Nonnegative Representation Research Articles

Discriminative Subspace Learning With Adaptive Graph Regularization

Abstract Many subspace learning methods based on low-rank representation employ the nearest neighborhood graph to preserve the local structure. However, in these methods, the nearest neighborhood graph is a binary matrix, which fails to precisely capture the similarity between distinct samples. Additionally, these methods need to manually select an appropriate number of neighbors, and they cannot adaptively update the similarity graph during projection learning. To tackle these issues, we introduce Discriminative Subspace Learning with Adaptive Graph Regularization (DSL_AGR), an innovative unsupervised subspace learning method that integrates low-rank representation, adaptive graph learning and nonnegative representation into a framework. DSL_AGR introduces a low-rank constraint to capture the global structure of the data and extract more discriminative information. Furthermore, a novel graph regularization term in DSL_AGR is guided by nonnegative representations to enhance the capability of capturing the local structure. Since closed-form solutions for the proposed method are not easily obtained, we devise an iterative optimization algorithm for its resolution. We also analyze the computational complexity and convergence of DSL_AGR. Extensive experiments on real-world datasets demonstrate that the proposed method achieves competitive performance compared with other state-of-the-art methods.

Discriminative dictionary learning for nonnegative representation based classification

Representation based classification (RC) algorithms have been successfully applied to pattern classification. However, most existing RC algorithms are not robust to bad training samples, since they ignore learning more discriminative dictionary atoms and instead directly use training samples as dictionary atoms. In addition, in order to improve expression ability and recognition accuracy, RC algorithms often need to expand the number of dictionary atoms, resulting in a surge in storage and computing costs. To obtain a more discriminative and compact dictionary, this study proposes discriminative dictionary learning for nonnegative representation based classification (DDLNRC). Specifically, in the DDLNRC, this paper utilizes nonnegative constraint to obtain a nonnegative representation for each training sample on the dictionary. In the dictionary learning stage, for a training sample, the DDLNRC minimizes the intra-class reconstruction error of the training sample and simultaneously enlarges the distance between the training sample and the atom that has the most influence on inter-class reconstruction error. Experiments demonstrate the effectiveness of the DDLNRC. Combined with the deep neural network features, it also can achieve higher accuracy than using the Softmax.

Density-Based Discriminative Nonnegative Representation Model for Imbalanced Classification

Representation-based methods have found widespread applications in various classification tasks. However, these methods cannot deal effectively with imbalanced data scenarios. They tend to neglect the importance of minority samples, resulting in bias toward the majority class. To address this limitation, we propose a density-based discriminative nonnegative representation approach for imbalanced classification tasks. First, a new class-specific regularization term is incorporated into the framework of a nonnegative representation based classifier (NRC) to reduce the correlation between classes and improve the discrimination ability of the NRC. Second, a weight matrix is generated based on the hybrid density information of each sample’s neighbors and the decision boundary, which can assign larger weights to minority samples and thus reduce the preference for the majority class. Furthermore, the resulting model can be efficiently optimized through the alternating direction method of multipliers. Extensive experimental results demonstrate that our proposed method is superior to numerous state-of-the-art imbalanced learning methods.

Incomplete Multiview Nonnegative Representation Learning With Graph Completion and Adaptive Neighbors.

Despite incomplete multiview clustering (IMC) being widely studied in the past decade, it is still difficult to model the correlation among multiple views due to the absence of partial views. Most existing works for IMC only mine the correlation among multiple views from available views and ignore the importance of missing views. To address this issue, we propose a novel Incomplete Multiview Nonnegative representation learning model with Graph completion and Adaptive neighbors (IMNGA), which performs common graph learning, missing graph completion, and consensus nonnegative representation learning simultaneously. In IMNGA, the common graph on all views and the incomplete graph of each view are used to reconstruct the completed graph of the corresponding view, where the common graph satisfies the neighbor constraints of incomplete multiview data and consensus representation. IMNGA gets consensus representation by factorizing completed and incomplete graphs, where consensus representation satisfies the common graph constraint. IMNGA shows its effectiveness by outperforming other state-of-the-art methods.

