Robust Nonnegative Matrix Factorization Research Articles

Robust Nonnegative Matrix Factorization With Self-Initiated Multigraph Contrastive Fusion.

Graph regularized nonnegative matrix factorization (GNMF) has been widely used in data representation due to its excellent dimensionality reduction. When it comes to clustering polluted data, GNMF inevitably learns inaccurate representations, leading to models that are unusually sensitive to outliers in the data. For example, in a face dataset, obscured by items such as a mask or glasses, there is a high probability that the graph regularization term incorrectly describes the association relationship for that sample, resulting in an incorrect elicitation in the matrix factorization process. In this article, a novel self-initiated unsupervised subspace learning method named robust nonnegative matrix factorization with self-initiated multigraph contrastive fusion (RNMF-SMGF) is proposed. RNMF-SMGF is capable of creating samples with different angles and learning different graph structures based on these different angles in a self-initiated method without changing the original data. In the process of subspace learning guided by graph regularization, these different graph structures are fused into a more accurate graph structure, along with entropy regularization, L2,1/2 -norm constraints to facilitate the robust learning of the proposed model and the formation of different clusters in the low-dimensional space. To demonstrate the effectiveness of the proposed model in robust clustering, we have conducted extensive experiments on several benchmark datasets and demonstrated the effectiveness of the proposed method. The source code is available at: https://github.com/LstinWh/RNMF-SMGF/.

Clutter Suppression for Through-the-Wall Radar Based on Robust Non-Negative Matrix Factorization in Dual-Domain

Clutter Suppression for Through-the-Wall Radar Based on Robust Non-Negative Matrix Factorization in Dual-Domain

Comodule Estimation of Cognitive Sensor Networks Based on Partial Clustering for Partial Observed Data

The proposed study is on the partial clustering algorithms for cognitive sensor networks that deal with partially observed data. The proposed algorithms aim to estimate clusters in the presence of missing values and leverage data imputation techniques to fill in the gaps in the target and station device matrices. A modified loss function is introduced to shape the cluster centers, and robust Non-negative Matrix Factorization (NMF) algorithms are utilized to enhance the robustness of the clustering process. This research contributes to the field of cognitive sensor networks by providing insights into the challenges of partial clustering and presenting effective algorithms to address them. The proposed methods have the potential to enhance the performance of clustering tasks in various domains, including sensor networks, by accounting for missing data and producing accurate cluster reconstructions.

Nonnegative Matrix Factorization: A Review

Recent developments in Non-negative Matrix Factorization (NMF) have focused on addressing several challenges and advancing its applicability. New algorithmic variations, such as robust NMF, deep NMF, and graph-regularized NMF, have emerged to improve NMF's performance in various domains. These developments aim to enhance the interpretability, scalability, and robustness of NMF-based solutions. NMF is now widely used in audio source separation, text mining, recommendation systems, and image processing. However, NMF still faces challenges, including sensitivity to initialization, the determination of the appropriate rank, and computational complexity. Overlapping sources in audio and data sparsity in some applications remain challenging issues. Additionally, ensuring the consistency and stability of NMF results in noisy environments is a subject of ongoing research. The quest for more efficient and scalable NMF algorithms continues, especially for handling large datasets. While NMF has made significant strides in recent years, addressing these challenges is crucial for unlocking its full potential in diverse data analysis and source separation tasks.

RRNMF-MAGL: Robust regularization non-negative matrix factorization with multi-constraint adaptive graph learning for dimensionality reduction

In this paper, a new unsupervised dimensionality reduction method named robust regularization non-negative matrix factorization with multi-constraint adaptive graph learning (RRNMF-MAGL) is developed. Compared with the existing methods, RRNMF-MAGL can extract robust low-dimensional features and adaptively learn a manifold structure to well reflect the data distribution. Specifically, to alleviate the influence of outliers and noises, a robust non-negative matrix factorization (RNMF) approach with L21-norm loss function is first constructed. Then, a multi-constraint adaptive graph learning (MAGL) model is designed based on low-dimensional features to reduce the computational complexity and avoid the adverse influence of redundant information. Moreover, multiple constraints (i.e., sparsity and locality) are incorporated into graph learning for enhancing the discrimination ability of graph structure. Next, to make the learned low-dimensional features well maintain the local geometric structure information of data, a graph Laplacian regularization (GLR) is designed. Finally, an iterative update strategy is proposed to optimize RRNMF-MAGL and its convergence is verified by numerical experiments. The superior effectiveness and robustness of RRNMF-MAGL is demonstrated by extensive experiments on eight publicly available datasets.

