Constrained Nonnegative Matrix Factorization Research Articles

Employing Constrained Nonnegative Matrix Factorization for Microstructure Segmentation.

Materials characterization using electron backscatter diffraction (EBSD) requires indexing the orientation of the measured region from Kikuchi patterns. The quality of Kikuchi patterns can degrade due to pattern overlaps arising from two or more orientations, in the presence of defects or grain boundaries. In this work, we employ constrained nonnegative matrix factorization to segment a microstructure with small grain misorientations, (<1∘), and predict the amount of pattern overlap. First, we implement the method on mixed simulated patterns-that replicates a pattern overlap scenario, and demonstrate the resolution limit of pattern mixing or factorization resolution using a weight metric. Subsequently, we segment a single-crystal dendritic microstructure and compare the results with high-resolution EBSD. By utilizing weight metrics across a low-angle grain boundary, we demonstrate how very small misorientations/low-angle grain boundaries can be resolved at a pixel level. Our approach constitutes a versatile and robust tool, complementing other fast indexing methods for microstructure characterization.

Constrained Nonnegative Matrix Factorization Based on Label Propagation for Data Representation

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nonnegative matrix factorization</i> (NMF) algorithms are a series of dimensional reduction techniques widely used in data preprocessing. To improve the performance of clustering and the discrimination of the low-dimensional representation in NMF, we proposed a novel semi-supervised <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constrained nonnegative matrix factorization based on label propagation</i> (LpCNMF). Specifically, the proposed LpCNMF adopts graph and label propagation as regularization terms, then makes use of a small amount of labeled data to predict the label information of the unlabeled data and finally obtains a predictive membership matrix with more label information. At the same time, we introduce an efficient alternating iterative algorithm to solve the optimization problem of the objective function in the LpCNMF. Unlike other NMF algorithms that only update the basis and coefficient matrices, the LpCNMF algorithm increases the update of the predictive membership matrix obtained by label propagation. Experimental results on various benchmark datasets demonstrate the superiority of our algorithm over existing state-of-the-art NMF algorithms. The code is publicly available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/ycwang-libra/LpCNMF_github.git.</uri>

Dual-Graph-Regularization Constrained Nonnegative Matrix Factorization with Label Discrimination for Data Clustering

NONNEGATIVE matrix factorization (NMF) is an effective technique for dimensionality reduction of high-dimensional data for tasks such as machine learning and data visualization. However, for practical clustering tasks, traditional NMF ignores the manifold information of both the data space and feature space, as well as the discriminative information of the data. In this paper, we propose a semisupervised NMF called dual-graph-regularization-constrained nonnegative matrix factorization with label discrimination (DCNMFLD). DCNMFLD combines dual graph regularization and prior label information as additional constraints, making full use of the intrinsic geometric and discriminative structures of the data, and can efficiently enhance the discriminative and exclusionary nature of clustering and improve the clustering performance. The evaluation of the clustering experimental results on four benchmark datasets demonstrates the effectiveness of our new algorithm.

Single channel speech enhancement using iterative constrained NMF based adaptive wiener gain

Single channel speech enhancement using iterative constrained NMF based adaptive wiener gain

Enhanced Extraction of Blood and Tissue Time-Activity Curves in Cardiac Mouse FDG PET Imaging by Means of Constrained Nonnegative Matrix Factorization.

We propose an enhanced method to accurately retrieve time-activity curves (TACs) of blood and tissue from dynamic 2-deoxy-2-[18F]fluoro-D-glucose ([18F]FDG) positron emission tomography (PET) cardiac images of mice. The method is noninvasive and consists of using a constrained nonnegative matrix factorization algorithm (CNMF) applied to the matrix (A) containing the intensity values of the voxels of the left ventricle (LV) PET image. CNMF factorizes A into nonnegative matrices H and W, respectively, representing the physiological factors (blood and tissue) and their associated weights, by minimizing an extended cost function. We verified our method on 32 C57BL/6 mice, 14 of them with acute myocardial infarction (AMI). With CNMF, we could break down the mouse LV into myocardial and blood pool images. Their corresponding TACs were used in kinetic modeling to readily determine the [18F]FDG influx constant (Ki) required to compute the myocardial metabolic rate of glucose. The calculated Ki values using CNMF for the heart of control mice were in good agreement with those published in the literature. Significant differences in Ki values for the heart of control and AMI mice were found using CNMF. The values of the elements of W agreed well with the LV structural changes induced by ligation of the left coronary artery. CNMF was compared with the recently published method based on robust unmixing of dynamic sequences using regions of interest (RUDUR). A clear improvement of signal separation was observed with CNMF compared to the RUDUR method.