Locality-Constraint Discriminative Nonnegative Representation for Pattern Classification

Representation-based classification methods (RBCM) have recently garnered notable attention in the field of pattern classification. Diverging from conventional methods reliant on ℓ1 or ℓ2-norms, the nonnegative representation-based classifier (NRC) enforces a nonnegative constraint on the representation vector, thus enhancing the representation capabilities of positively correlated samples. While NRC has achieved substantial success, it falls short in fully harnessing the discriminative information associated with the training samples and neglects the locality constraint inherent in the sample relationships, thereby limiting its classification power. In response to these limitations, we introduce the locality-constraint discriminative nonnegative representation (LDNR) method. LDNR extends the NRC framework through the incorporation of a competitive representation term. Recognizing the pivotal role played by the estimated samples in the classification process, we include estimated samples that involve discriminative information in this term, establishing a robust connection between representation and classification. Additionally, we assign distinct local weights to different estimated samples, augmenting the representation capacity of homogeneous samples and, ultimately, elevating the performance of the classification model. To validate the effectiveness of LDNR, extensive comparative experiments are conducted on various pattern classification datasets. The findings demonstrate the competitiveness of our proposed method.

Subspace Clustering via Adaptive Non-Negative Representation Learning and Its Application to Image Segmentation

Self-representation subspace clustering based on graphs has the merits of capability and efficiency. However, the graph built by the self-representation methods has two issues: (i) usually lacking conciseness and informativeness due to the negative representation coefficients. (ii) no guarantee of an overall optimal solution due to the separation of representation learning and graph construction. To alleviate these issues, we propose a novel subspace clustering via learning non-negative representation with an adaptive graph. Specifically, we explicitly impose the non-negative constraint on the self-representation learning, ensuring that each data point is approximated from a group of homogeneous samples and enhancing the distinguishability of data representation. Meanwhile, an adaptive graph is developed so that both representation and the geometric structure of data are simultaneously learned in a unified procedure. Moreover, the learned representation is less sensitive to data noise imposed by the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm, so the adaptive graph will be further improved. An efficient optimization procedure is developed to find the optimal solution. Extensive experiments on subspace clustering and the extension application to image segmentation validate the advantages of our method against state-of-the-art methods.

Joint Learning of Correlation-Constrained Fuzzy Clustering and Discriminative Non-Negative Representation for Hyperspectral Band Selection

Hyperspectral band selection plays an important role in overcoming the curse of dimensionality. Recently, clustering-based band selection methods have shown promise in the selection of informative and representative bands from hyperspectral images (HSIs). However, most existing clustering-based band selection methods involve the clustering of original HSIs, limiting their performance because of the high dimensionality of hyperspectral bands. To tackle this problem, a novel hyperspectral band selection method termed joint learning of correlation-constrained fuzzy clustering and discriminative non-negative representation for hyperspectral band selection (CFNR) is presented. In CFNR, graph regularized non-negative matrix factorization (GNMF) and constrained fuzzy C-means (FCM) are integrated into a unified model to perform clustering on the learned feature representation of bands rather than on the original high-dimensional data. Specifically, the proposed CFNR aims to learn the discriminative non-negative representation of each band for clustering by introducing GNMF into the model of the constrained FCM and making full use of the intrinsic manifold structure of HSIs. Moreover, based on the band correlation property of HSIs, a correlation constraint, which enforces the similarity of clustering results between neighboring bands, is imposed on the membership matrix of FCM in the CFNR model to obtain clustering results that meet the needs of band selection. The alternating direction multiplier method is adopted to solve the joint optimization model. Compared with existing methods, CFNR can obtain a more informative and representative band subset, thus can improve the reliability of hyperspectral image classifications. Experimental results on five real hyperspectral datasets demonstrate that CFNR can achieve superior performance compared with several state-of-the-art methods.

Direct multi-view spectral clustering with consistent kernelized graph and convolved nonnegative representation

Direct multi-view spectral clustering with consistent kernelized graph and convolved nonnegative representation

Joint Dual-Structural Constrained and Non-negative Analysis Representation Learning for Pattern Classification

ABSTRACT In recent years, analysis dictionary learning (ADL) model has attracted much attention from researchers, owing to its scalability and efficiency in representation-based classification. Despite the supervised label information embedding, the classification performance of analysis representation suffers from the redundant and noisy samples in real-world datasets. In this paper, we propose a joint Dual-Structural constrained and Non-negative Analysis Representation (DSNAR) learning model. First, the supervised latent structural transformation term is considered implicitly to generate a roughly block diagonal representation for intra-class samples. However, this discriminative structure is fragile and weak in the presence of noisy and redundant samples. To highlight both intra-class similarity and inter-class separation for class-oriented representation, we then explicitly incorporate an off-block suppressing term on the ADL model, together with a non-negative representation constraint, to achieve a well-structured and meaningful interpretation of the contributions from all class-oriented atoms. Moreover, a robust classification scheme in latent space is proposed to avoid accidental incorrect predictions with noisy information. Finally, the DSNAR model is alternatively solved by the K-SVD method, iterative re-weighted method and gradient method efficiently. Extensive classification results on five benchmark datasets validate the performance superiority of our DSNAR model compared to other state-of-the-art DL models.