Robust dual-graph discriminative NMF for data classification

In this paper, we propose a new supervised non-negative matrix factorization algorithm, named Robust Dual-graph Discriminative Non-negative Matrix Factorization (RDGDNMF). This model not only considers the differentiability between data samples, but also explores the intrinsic geometric structure information of data and feature space simultaneously, so it can obtain a more effective low-dimensional representation. Considering that the real data usually contains noise and outliers, we adopt ℓ2,12 norm to minimize the loss function of Non-negative Matrix Factorization (NMF) to improve the robustness of the algorithm. In addition, we also give the multiplication update rules and prove the convergence of the algorithm. Then, we use this model and K-Nearest Neighbor (KNN) to reduce dimension and classify data. By comparing the classification results with other advanced methods on multiple datasets, the effectiveness and robustness of the proposed method are demonstrated.

Robust local-coordinate non-negative matrix factorization with adaptive graph for robust clustering

With its unique geometric properties, non-negative matrix factorization (NMF) has become one of the widely used clustering methods in the field of data mining. Regrettably, most existing NMF methods are sensitive to super-noise (super-outliers). This paper proposes a novel robust clustering method to address this issue. Based on the Hx loss function, this method establishes a novel robust adaptive local structure learning strategy, reducing the interference of noise (outliers) on data reconstruction and space exploration. In addition, a new orthogonal regularization term is incorporated into the model, ensuring the orthogonality of the factor matrix and enhancing the discriminant ability. Finally, we develop an efficient algorithm to solve the resultant model and analyze its convergence from theoretical and experimental aspects. Experimental results on random synthetic data sets and benchmark databases demonstrate that the proposed method outperforms the existing robust NMF methods in terms of spatial structure learning, discriminant power, and robustness.

RNMFLP: Predicting circRNA-disease associations based on robust nonnegative matrix factorization and label propagation.

Circular RNAs (circRNAs) are a class of structurally stable endogenous noncoding RNA molecules. Increasing studies indicate that circRNAs play vital roles in human diseases. However, validating disease-related circRNAs in vivo is costly and time-consuming. A reliable and effective computational method to identify circRNA-disease associations deserves further studies. In this study, we propose a computational method called RNMFLP that combines robust nonnegative matrix factorization (RNMF) and label propagation algorithm (LP) to predict circRNA-disease associations. First, to reduce the impact of false negative data, the original circRNA-disease adjacency matrix is updated by matrix multiplication using the integrated circRNA similarity and the disease similarity information. Subsequently, the RNMF algorithm is used to obtain the restricted latent space to capture potential circRNA-disease pairs from the association matrix. Finally, the LP algorithm is utilized to predict more accurate circRNA-disease associations from the integrated circRNA similarity network and integrated disease similarity network, respectively. Fivefold cross-validation of four datasets shows that RNMFLP is superior to the state-of-the-art methods. In addition, case studies on lung cancer, hepatocellular carcinoma and colorectal cancer further demonstrate the reliability of our method to discover disease-related circRNAs.

Robust multi-view non-negative matrix factorization for clustering

Non-negative matrix factorization (NMF) has attracted much attention for multi-view clustering due to its good theoretical and practical values. Although existing multi-view NMF methods have achieved satisfactory performance to some extent, there still exist the following problems: 1) most existing methods only consider the first-order relationship to construct the similarity matrix, which cannot fully explore the neighborhood information; 2) most existing methods only consider the common information shared by different views, and the complementary information contained in different views is often ignored. To tackle the above-mentioned shortcomings, we present a novel multi-view clustering approach, called robust multi-view NMF (RMNMF). Specifically, in RMNMF, we consider the high-order relationship among features, where the first-order and second-order relationship is utilized to obtain an optimal neighborhood structure. Also, we introduce the Hilbert-Schmidt independence criterion (HSIC) to fully explore the complementary information in different views. Extensive experimental results on several benchmark datasets prove the effectiveness of our proposed approach.

RNMF-Guided Deep Network for Signal Separation of GPR Without Labeled Data

The clutter encountered in the ground-penetrating radar (GPR) system severely obscures the visibility of subsurface objects, especially in the case of overlapping target responses and clutter. In this letter, a novel self-supervised learning strategy with dual-network architecture and pseudolabels is proposed. First, the dual-network consists of two subnetworks: one is to simulate the low-rank part, and another simulates the sparse part. Second, the raw GPR data are decomposed as the sum of low-rank and sparse matrices by robust nonnegative matrix factorization (RNMF), termed two pseudolabels. Then, these pseudolabels guide the two subnetworks to accurately reconstruct the target response and clutter trace by trace, respectively. Results based on simulated data by gprMax and real datasets demonstrate that the proposed method is effective in separating target response from clutter and can achieve a similar effect as RNMF in less time without any prior information.