A Generalized Deep Learning Clustering Algorithm Based on Non-Negative Matrix Factorization

Clustering is a popular research topic in the field of data mining, in which the clustering method based on non-negative matrix factorization (NMF) has been widely employed. However, in the update process of NMF, there is no learning rate to guide the update as well as the update depends on the data itself, which leads to slow convergence and low clustering accuracy. To solve these problems, a generalized deep learning clustering (GDLC) algorithm based on NMF is proposed in this article. Firstly, a nonlinear constrained NMF (NNMF) algorithm is constructed to achieve sequential updates of the elements in the matrix guided by the learning rate. Then, the gradient values corresponding to the element update are transformed into generalized weights and generalized biases, by inputting the elements as well as their corresponding generalized weights and generalized biases into the nonlinear activation function to construct the GDLC algorithm. In addition, for improving the understanding of the GDLC algorithm, its detailed inference procedure and algorithm design are provided. Finally, the experimental results on eight datasets show that the GDLC algorithm has efficient performance.

Micro-Doppler Extraction for Cone-Shaped Target Using Constrained Nonnegative Matrix Factorization

Micro-Doppler (MD) extraction is the precondition for target classification based on micro-motion. This letter proposes a method for MD extraction based on constrained nonnegative matrix factorization (NMF). The proposed algorithm is applied to the time-frequency spectrogram of the cone-shaped precession target. Taking the sparsity constraint, temporal continuity constraint and approximate orthogonality constraint into consideration, the basic NMF is improved to match the MD separation problem, and thus the time-frequency spectrogram of each scattering center is reconstructed by deriving the basis matrix and coefficient matrix. Morphological processing, valid frequency extraction and MD curve fitting are conducted on the reconstructed spectrograms to extract the MD accurately. Experiment results show that the proposed approach outperforms other algorithms with better accuracy and robustness.

General Community Detection in Attributed Networks with Consistent-Module Constrained Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) model has been successfully applied to discover latent community structures due to its good performance and interpretability advantages in extracting hidden patterns. However, most previous studies explore only the structural information of the network while ignoring the rich attributes. Besides, they aim at detecting densely connected communities (also called community structures) and fail to identify general structures, such as bipartite structures and mixture structures. In this paper, we research on general structure discovery and propose a new method GCDNMF (General Community Detection based on Nonnegative Matrix Factorization), which integrates structural information and node attributes through consistency module constraint to capture the community interactions. It can discover the general community structures of nodes by iteratively updating the community-interaction matrix and the node-membership matrix. We also introduce matrix initialization based on centrality and dispersion of nodes for center selection to reduce the sensitivity of random initialization. Experimental results on real-world networks with a variety of characteristics validate the performance of our approach, especially on networks with general structures. In addition, the associated initialization evaluations demonstrate the effectiveness of our method in obtaining stable results.

Metastasis-related gene identification by compound constrained NMF and a semisupervised cluster approach using pancancer multiomics features

In recent years, with the gradual increase in pancancer-related research, more attention has been given to the field of pancancer metastasis. However, the molecular mechanism of pancancer metastasis is very unclear, and identification methods for pancancer metastasis-related genes are still lacking. In view of this research status, we developed a novel pipeline to identify pancancer metastasis-related genes based on compound constrained nonnegative matrix factorization (CCNMF). To solve the above problems, the following modules were designed. A correntropy operator and feature similarity fusion (FSF) were first adopted to process the multiomics features of genes; thus, the influences caused by irrelevant biomolecular patterns, manifested as non-Gaussian noise, were minimized. CCNMF was then adopted to handle the above features with compound constraints consisting of a gene relation network and a “metastasis-related” gene set, which maximizes the biological interpretability of the metafeatures generated by NMF. Since a negative set of pancancer “metastasis-related” genes could hardly be obtained, semisupervised analyses were performed on gene features acquired by each step in our pipeline to examine our method’s effect. 83% of the 236 candidates identified by the above method were associated with the metastasis of one or more cancers, 71.9% candidates were identified immune-related in pancancer in addition to the hallmark genes. Our study provides an effective and interpretable method for identifying metastasis-related as well as immune-related genes, and the method is successfully applied to TCGA pancancer data.

