Non-negative Low-rank Representation Research Articles

Non-Negative Low-Rank Representation With Similarity Correction for Cell Type Identification in scRNA-Seq Data.

Single-cell RNA sequencing (scRNA-Seq) technology has emerged as a powerful tool to investigate cellular heterogeneity within tissues, organs, and organisms. One fundamental question pertaining to single-cell gene expression data analysis revolves around the identification of cell types, which constitutes a critical step within the data processing workflow. However, existing methods for cell type identification through learning low-dimensional latent embeddings often overlook the intercellular structural relationships. In this paper, we present a novel non-negative low-rank similarity correction model (NLRSIM) that leverages subspace clustering to preserve the global structure among cells. This model introduces a novel manifold learning process to address the issue of imbalanced neighbourhood spatial density in cells, thereby effectively preserving local geometric structures. This procedure utilizes a position-sensitive hashing algorithm to construct the graph structure of the data. The experimental results demonstrate that the NLRSIM surpasses other advanced models in terms of clustering effects and visualization experiments. The validated effectiveness of gene expression information after calibration by the NLRSIM model has been duly ascertained in the realm of relevant biological studies. The NLRSIM model offers unprecedented insights into gene expression, states, and structures at the individual cellular level, thereby contributing novel perspectives to the field.

HOMLC-Hyperparameter Optimization for Multi-Label Classification of Intrusion Detection Data for Internet of Things Network.

The comparison of low-rank-based learning models for multi-label categorization of attacks for intrusion detection datasets is presented in this work. In particular, we investigate the performance of three low-rank-based machine learning (LR-SVM) and deep learning models (LR-CNN), (LR-CNN-MLP) for classifying intrusion detection data: Low Rank Representation (LRR) and Non-negative Low Rank Representation (NLR). We also look into how these models' performance is affected by hyperparameter tweaking by using Guassian Bayes Optimization. The tests has been run on merging two intrusion detection datasets that are available to the public such as BoT-IoT and UNSW- NB15 and assess the models' performance in terms of key evaluation criteria, including precision, recall, F1 score, and accuracy. Nevertheless, all three models perform noticeably better after hyperparameter modification. The selection of low-rank-based learning models and the significance of the hyperparameter tuning log for multi-label classification of intrusion detection data have been discussed in this work. A hybrid security dataset is used with low rank factorization in addition to SVM, CNN and CNN-MLP. The desired multilabel results have been obtained by considering binary and multi-class attack classification as well. Low rank CNN-MLP achieved suitable results in multilabel classification of attacks. Also, a Gaussian-based Bayesian optimization algorithm is used with CNN-MLP for hyperparametric tuning and the desired results have been achieved using c and γ for SVM and α and β for CNN and CNN-MLP on a hybrid dataset. The results show the label UDP is shared among analysis, DoS and shellcode. The accuracy of classifying UDP among three classes is 98.54%.

NLRRC: A Novel Clustering Method of Jointing Non-Negative LRR and Random Walk Graph Regularized NMF for Single-Cell Type Identification.

The development of single-cell RNA sequencing (scRNA-seq) technology has opened up a new perspective for us to study disease mechanisms at the single cell level. Cell clustering reveals the natural grouping of cells, which is a vital step in scRNA-seq data analysis. However, the high noise and dropout of single-cell data pose numerous challenges to cell clustering. In this study, we propose a novel matrix factorization method named NLRRC for single-cell type identification. NLRRC joins non-negative low-rank representation (LRR) and random walk graph regularized NMF (RWNMFC) to accurately reveal the natural grouping of cells. Specifically, we find the lowest rank representation of single-cell samples by non-negative LRR to reduce the difficulty of analyzing high-dimensional samples and capture the global information of the samples. Meanwhile, by using random walk graph regularization (RWGR) and NMF, RWNMFC captures manifold structure and cluster information before generating a cluster allocation matrix. The cluster assignment matrix contains cluster labels, which can be used directly to get the clustering results. The performance of NLRRC is validated on simulated and real single-cell datasets. The results of the experiments illustrate that NLRRC has a significant advantage in single-cell type identification.

