Graph Regularized Non-negative Matrix Factorization Research Articles

Dual semi-supervised hypergraph regular multi-view NMF with anchor graph embedding

Graph regularized nonnegative matrix factorization (GNMF) has been widely used in multi-view clustering tasks due to its good clustering properties. However, it uses a simple graph to describe the complex data relationship of multiple views and tries to obtain a consistent low-dimensional representation, which undoubtedly brings challenges to its clustering performance. In addition, clustering a large amount of high-dimensional data from multiple views undoubtedly faces a huge computational burden. In order to effectively improve the performance and efficiency of GNMF based multi-view clustering algorithm, this paper proposes a dual semi-supervised hypergraph regular multi-view clustering method with anchor graph embedding (DSSHMNMFAE). Specifically, DSSHMNMFAE develops a new anchor selection method to generate anchors and the anchor bipartite graph is constructed to embed the matrix factorization process. DSSHMNMFAE constructs a hypergraph to effectively learn the high-order relationship between data from multiple views. In order to perform semi-supervised learning more efficiently, DSSHMNMFAE integrates pairwise constraint information and label constraint information into the clustering process as dual label information. In addition, DSSHMNMFAE considers the learning of both consistency information and complementarity information, and adopts adaptive measures to distinguish the contributions of different views. We use the alternating iterative algorithm to optimize the objective function of DSSHMNMFAE. The experimental results on eight real datasets show that the performance of DSSHMNMFAE is comparable to other algorithms.

Graph-Regularized Non-Negative Matrix Factorization for Single-Cell Clustering in scRNA-Seq Data.

The advent of single-cell RNA sequencing (scRNA-seq) has brought forth fresh perspectives on intricate biological processes, revealing the nuances and divergences present among distinct cells. Accurate single-cell analysis is a crucial prerequisite for in-depth investigation into the underlying mechanisms of heterogeneity. Due to various technical noises, like the impact of dropout values, scRNA-seq data remains challenging to interpret. In this work, we propose an unsupervised learning framework for scRNA-seq data analysis (aka Sc-GNNMF). Based on the non-negativity and sparsity of scRNA-seq data, we propose employing graph-regularized non-negative matrix factorization (GNNMF) algorithm for the analysis of scRNA-seq data, which involves estimating cell-cell sparse similarity and gene-gene sparse similarity through Laplacian kernels and p-nearest neighbor graphs ( p-NNG). By assuming intrinsic geometric local invariance, we use a weighted p-nearest known neighbors ( p-NKN) to optimize the scRNA-seq data. The optimized scRNA-seq data then participates in the matrix decomposition process, promoting the closeness of cells with similar types in cell-gene data space and determining a more suitable embedding space for clustering. Sc-GNNMF demonstrates superior performance compared to other methods and maintains satisfactory compatibility and robustness, as evidenced by experiments on 11 real scRNA-seq datasets. Furthermore, Sc-GNNMF yields excellent results in clustering tasks, extracting useful gene markers, and pseudo-temporal analysis.

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/.

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.

Action Recognition using Spatial and Temporal Features with Kernel SVM

A new low-level visual feature, called Spatio-temporal context distribution feature of interest points is used to describe human actions. Each action video is expressed as a set of relative XYT coordinates between interest points listed pair wise in a local region. From the input image frames the Locally Weighted Word Context (LWWC ) descriptor encodes the spatial context interest points rather than being limited to a single interest point and the Graph Regularized Nonnegative Matrix Factorization (GNMF) is used to encode the geometrical information by constructing a nearest neighbour graph. By extracting the kernel weights of the obtained feature variables , the kernel weighted SVM is modelled to jointly capture the compatibility between multilevel action features and action classes and the compatibility between multilevel scene features and scene classes. The contextual relationship between action classes and scene classes is derived using the kernel weight as a variable.

Graph Regularized Sparse Non-Negative Matrix Factorization for Clustering

The graph regularized nonnegative matrix factorization (GNMF) algorithms have received a lot of attention in the field of machine learning and data mining, as well as the square loss method is commonly used to measure the quality of reconstructed data. However, noise is introduced when data reconstruction is performed; and the square loss method is sensitive to noise, which leads to degradation in the performance of data analysis tasks. To solve this problem, a novel graph regularized sparse NMF (GSNMF) is proposed in this article. To obtain a cleaner data matrix to approximate the high-dimensional matrix, the l₁-norm to the low-dimensional matrix is added to achieve the adjustment of data eigenvalues in the matrix and sparsity constraint. In addition, the corresponding inference and alternating iterative update algorithm to solve the optimization problem are given. Then, an extension of GSNMF, namely, graph regularized sparse nonnegative matrix trifactorization (GSNMTF), is proposed, and the detailed inference procedure is also shown. Finally, the experimental results on eight different datasets demonstrate that the proposed model has a good performance.

