improve the performance of radiometric identification. This method attempts to find a low-rank representation matrix of original data and the optimal classifier parameter simultaneously, by imposing a regularization item of minimum prediction error. Since the recovered radio-frequency fingerprint features are discriminative, the proposed method is suitable for radiometric identification. Experiments on real data sets demonstrate that the proposed method not only outperforms the competitive methods with a higher accuracy of radiometric identification but also has a better robustness against noise. The results indicate that the proposed algorithm can discriminate different emitters with high classification accuracy even if they are from the same manufacturer.

Modern industrial processes are characterized by increasing complexity, often exhibiting pronounced dynamic behaviors and significant nonlinearity. Addressing these dynamic and nonlinear characteristics is essential for effective process monitoring. However, many existing methods for process monitoring and fault diagnosis are insufficient in handling these challenges. In this article, we present a novel process monitoring approach, CVA-DisDAE, which integrates an improved Denoising Autoencoder (DAE) with Canonical Variate Analysis (CVA) to address the challenges posed by dynamic behaviors and nonlinear relationships in industrial processes. First, CVA is employed to reduce data dimensionality and minimize information redundancy by maximizing correlations between past and future observations, thereby effectively capturing process dynamics. Following this, we introduce a discriminative DAE model (DisDAE) designed to serve as a semi-supervised denoising autoencoder for precise feature extraction. This is achieved by incorporating both between-class separability and within-class variability into the traditional DAE framework. The key distinction between the proposed DisDAE and the conventional DAE lies in the integration of a linear discriminant analysis (LDA) penalty into the DAE’s loss function, resulting in extracted features that are more conducive to fault classification. Finally, we validate the effectiveness of the proposed semi-supervised dynamic process monitoring approach through its application to the Tennessee Eastman benchmark process, demonstrating its superior performance.