Multi-view clustering with Laplacian rank constraint based on symmetric and nonnegative low-rank representation

Multi-view spectral clustering has attracted more and more attention due to its promising advantages in data clustering, and many related methods have been proposed, among which the method based on low-rank representation have become increasingly popular. However, the similarity matrices learned by the existing methods inevitably contain some negative entries and are generally nonsymmetric. In order to guarantee weight consistency for each pair of data points and highly correlated data points to be together, we propose a new multi-view spectral clustering model based on the symmetric and nonnegative low-rank representation. This model can learn the view-specific consistent similarity matrix and also capture the local structure and discriminative information among data by imposing symmetric and nonnegative constraints on the representation matrix. By employing the compatible and complementary information from multi-view data points, it can also learn the consensus similarity matrix for all views and perform the spectral clustering simultaneously. By the augmented Lagrangian multiplier method, an alternating iterative optimization algorithm is designed for solving this model and its computational complexity and convergence is analyzed. Comprehensive experiments on multiple multi-view data sets also verify the effectiveness and superiority of the proposed approach.

Non-negative low-rank representation based on dictionary learning for single-cell RNA-sequencing data analysis

In the analysis of single-cell RNA-sequencing (scRNA-seq) data, how to effectively and accurately identify cell clusters from a large number of cell mixtures is still a challenge. Low-rank representation (LRR) method has achieved excellent results in subspace clustering. But in previous studies, most LRR-based methods usually choose the original data matrix as the dictionary. In addition, the methods based on LRR usually use spectral clustering algorithm to complete cell clustering. Therefore, there is a matching problem between the spectral clustering method and the affinity matrix, which is difficult to ensure the optimal effect of clustering. Considering the above two points, we propose the DLNLRR method to better identify the cell type. First, DLNLRR can update the dictionary during the optimization process instead of using the predefined fixed dictionary, so it can realize dictionary learning and LRR learning at the same time. Second, DLNLRR can realize subspace clustering without relying on spectral clustering algorithm, that is, we can perform clustering directly based on the low-rank matrix. Finally, we carry out a large number of experiments on real single-cell datasets and experimental results show that DLNLRR is superior to other scRNA-seq data analysis algorithms in cell type identification.

Adaptive distance penalty based nonnegative low-rank representation for semi-supervised learning

Adaptive distance penalty based nonnegative low-rank representation for semi-supervised learning

Visualization and Analysis of Single Cell RNA-Seq Data by Maximizing Correntropy Based Non-Negative Low Rank Representation.

The exploration of single cell RNA-sequencing (scRNA-seq) technology generates a new perspective to analyze biological problems. One of the major applications of scRNA-seq data is to discover subtypes of cells by cell clustering. Nevertheless, it is challengeable for traditional methods to handle scRNA-seq data with high level of technical noise and notorious dropouts. To better analyze single cell data, a novel scRNA-seq data analysis model called Maximum correntropy criterion based Non-negative and Low Rank Representation (MccNLRR) is introduced. Specifically, the maximum correntropy criterion, as an effective loss function, is more robust to the high noise and large outliers existed in the data. Moreover, the low rank representation is proven to be a powerful tool for capturing the global and local structures of data. Therefore, some important information, such as the similarity of cells in the subspace, is also extracted by it. Then, an iterative algorithm on the basis of the half-quadratic optimization and alternating direction method is developed to settle the complex optimization problem. Before the experiment, we also analyze the convergence and robustness of MccNLRR. At last, the results of cell clustering, visualization analysis, and gene markers selection on scRNA-seq data reveal that MccNLRR method can distinguish cell subtypes accurately and robustly.

Subspace structural constraint-based discriminative feature learning via nonnegative low rank representation.

Feature subspace learning plays a significant role in pattern recognition, and many efforts have been made to generate increasingly discriminative learning models. Recently, several discriminative feature learning methods based on a representation model have been proposed, which have not only attracted considerable attention but also achieved success in practical applications. Nevertheless, these methods for constructing the learning model simply depend on the class labels of the training instances and fail to consider the essential subspace structural information hidden in them. In this paper, we propose a robust feature subspace learning approach based on a low-rank representation. In our approach, the low-rank representation coefficients are considered as weights to construct the constraint item for feature learning, which can introduce a subspace structural similarity constraint in the proposed learning model for facilitating data adaptation and robustness. Moreover, by placing the subspace learning and low-rank representation into a unified framework, they can benefit each other during the iteration process to realize an overall optimum. To achieve extra discrimination, linear regression is also incorporated into our model to enforce the projection features around and close to their label-based centers. Furthermore, an iterative numerical scheme is designed to solve our proposed objective function and ensure convergence. Extensive experimental results obtained using several public image datasets demonstrate the advantages and effectiveness of our novel approach compared with those of the existing methods.