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.

Robust Exponential Graph Regularization Non-Negative Matrix Factorization Technology for Feature Extraction

Graph regularized non-negative matrix factorization (GNMF) is widely used in feature extraction. In the process of dimensionality reduction, GNMF can retain the internal manifold structure of data by adding a regularizer to non-negative matrix factorization (NMF). Because Ga NMF regularizer is implemented by local preserving projections (LPP), there are small sample size problems (SSS). In view of the above problems, a new algorithm named robust exponential graph regularized non-negative matrix factorization (REGNMF) is proposed in this paper. By adding a matrix exponent to the regularizer of GNMF, the possible existing singular matrix will change into a non-singular matrix. This model successfully solves the problems in the above algorithm. For the optimization problem of the REGNMF algorithm, we use a multiplicative non-negative updating rule to iteratively solve the REGNMF method. Finally, this method is applied to AR, COIL database, Yale noise set, and AR occlusion dataset for performance test, and the experimental results are compared with some existing methods. The results indicate that the proposed method is more significant.

Semi-supervised non-negative matrix tri-factorization with adaptive neighbors and block-diagonal learning

Graph-regularized non-negative matrix factorization (GNMF) is proved to be effective for the clustering of nonlinear separable data. Existing GNMF variants commonly improve model performance by adding different additional constraints or refining the model factorization form, which can lead to problems such as increased algorithm complexity or insufficient performance release. In this paper, we propose semi-supervised non-negative matrix tri-factorization with adaptive neighbors and block-diagonal (ABNMTF). Different from existing methods, in ABNMTF the similarity graph matrix is learned from the original data by adaptive neighbors k-nearest model, and a block diagonal matrix is constructed based on a few labeled data to update the similarity matrix. Our approach reconstructs the block diagonal structure into the adaptive similarity matrix, which enables simultaneous learning of the similarity matrix and label binding during factorization, engendering a distinguishable subspace representation matrix and therefore improving the clustering performance without significantly increasing the complexity of the algorithm. We also represent an optimization method to solve the ABNMTF and provide analyses of convergence and computational complexity. Extensive experiments on 8 real image datasets show that the proposed algorithm reports superior performance against several state-of-the-art approaches. Code has been made available at:https://github.com/LstinWh/ABNMTF.

Graph Regularized Nonnegative Matrix Factorization for Community Detection in Attributed Networks

Community detection has become an important research topic in machine learning due to the proliferation of network data. However, most existing methods have been developed based on only exploiting the topology structures of the network, which can result in missing the advantage of using the nodes' attribute information. As a result, it is expected that much valuable information that could be used to improve the quality of discovered communities will be ignored. To solve this limitation, we propose a novel Augment Graph Regularization Nonnegative Matrix Factorization for Attributed Networks (AGNMF-AN) method, which is simple yet effective. Firstly, Augment Attributed Graph (AAG) is applied to combine both the topological structure and attributed nodes of the network. Secondly, we introduced an effective framework to update the affinity matrix, in which the affinity matrix's weight in each iteration is modified adaptively instead of using a fixed affinity matrix in the classical graph regularization-based nonnegative matrix factorization methods. Thirdly, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2,1}$</tex-math></inline-formula> -norm is utilized to reduce the effect of random noise and outliers in the quality of structure community. Experimental results show that our method performs unexpectedly well in comparison to existing state-of-the-art methods in attributed networks.

Attribute community detection based on latent representation learning and graph regularized non-negative matrix factorization

In recent years, complex networks have become increasingly difficult to detect effectively with the rapid development of networks. On the one hand, the scale of the network has increased sharply, and on the other hand, the nodes in the network contain rich content. The existing algorithms do not take the different richness of attribute information of nodes in the attribute network into account. And the topology information of the node is inconsistent with the attribute information. Thus, this paper proposes an attribute community detection algorithm based on latent representation learning and graph-regularized non-negative matrix factorization (LRL-GNMF). First, the topological information and attribute information in the attribute network is decomposed based on non-negative matrix factorization respectively. Thereby, the member distribution matrix and the attribute distribution matrix are obtained. Secondly, an affinity matrix is constructed for the attribute matrix, and the latent representation of the attribute information is obtained using the latent representation learning method. In addition, a transition matrix is constructed according to the Markov transition probability. The node membership distribution matrix and the attribute distribution matrix are linked. Finally, since the attribute information of nodes in the network is different, a topology-dominated model and an attribute-dominated model are respectively constructed to solve this problem. At the same time, a graph regularization term is introduced to guide the model to obtain more accurate community detection. This paper conducts experimental analysis on 8 real networks. The experimental results show that the proposed algorithm in this paper outperforms the other 11 compared algorithms in the evaluation indicators of community detection accuracy and standard mutual information.