Double Discriminative Constraint-Based Affine Nonnegative Representation for Few-Shot Remote Sensing Scene Classification

Remote sensing scene classification (RSSC) has recently attracted more attention. However, due to restrictions in the imaging environment and equipment, it is difficult to get a large number of labeled images in remote sensing. This has led to the emergence of few-shot learning for RSSC, which aims to achieve better performance with few labeled samples. Remote sensing images’ large interclass similarity may cause classification confusion. To overcome this issue, this study proposes a double discriminative constraints-based affine nonnegative representation for few-shot RSSC. To be specific, we devise a novel representation-based classifier with two discriminative constraint terms in the objective function and utilize affine nonnegative constraints to restrict the learned parameters. These constraints reduce the correlation between classes and strengthen the class specificity of the learned parameters. Experiments on benchmark datasets demonstrate the effectiveness of our method.

Label consistent non-negative representation of ECG signals for automated recognition of cardiac arrhythmias

Label consistent non-negative representation of ECG signals for automated recognition of cardiac arrhythmias

Nonnegative collaborative representation for hyperspectral anomaly detection

ABSTRACT Recently, collaborative representation detector (CRD) is widely studied since it is easy to implement and offers higher detection accuracy for hyperspectral anomaly detection. However, the original CRD introduces a regularization parameter that is hard to tune in practice; and the coefficient vector under the sum-to-one constraint can be negative, which has no physical meaning, thus leading to unstable results. To solve these problems, we impose strict nonnegative and -norm constraints on the coefficient vector to obtain a more accurate and meaningful coefficient vector. To facilitate the optimization procedure, we apply the accelerated projected gradient algorithm to solve this model. The experimental results on four real datasets demonstrate the superior performance of the proposed method compared with CRD.

Competitive Non-negative Representation with Image Gradient Orientations for Face Recognition

Competitive Non-negative Representation with Image Gradient Orientations for Face Recognition

Incomplete multiview nonnegative representation learning with multiple graphs

Multiview clustering has become an important research topic during the past decade. However, partial views of many data instances are missing in some realistic multiview learning scenarios. To handle this problem, we develop an effective incomplete multiview nonnegative representation learning (IMNRL) framework, which is suitable for incomplete multiview clustering in various situations. The IMNRL framework performs matrix factorization on multiple incomplete graphs and decomposes these incomplete graphs into a consensus nonnegative representation and view-specific spectral representations, which integrates the advantages of multiview nonnegative representation learning and graph learning. The proposed framework has the following merits: (1) it learns a consensus nonnegative embedding and view-specific embeddings simultaneously; (2) the nonnegative embedding satisfies the neighbor constraint on each incomplete view, which directly reveals the multiview clustering results. Experimental results show that the proposed framework outperforms other state-of-the-art incomplete multiview clustering algorithms.

Non-negative discriminative collective target nearest-neighbor representation

In intelligent warehouse logistics, image classification is widely used. However, the performance of traditional image classifiers suffers when deployed in new environments because of the lack of labels collected. In this paper, aiming at solving the problem above, a novel method named non-negative discriminative collective target nearest-neighbour representation (NDCTNNR) is proposed. Inspired by the Collective target nearest-neighbour representation (CTNNR), this method introduces a novel regularization term to integrate class discrimination and data locality. Moreover, our method uses non-negative representations to make collaborative representation sparser. The experimental results confirm the effectiveness of the proposed method.

18F-FDG-PET/CT Whole-Body Imaging Lung Tumor Diagnostic Model: An Ensemble E-ResNet-NRC with Divided Sample Space.

Under the background of 18F-FDG-PET/CT multimodal whole-body imaging for lung tumor diagnosis, for the problems of network degradation and high dimension features during convolutional neural network (CNN) training, beginning with the perspective of dividing sample space, an E-ResNet-NRC (ensemble ResNet nonnegative representation classifier) model is proposed in this paper. The model includes the following steps: (1) Parameters of a pretrained ResNet model are initialized using transfer learning. (2) Samples are divided into three different sample spaces (CT, PET, and PET/CT) based on the differences in multimodal medical images PET/CT, and ROI of the lesion was extracted. (3) The ResNet neural network was used to extract ROI features and obtain feature vectors. (4) Individual classifier ResNet-NRC was constructed with nonnegative representation NRC at a fully connected layer. (5) Ensemble classifier E-ResNet-NRC was constructed using the “relative majority voting method.” Finally, two network models, AlexNet and ResNet-50, and three classification algorithms, nearest neighbor classification algorithm (NNC), softmax, and nonnegative representation classification algorithm (NRC), were combined to compare with the E-ResNet-NRC model in this paper. The experimental results show that the overall classification performance of the Ensemble E-ResNet-NRC model is better than the individual ResNet-NRC, and specificity and sensitivity are more higher; the E-ResNet-NRC has better robustness and generalization ability.