GPR Clutter Removal Based on Factor Group-Sparse Regularization

Clutter removal is of vital importance to underground detection via ground penetrating radar (GPR) since the target response is usually overwhelmed by strong clutter. The low-rank and sparse decomposition (LRSD) method, which decomposes the GPR data into a low-rank background matrix and a sparse target matrix, has been applied in GPR. However, the existing LRSD-based methods, such as robust principal component analysis (RPCA) and robust non-negative matrix factorization, are sensitive to the regularization parameter or have high computation complexity. In this letter, a novel clutter removal based on factor group-sparse regularization is proposed. It uses a nonconvex matrix factorization as a surrogate for the matrix rank rather than the nuclear norm as in the RPCA. It has good efficiency and robustness to the parameters. Simulation and experimental results demonstrate that the proposed method has higher performance in terms of the improvement factor values and lower computational complexity than the state-of-the-art methods.

Mitral Valve Segmentation Using Robust Nonnegative Matrix Factorization.

Analyzing and understanding the movement of the mitral valve is of vital importance in cardiology, as the treatment and prevention of several serious heart diseases depend on it. Unfortunately, large amounts of noise as well as a highly varying image quality make the automatic tracking and segmentation of the mitral valve in two-dimensional echocardiographic videos challenging. In this paper, we present a fully automatic and unsupervised method for segmentation of the mitral valve in two-dimensional echocardiographic videos, independently of the echocardiographic view. We propose a bias-free variant of the robust non-negative matrix factorization (RNMF) along with a window-based localization approach, that is able to identify the mitral valve in several challenging situations. We improve the average f1-score on our dataset of 10 echocardiographic videos by 0.18 to a f1-score of 0.56.

A novel industrial process fault monitoring method based on kernel robust non-negative matrix factorization

Industrial processes are characterized by large amounts of nonlinear and noisy data, which pose a critical challenge to the accuracy and rapidity of fault detection. In this paper, an industrial process fault monitoring method based on kernel robust non-negative matrix factorization is proposed. This method uses the kernel technique to map the nonlinear data to high-dimensional linear space, where the local features of the sample will be extracted by the non-negative matrix factorization (NMF) method. However, noise signals will inevitably be mixed. Therefore, a sparse error matrix is introduced to isolate fault and noise information. Finally, a new monitoring statistics and a fault detection framework are constructed. On the TE platform, the algorithm proposed in this paper is compared with kernel principal component analysis and kernel NMF methods in nonlinear experiments and robustness experiments through two performance indicators: fault detection rate and fault delay. The results prove the effectiveness of the algorithm in this paper.

Robust Non-Negative Matrix Factorization Based on Noise Fuzzy Clustering Mechanism and Application to Environmental Observation Data Analysis

Robust Non-Negative Matrix Factorization Based on Noise Fuzzy Clustering Mechanism and Application to Environmental Observation Data Analysis

Music Signal Separation Using Supervised Robust Non-Negative Matrix Factorization with β-divergence

We propose a supervised method based on robust non-negative matrix factorization (RNMF) for music signal separation with β-divergence called supervised robust non-negative matrix factorization (SRNMF). Although RNMF method is an effective method for separating music signals, its separation performance degrades due to has no prior knowledge. To address this problem, in this paper, we develop SRNMF that unifying the robustness of RNMF and the prior knowledge to improve such separation performance on instrumental sound signals (e.g., piano, oboe and trombone). Application to the observed instrumental sound signals is an effective strategy by extracting the spectral bases of training sequences by using RNMF. In addition, β-divergence based on SRNMF be extended. The results obtained from our experiments on instrumental sound signals are promising for music signal separation. The proposed method achieves better separation performance than the conventional methods.

Robust semi-supervised non-negative matrix factorization for binary subspace learning

Non-negative matrix factorization and its extensions were applied to various areas (i.e., dimensionality reduction, clustering, etc.). When the original data are corrupted by outliers and noise, most of non-negative matrix factorization methods cannot achieve robust factorization and learn a subspace with binary codes. This paper puts forward a robust semi-supervised non-negative matrix factorization method for binary subspace learning, called RSNMF, for image clustering. For better clustering performance on the dataset contaminated by outliers and noise, we propose a weighted constraint on the noise matrix and impose manifold learning into non-negative matrix factorization. Moreover, we utilize the discrete hashing learning method to constrain the learned subspace, which can achieve a binary subspace from the original data. Experimental results validate the robustness and effectiveness of RSNMF in binary subspace learning and image clustering on the face dataset corrupted by Salt and Pepper noise and Contiguous Occlusion.