GNMF-based quadratic feature extraction in SSTFT domain for epileptic EEG detection

The EEG is an indispensable tool for clinical diagnosis of neurological disorders. The issue that how to correctly decoding the pathological information from EEG has been attracting a lot of interest. This paper creates a robust feature extraction scheme based on synchrosqueezing short-time Fourier transform (SSTFT) and graph regularized non-negative matrix factorization (GNMF), which is applied to epileptic EEG detection. The SSTFT is employed to analyze the EEG in time–frequency domain, followed by a GNMF decomposition that maps these components into a low-dimensional representation where latent clues are easily emphasized and learned, and finally the logarithmic energy, computed as features, is fed to a fuzzy K-Nearest Neighbor classifier for the purpose of discriminating seizure events. Our method is evaluated using two public databases including Bonn database and CHB-MIT database. Obtained results confirm the superiority of the proposed features by achieving classification accuracy of at least 98.0% for both short-term and long-term EEG recordings. It is expected to offer a new thought and perspective for the study and design of the automatic EEG monitoring system.

HyperNTF: A hypergraph regularized nonnegative tensor factorization for dimensionality reduction

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by tensors. However, most of tensor decomposition methods are the linear feature extraction techniques, which are unable to reveal the nonlinear structure within high-dimensional data. To address such problem, a lot of algorithms have been proposed for simultaneously performs linear and non-linear feature extraction. A representative algorithm is the Graph Regularized Nonnegative Matrix Factorization (GNMF) for image clustering. However, the normal 2-order graph can only model the pairwise similarity of objects, which cannot sufficiently exploit the complex structures of samples. Thus, we propose a novel method, named Hypergraph Regularized Nonnegative Tensor Factorization (HyperNTF), which utilizes hypergraph to model the complex connections among samples and employs the factor matrix corresponding with last mode of Canonical Polyadic (CP) decomposition as low-dimensional representation of original data. Extensive experiments on synthetic manifolds, real-world image datasets, and EEG signals, demonstrating that HyperNTF outperforms the state-of-the-art methods in terms of dimensionality reduction, clustering, and classification.

Robust graph regularization nonnegative matrix factorization for link prediction in attributed networks

Robust graph regularization nonnegative matrix factorization for link prediction in attributed networks

M6Adecom: Analysis of m6A profile matrix based on graph regularized non-negative matrix factorization.

Epitranscriptomic m6A methylation is shown to mediate extensive regulations under the context of various RNA binding protein (RBP) readers. With m6A methylation data has reached a sizable scale, the functional context-aware analysis of m6A profiles is becoming more feasible and demanded. In this study, we employed graph regularized non-negative matrix factorization (GNMF) for m6A profile analysis and comparison, where the RBP binding preference of m6A sites were incorporated as the functional context-based graph constraint term. Compared to the baseline non-negative matrix factorization (NMF) method, this GNMF-based method could better capture the distinctions in multiple functional characteristics between different group of m6A sites, including but not limited to the associated biological pathways and disease genes. We further established m6Adecom, an online tool that can be used for correlation and enrichment analysis of m6A profiles using the matrix decomposition result from GNMF, and gene set enrichment analysis based on the high-score m6A sites. m6Adecom is freely accessible at http://www.rnanut.net/m6adecom.

Automatic Epileptic Seizure Detection Using Graph-Regularized Non-Negative Matrix Factorization and Kernel-Based Robust Probabilistic Collaborative Representation.

Automatic seizure detection system can serve as a meaningful clinical tool for the treatment and analysis of epilepsy using electroencephalogram (EEG) and has obtained rapid development. An automatic detection of epileptic seizure method based on kernel-based robust probabilistic collaborative representation (ProCRC) combined with graph-regularized non-negative matrix factorization (GNMF) is proposed in this work. The raw EEG signals are pre-processed through the wavelet transform to obtain time-frequency distribution of EEG signals as preliminary feature information and GNMF is further employed for dimension reduction, retaining and enhancing the productive feature information of EEG signals. Then, the test sample is represented using robust ProCRC that can decide whether the testing sample belongs to each class (seizure or non-seizure) by jointly maximizing the likelihood. In addition, the kernel trick is applied to improve the separability of non-linear high dimensional EEG signals in robust ProCRC. Finally, post-processing techniques are introduced to generate more accurate and reliable results. The average epoch-based sensitivity of 96.48%, event-based sensitivity of 93.65% and specificity of 98.55% are acquired in this method, which is evaluated on the public Freiburg EEG database.