Discriminative non-negative representation based classifier for image recognition

During the past decade, representation based classification method has received considerable attention in the community of pattern recognition. The recently proposed non-negative representation based classifier achieved superb recognition results in diverse pattern classification tasks. Unfortunately, discriminative information of training data is not fully exploited in non-negative representation based classifier, which undermines its classification performance in practical applications. To address this problem, we introduce a decorrelation regularizer into the formulation of non-negative representation based classifier and propose a discriminative non-negative representation based classifier for pattern classification. The decorrelation regularizer is able to reduce the correlation of representation results of different classes, thus promoting the competition among them. Experimental results on benchmark datasets validate the efficacy of the proposed discriminative non-negative representation based classifier, and it can outperform some state-of-the-art deep learning based methods. The source code of our proposed discriminative non-negative representation based classifier is accessible at https://github.com/yinhefeng/DNRC .

Graph regularization-based joint nonnegative representation for the classification of hyperspectral images

ABSTRACT The hyperspectral image classification methods based on sparse representation and collaborative representation have achieved some satisfactory results. However, some of the representation coefficients obtained from them may be negative, which is physically difficult to explain. In addition, existing methods do not consider the local geometric relationships between pixels. To address these problems, this paper proposes a joint nonnegative representation model based on the graph regularization for the hyperspectral image classification. First, for a testing pixel, the similarity between the neighbouring pixels and the testing pixel is used to collect some neighbouring pixels in a window centred at a testing pixel and construct a new neighbourhood pixel set. Each pixel in this neighbourhood pixel set is approximated by a nonnegative linear combination of training pixels from a given over-completed training pixel set. The nonnegative constraint here can ensure to some extent that the representation coefficients of those homogeneous training pixels of the testing pixel from the same class are nonnegative, while ones of those heterogeneous training pixels from different classes are as close to zero as possible. Thus, the obtained coefficients are sparse and physically explicable. Secondly, in order to preserve the manifold structure of training pixels, we also introduce a graph-based regularization constraint. Compared with some other existing methods, our model can obtain a sparse and more discriminative representation coefficient. Furthermore, it can also reveal the local structure of training pixels. The alternative iteration optimization algorithm is devised to solve the proposed model and gives its closed-form solutions in each iteration. Experiment results on four remote sensing image data sets show the superiority of the proposed method.

Nonnegative representation based discriminant projection for face recognition

Dimensionality reduction (DR) has been widely used to deal with high-dimensional data, and plays an important role in alleviating the so-called “curse of dimensionality”. In this paper, we propose a novel unsupervised DR method with applications to face recognition, i.e., Nonnegative Representation based Discriminant Projection (NRDP). Different with other locality or globality preserving DR methods, NRDP focuses on both locality and nonlocality of data points and learns a discriminant projection by maximizing the nonlocal scatter and minimizing the local scatter simultaneously. A nonnegative representation model is designed in NRDP to discover the local structure and nonlocal structure of data. The $$\ell _1$$ -norm is used as metric in nonnegative representation to enhance the robustness against noises, and an iterative algorithm is presented to solve the optimization model. NRDP is able to learn features with large inter-class or subspace scatter and small intra-class scatter in the case that label information is unavailable, which significantly improves the representation power and discrimination. Experimental results on several popular face datasets demonstrate the effectiveness of our proposed method.

Class-specific residual constraint non-negative representation for pattern classification

Representation-based classification methods (RBCM) remain one of the hottest topics in the community of pattern recognition, and the recently proposed non-negative representation-based classification (NRC) achieved impressive recognition results in various classification tasks. However, NRC ignores the relationship between the coding and classification stages. Moreover, there is no regularization term other than the reconstruction error term in the formulation of NRC, which may result in an unstable solution leading to misclassification. To overcome these drawbacks of NRC, we propose a class-specific residual constraint non-negative representation (CRNR) for pattern classification. CRNR introduces a class-specific residual constraint into the formulation of NRC, which encourages training samples from different classes to competitively represent the test sample. Based on the proposed CRNR, we develop a CRNR-based classifier (CRNRC) for pattern classification. Experimental results on several benchmark datasets demonstrate the superiority of CRNRC over conventional RBCM as well as the recently proposed NRC. Moreover, CRNRC works better than or comparable to some state-of-the-art deep approaches on diverse challenging pattern classification tasks.