Label prediction based constrained non-negative matrix factorization for semi-supervised multi-view classification

Semi-supervised multi-view classification can improve the performance by leveraging the information from both labeled and unlabeled data. But it is often a challenge to capture the information from the unlabeled multi-view data. By analyzing the relation between labeled and unlabeled data under multi-view scenario, we propose a novel model with the ability of leveraging the latent label information from the unlabeled data. In our model, a label prediction (LP) term is proposed to jointly obtain the predicted labels of unlabeled data from multiple views. The LP term is integrated into a constrained non-negative matrix factorization based multi-view framework. In this way, the LP and the multi-view representation learning are integrated into one joint learning problem, where they boost each other. Particularly, the predicted label vector is formulated to be the one-hot vector, such that the labels can be obtained directly. Moreover, we propose a new lemma about the gradient of the ℓ2,1 norm in the case of 3-factor matrix decomposition and its corollary about multi-factor matrix decomposition. Based on which, we develop an efficient algorithm and prove its convergence. Experimental results verify that our method can obtain state-of-the-art performance.

Emotional Analysis and Personalized Recommendation Analysis in Music Performance

Music performance belongs to music recreation activities, is through singing, musical instrument performance, and vocal conductor, including a variety of artistic means, to convey music to the audience with real sound effects that can be felt, and can play its social function. Emotional state is a part of the whole attitude, which is consistent with introverted feelings and intentions in attitude, and is a complex and stable physiological evaluation and experience of attitude in physiology. This paper first introduces the concepts of music performance from the perspective of music appreciation and music ability. Then based on the emotional feature learning of matrix factorization constrained nonnegative matrix factorization and model optimization algorithm are used to analyze the emotional aspects of music. Finally, through the experimental comparison of the difficulty of emotion in various artistic creations, a conclusion is drawn. The research involves matrix decomposition, mathematical modeling, model optimization, digital audio technology application, and other fields. In the third part of this paper, the constrained nonnegative matrix factorization, the constrained nonnegative matrix factorization with external information, and the model optimization algorithm are used to study the mathematical modeling.

Low computational-cost cell detection method for calcium imaging data

The rapid progress of calcium imaging techniques has reached a point where the activity of thousands to tens of thousands of cells can be recorded simultaneously with single-cell resolution in a field-of-view (FOV) of about ten mm2. Consequently, there is a pressing need for developing automatic cell detection methods for large-scale image data. Several research groups have proposed automatic cell detection algorithms. Almost all algorithms can solve large-scale optimization problems for data, including hundreds of cells recorded from a conventional FOV at a resolution of 512 × 512 pixels, but the solution becomes more difficult as the data size increases beyond that. To handle large-scale data acquired with the latest large FOV microscopes, we propose a method called low computational cost cell detection (LCCD) that is based on filtering and thresholding. We compared LCCD with two other methods, constrained non-negative matrix factorization (CNMF) and Suite2P. We found that LCCD makes it possible to detect cells in artificial and actual data showing a high number density of cells within a shorter time and with an accuracy comparable to or better than those of CNMF and Suite2P. Moreover, LCCD succeeded in detecting more than 20,000 active cells from data acquired with the latest microscopy, called FASHIO-2PM, with a FOV of 3.0 mm × 3.0 mm.

A Novel Constrained Non-negative Matrix Factorization Method for Group Functional Magnetic Resonance Imaging Data Analysis of Adult Attention-Deficit/Hyperactivity Disorder.