Adaptive weighted nonnegative low-rank representation

Conventional graph based clustering methods treat all features equally even if they are redundant features or noise in the stage of graph learning, which is obviously unreasonable. In this paper, we propose a novel graph learning method named adaptive weighted nonnegative low-rank representation (AWNLRR) for data clustering. Based on the observation that noise and outliers usually cannot be represented well and suffer from larger reconstruction errors than the important features (clean features) in low-rank or sparse representation, we impose an adaptive weighted matrix on the data reconstruction errors to reinforce the role of the important features in the joint representation and thus a robust graph can be obtained. In addition, a locality constraint, i.e., distance regularization term, is introduced to capture the local structure of data and enable the obtained graph to be sparser. These appealing properties allow AWNLRR to well capture the intrinsic structure of data, and thus AWNLRR has potential to achieve a better clustering performance than other methods. Experimental results on synthetic and real databases show that the proposed method obtains the best clustering performance than some state-of-the-art methods.

Nonnegative low-rank representation based manifold embedding for semi-supervised learning

The low-rank representation (LRR) can get essential row-representation of data and it is robust to illumination variation, occlusions and other types of noise. This paper presents a novel manifold embedding classification algorithm based on nonnegative low-rank representation for semi-supervised learning (MEC-NNLRR). In the proposed algorithm, label fitness, manifold smoothness and low-rank representation are integrated, and the label information from the labeled data and the manifold structure from all data are fully and effectively utilized. Based on LRR and manifold learning, the proposed MEC-NNLRR can capture the global and local structure information of the observed data. The obtained nonnegative low-rank representation coefficients can be used as a graph similarity matrix. Considering the physical interpretation of the graph matrix, we impose the non-negativity constraint on the coefficients. In addition, no matter whether the training samples or test samples are corrupted, the proposed MEC-NNLRR is little affected by noise. Extensive experiments on public image databases demonstrate that the proposed MEC-NNLRR is an excellent algorithm and achieves satisfactory results.

A non-negative low-rank representation for hyperspectral band selection

ABSTRACTHyperspectral images are widely used in real applications due to their rich spectral information. However, the large volume brings a lot of inconvenience, such as storage and transmission. Hyperspectral band selection is an important technique to cope with this issue by selecting a few spectral bands to replace the original image. This article proposes a novel band selection algorithm that first estimates the redundancy through analysing relationships among spectral bands. After that, spectral bands are ranked according to their relative importance. Subsequently, in order to remove redundant spectral bands and preserve the original information, a maximal linearly independent subset is constructed as the optimal band combination. Contributions of this article are listed as follows: (1) A new strategy for band selection is proposed to preserve the original information mostly; (2) A non-negative low-rank representation algorithm is developed to discover intrinsic relationships among spectral bands; (3) A smart strategy is put forward to adaptively determine the optimal combination of spectral bands. To verify the effectiveness, experiments have been conducted on both hyperspectral unmixing and classification. For unmixing, the proposed algorithm decreases the average root mean square errors (RMSEs) by 0.05, 0.03, and 0.05 for the Urban, Cuprite, and Indian Pines data sets, respectively. With regard to classification, our algorithm achieves the overall accuracies of 77.07% and 89.19% for the Indian Pines and Pavia University data sets, respectively. These results are close to the performance with original images. Thus, comparative experiments not only illustrate the superiority of the proposed algorithm, but also prove the validity of band selection on hyperspectral image processing.

Robust Semi-Supervised Subspace Clustering via Non-Negative Low-Rank Representation.

Low-rank representation (LRR) has been successfully applied in exploring the subspace structures of data. However, in previous LRR-based semi-supervised subspace clustering methods, the label information is not used to guide the affinity matrix construction so that the affinity matrix cannot deliver strong discriminant information. Moreover, these methods cannot guarantee an overall optimum since the affinity matrix construction and subspace clustering are often independent steps. In this paper, we propose a robust semi-supervised subspace clustering method based on non-negative LRR (NNLRR) to address these problems. By combining the LRR framework and the Gaussian fields and harmonic functions method in a single optimization problem, the supervision information is explicitly incorporated to guide the affinity matrix construction and the affinity matrix construction and subspace clustering are accomplished in one step to guarantee the overall optimum. The affinity matrix is obtained by seeking a non-negative low-rank matrix that represents each sample as a linear combination of others. We also explicitly impose the sparse constraint on the affinity matrix such that the affinity matrix obtained by NNLRR is non-negative low-rank and sparse. We introduce an efficient linearized alternating direction method with adaptive penalty to solve the corresponding optimization problem. Extensive experimental results demonstrate that NNLRR is effective in semi-supervised subspace clustering and robust to different types of noise than other state-of-the-art methods.