Automatic detection for epileptic seizure using graph-regularized nonnegative matrix factorization and Bayesian linear discriminate analysis

Epilepsy is a neurological disorder characterized by excessive neuronal discharge which results in many problems in terms of behavior, state of mind, consciousness, and can threaten the lives of patients. An automatic epileptic seizure detection method with graph-regularized non-negative matrix factorization (GNMF) and Bayesian linear discriminate analysis (BLDA) is presented in this paper. First, discrete wavelet decomposition is applied to analyze raw electroencephalogram (EEG) signals, and the normalization based on differential operator is used to guarantee the nonnegative constraint and reinforce the distinction between seizure and non-seizure signals. Then, GNMF is employed to dimensionality reduction and feature extraction for EEG data, which could capture a parts-based representation of samples and obtain more discriminative features. The EEG features are calculated and entered into the BLDA classifier for categorized results. The public Freiburg EEG database is used to evaluate the performance of the proposed seizure detection method. The results showed event-based sensitivity of 95.24%, epoch-based sensitivity of 93.20%, and a false-alarm rate of 0.5/h. These results demonstrate the potential clinical value of this method for automatic seizure detection.

Orthogonal Dual Graph-Regularized Nonnegative Matrix Factorization for Co-Clustering

Nonnegative Matrix Factorization (NMF) has received great attention in the era of big data, owing to its roles in efficiently reducing data dimension and producing feature-based data representation. In this paper, we first propose two new NMF optimization models, called an orthogonal dual graph regularized nonnegative matrix factorization (ODGNMF) method and its modified version: an orthogonal dual graph regularized nonnegative matrix tri-factorization (ODGNMTF) method. Compared with the existing models, our models can preserve the geometrical structures of data manifold and feature manifold by constructing two graphs, and ensure the orthogonality of factor matrices such that they have better NMF performance. Then, two efficient algorithms are developed to solve the models, and the convergence theory of the algorithms is established. Numerical tests by applying our algorithms to mine randomly generated data sets and well-known public databases demonstrate that ODGNMF and ODGNMTF have better numerical performance than the state-of-the-art algorithms in view of computational cost, robustness, sensitivity and sparseness.

Sparse robust graph-regularized non-negative matrix factorization based on correntropy.

Non-negative Matrix Factorization (NMF) is a popular data dimension reduction method in recent years. The traditional NMF method has high sensitivity to data noise. In the paper, we propose a model called Sparse Robust Graph-regularized Non-negative Matrix Factorization based on Correntropy (SGNMFC). The maximized correntropy replaces the traditional minimized Euclidean distance to improve the robustness of the algorithm. Through the kernel function, correntropy can give less weight to outliers and noise in data but give greater weight to meaningful data. Meanwhile, the geometry structure of the high-dimensional data is completely preserved in the low-dimensional manifold through the graph regularization. Feature selection and sample clustering are commonly used methods for analyzing genes. Sparse constraints are applied to the loss function to reduce matrix complexity and analysis difficulty. Comparing the other five similar methods, the effectiveness of the SGNMFC model is proved by selection of differentially expressed genes and sample clustering experiments in three The Cancer Genome Atlas (TCGA) datasets.

Graph-Based Blind Hyperspectral Unmixing via Nonnegative Matrix Factorization

Hyperspectral unmixing (HU) is a crucial step in the hyperspectral image (HSI) analysis. It aims at decomposing the observed spectrum at each pixel into a collection of constituent endmembers, weighted by their abundances. In a close spatial neighborhood, due to spatial autocorrelation, the abundances of an endmember tend to be similar to each other. Therefore, the spectra at the neighboring pixels are also very much alike. Recently, many studies have focused on graph-regularized nonnegative matrix factorization (NMF) approaches to address the blind HU problem. This is mainly because graph structures allow spatial–spectral relations to be effectively embedded in the NMF framework. This article takes one step further by defining each abundance map as a signal on a suitable graph, which enables the HU problem to be analyzed for the first time from a graph signal processing perspective. This article introduces a novel Laplacian regularizer based on the $l_{1}$ -norm, where graph spectral analysis is utilized to show that the regularizer has natural piecewise smooth (PWS) signal promotion and noise rejection capabilities. A graph-based blind HU algorithm is developed by incorporating this regularizer and an $l_{1/2}$ -abundance sparsity constraint into the NMF problem. Since the featured regularizer exploits the PWS property of abundance maps, the proposed method is effective in HU. The experiments conducted on synthetic and real HSIs demonstrate that it has superior performance compared with several popular HU algorithms.