Data representation using robust nonnegative matrix factorization for edge computing.

As a popular data representation technique, Nonnegative matrix factorization (NMF) has been widely applied in edge computing, information retrieval and pattern recognition. Although it can learn parts-based data representations, existing NMF-based algorithms fail to integrate local and global structures of data to steer matrix factorization. Meanwhile, semi-supervised ones ignore the important role of instances from different classes in learning the representation. To solve such an issue, we propose a novel semi-supervised NMF approach via joint graph regularization and constraint propagation for edge computing, called robust constrained nonnegative matrix factorization (RCNMF), which learns robust discriminative representations by leveraging the power of both L2, 1-norm NMF and constraint propagation. Specifically, RCNMF explicitly exploits global and local structures of data to make latent representations of instances involved by the same class closer and those of instances involved by different classes farther. Furthermore, RCNMF introduces the L2, 1-norm cost function for addressing the problems of noise and outliers. Moreover, L2, 1-norm constraints on the factorial matrix are used to ensure the new representation sparse in rows. Finally, we exploit an optimization algorithm to solve the proposed framework. The convergence of such an optimization algorithm has been proven theoretically and empirically. Empirical experiments show that the proposed RCNMF is superior to other state-of-the-art algorithms.

Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization.

Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise) assumed on the data. In many applications, the noise model is unknown and difficult to estimate. In this paper, we define a multi-objective NMF (MO-NMF) problem, where several objectives are combined within the same NMF model. We propose to use Lagrange duality to judiciously optimize for a set of weights to be used within the framework of the weighted-sum approach, that is, we minimize a single objective function which is a weighted sum of the all objective functions. We design a simple algorithm based on multiplicative updates to minimize this weighted sum. We show how this can be used to find distributionally robust NMF (DR-NMF) solutions, that is, solutions that minimize the largest error among all objectives, using a dual approach solved via a heuristic inspired from the Frank-Wolfe algorithm. We illustrate the effectiveness of this approach on synthetic, document and audio data sets. The results show that DR-NMF is robust to our incognizance of the noise model of the NMF problem.

Robust distribution-based nonnegative matrix factorizations for dimensionality reduction

As a popular dimensionality-reduction technique, nonnegative matrix factorization (NMF) has been widely researched since it is consistent with human cognitive processes in the psychology and physiology. This paper presents a novel NMF framework, called robust distribution-based NMF (RDNMF), to learn the robustly discriminative representations for data. In this RDNMF, a Kullback–Leibler divergence to measure the similarity between the data and representations is introduced, which fully preserves the geometrical structure of data. Meanwhile, this RDNMF employs the l2,1-norm loss to reduce the influence of noise and outliers. This paper further proposes a semi-supervised RDNMF (SRDNMF) by enforcing the representations of labeled points in the same class to be aligned on the same axis. The proposed RDNMF and SRDNMF are solved by the modified multiplicative update rules. Clustering experiments on seven benchmark datasets demonstrate the effectiveness of our methods in comparison to other state-of-the-art methods.

A robust semi-supervised NMF model for single cell RNA-seq data.

BackgroundSingle-cell RNA-sequencing (scRNA-seq) technology is a powerful tool to study organism from a single cell perspective and explore the heterogeneity between cells. Clustering is a fundamental step in scRNA-seq data analysis and it is the key to understand cell function and constitutes the basis of other advanced analysis. Nonnegative Matrix Factorization (NMF) has been widely used in clustering analysis of transcriptome data and achieved good performance. However, the existing NMF model is unsupervised and ignores known gene functions in the process of clustering. Knowledges of cell markers genes (genes that only express in specific cells) in human and model organisms have been accumulated a lot, such as the Molecular Signatures Database (MSigDB), which can be used as prior information in the clustering analysis of scRNA-seq data. Because the same kind of cells is likely to have similar biological functions and specific gene expression patterns, the marker genes of cells can be utilized as prior knowledge in the clustering analysis.MethodsWe propose a robust and semi-supervised NMF (rssNMF) model, which introduces a new variable to absorb noises of data and incorporates marker genes as prior information into a graph regularization term. We use rssNMF to solve the clustering problem of scRNA-seq data.ResultsTwelve scRNA-seq datasets with true labels are used to test the model performance and the results illustrate that our model outperforms original NMF and other common methods such as KMeans and Hierarchical Clustering. Biological significance analysis shows that rssNMF can identify key subclasses and latent biological processes. To our knowledge, this study is the first method that incorporates prior knowledge into the clustering analysis of scRNA-seq data.