Attention-deficit/hyperactivity disorder (ADHD) is a common childhood psychiatric disorder that often persists into adulthood. Extracting brain networks from functional magnetic resonance imaging (fMRI) data can help explore neurocognitive disorders in adult ADHD. However, there is still a lack of effective methods to extract large-scale brain networks to identify disease-related brain network changes. Hence, this study proposed a spatial constrained non-negative matrix factorization (SCNMF) method based on the fMRI real reference signal. First, non-negative matrix factorization analysis was carried out on each subject to select the brain network components of interest. Subsequently, the available spatial prior information was mined by integrating the interested components of all subjects. This prior constraint was then incorporated into the NMF objective function to improve its efficiency. For the sake of verifying the effectiveness and feasibility of the proposed method, we quantitatively compared the SCNMF method with other classical algorithms and applied it to the dynamic functional connectivity analysis framework. The algorithm successfully extracted ten resting-state brain functional networks from fMRI data of adult ADHD and healthy controls and found large-scale brain network changes in adult ADHD patients, such as enhanced connectivity between executive control network and right frontoparietal network. In addition, we found that older ADHD spent more time in the pattern of relatively weak connectivity. These findings indicate that the method can effectively extract large-scale functional networks and provide new insights into understanding the neurobiological mechanisms of adult ADHD from the perspective of brain networks.

A novel constrained non-negative matrix factorization method based on users and items pairwise relationship for recommender systems

Non-negative matrix factorization (NMF) is a famous method to learn parts-based representations of non-negative data. It has been used successfully in various applications such as information retrieval and recommender systems. Most of the current NMF methods only focus on how each decomposed matrices vector should be modeled and disregard the relation among pairwise feature vectors of users and items. In recommender systems, the relationship between users’ factors or items’ features provides better factorization. This paper proposes a constrained non-negative matrix factorization for recommender systems (CNMF-RS), which puts constraints on pairwise vectors of users and items by applying penalties using similarity. Two cost functions are proposed to generate the corresponding updating rules for finding unknown ratings. The computational complexity analysis confirmed that CNMF-RS does not raise time complexity using constraints compared with the basic NMF. Experiments on benchmark datasets indicate that the suggested update rules converge quickly and obtain outstanding results compared to other methods.

Exploring dysconnectivity of the large-scale neurocognitive network across psychiatric disorders using spatiotemporal constrained nonnegative matrix factorization method.

Psychiatric disorders usually have similar clinical and neurobiological features. Nevertheless, previous research on functional dysconnectivity has mainly focused on a single disorder and the transdiagnostic alterations in brain networks remain poorly understood. Hence, this study proposed a spatiotemporal constrained nonnegative matrix factorization (STCNMF) method based on real reference signals to extract large-scale brain networks to identify transdiagnostic changes in neurocognitive networks associated with multiple diseases. Available temporal prior information and spatial prior information were first mined from the functional magnetic resonance imaging (fMRI) data of group participants, and then these prior constraints were incorporated into the nonnegative matrix factorization objective functions to improve their efficiency. The algorithm successfully obtained 10 resting-state functional brain networks in fMRI data of schizophrenia, bipolar disorder, attention deficit/hyperactivity disorder, and healthy controls, and further found transdiagnostic changes in these large-scale networks, including enhanced connectivity between right frontoparietal network and default mode network, reduced connectivity between medial visual network and default mode network, and the presence of a few hyper-integrated network nodes. Besides, each type of psychiatric disorder had its specific connectivity characteristics. These findings provide new insights into transdiagnostic and diagnosis-specific neurobiological mechanisms for understanding multiple psychiatric disorders from the perspective of brain networks.

A Bipartite Graph Partition-Based Coclustering Approach With Graph Nonnegative Matrix Factorization for Large Hyperspectral Images

Clustering large hyperspectral images (HSIs) is a very challenging problem because large HSIs have high dimensionality, large spectral variability, and large computational and memory consumption. Recently, sparse subspace clustering (SSC) has achieved remarkable success in HSI clustering. However, most SSC-based methods suffer from the following bottlenecks for large HSIs: 1) high computational consumption and memory space during the construction of the similarity matrix and decomposition of the graph Laplacian matrix and 2) failure to capture the relationships among dictionary atoms, sparse coefficients, and hyperspectral pixels. To address these challenges, we propose a novel algorithm that extends SSC to cocluster large HSIs, called bipartite graph partition with graph nonnegative matrix factorization (BGP-GNMF). Specifically, to fully explore the characteristics of the spectral and spatial contexts in HSIs, we propose a novel superpixel and pixel coclustering framework with bipartite graph partitioning in the joint sparse representation domain, where superpixel-based dictionary atoms are defined as disjoint vertex sets of the bipartite graph and the joint sparsity representation is mapped into the adjacency matrix of the undirected bipartite graph. To overcome the challenges of high computational consumption and large memory space for large HSIs, the bipartite graph partition with orthonormal constrained nonnegative matrix factorization is proposed to simultaneously cluster the structured dictionary atoms and hyperspectral pixels with an indicator matrix. Finally, to exploit the intrinsic geometry of HSIs, we incorporate manifold regularization into the bipartite graph partition to improve final clustering accuracy. The effectiveness and efficiency of the proposed method are verified on three classical HSIs, and the experimental results illustrate the superiority of the proposed method compared with other state-of-the-art HSI clustering methods.

Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review

Hyperspectral unmixing has been an important technique that estimates a set of endmembers and their corresponding abundances from a hyperspectral image (HSI). Nonnegative matrix factorization (NMF) plays an increasingly significant role to solve this problem. In this article, we present a comprehensive survey of the NMF-based methods proposed for hyperspectral unmixing. Taking the NMF model as a baseline, we show how to improve NMF by utilizing the main properties of HSIs (e.g., spectral, spatial, and structural information). We categorize three important development directions including constrained NMF, structured NMF, and generalized NMF. Furthermore, several experiments are conducted to illustrate the effectiveness of associated algorithms. Finally, we conclude the paper with possible future directions with the purposes of providing guidelines and inspiration to promote the development of hyperspectral unmixing.

Multichannel Blind Music Source Separation Using Directivity-Aware MNMF With Harmonicity Constraints

In this paper we present a harmonic constrained Multichannel Non-Negative Matrix Factorization (MNMF) method for the task of blind music source separation. In this model, the mixing filter encodes the spatial information in terms of magnitude and phase differences between channels whereas the source variances are modelled using a harmonic constrained NMF structure. In this work, the spatial covariance matrix is obtained from the constant-Q transform to account for the frequency logarithmic scale inherent in music signals and reduce the dimensionality of the parameters. Moreover, to mitigate the strong sensitivity to parameter initialization, we propose to initialize the spatial weights with the output of the steered response power (SRP) with the phase transform (PHAT) algorithm. The proposed method has been evaluated for the task of music source separation using a multichannel classical chamber music dataset with several polyphony and reverberation setups. Furthermore, a comparison with other state-of-the-art signal decomposition methods has been accomplished showing reliable results in terms of BSS_EVAL metrics.

Constrained non-negative matrix factorization enabling real-time insights of in situ and high-throughput experiments

Non-negative matrix factorization (NMF) is an appealing class of methods for performing unsupervised learning on streaming spectral data, particularly in time-sensitive applications such as in situ characterization of materials. These methods seek to decompose a dataset into a small number of components and weights that can compactly represent the underlying signal while effectively reconstructing the observations with minimal error. However, canonical NMF methods have no underlying requirement that the reconstruction uses components or weights that are representative of the true physical processes. In this work, we demonstrate how constraining a subset of the NMF weights or components as rigid priors, provided as known or assumed values, can provide significant improvement in revealing true underlying phenomena. We present a PyTorch-based method for efficiently applying constrained NMF and demonstrate its application to several synthetic examples. Our implementation allows an expert researcher-in-the-loop to provide and dynamically adjust the constraints during a live experiment involving streaming spectral data. Such interactive priors allow researchers to specify known or identified independent components, as well as functional expectations about the mixing or transitions between the components. We further demonstrate the application of this method to measured synchrotron x-ray total scattering data from in situ beamline experiments. In such a context, constrained NMF can result in a more interpretive and scientifically relevant decomposition than canonical NMF or other decomposition techniques. The details of the method are provided, along with general guidance for employing constrained NMF in the extraction of critical information and insights during time-sensitive experimental applications.

Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration

This paper presents a novel medical image registration algorithm named total variation constrained graph-regularization for non-negative matrix factorization (TV-GNMF). The method utilizes non-negative matrix factorization by total variation constraint and graph regularization. The main contributions of our work are the following. First, total variation is incorporated into NMF to control the diffusion speed. The purpose is to denoise in smooth regions and preserve features or details of the data in edge regions by using a diffusion coefficient based on gradient information. Second, we add graph regularization into NMF to reveal intrinsic geometry and structure information of features to enhance the discrimination power. Third, the multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given. Experiments conducted on datasets show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.