Use Of Nonnegative Matrix Factorization Research Articles

Advances in cancer DNA methylation analysis with methPLIER: use of non-negative matrix factorization and knowledge-based constraints to enhance biological interpretability

DNA methylation is an epigenetic modification that results in dynamic changes during ontogenesis and cell differentiation. DNA methylation patterns regulate gene expression and have been widely researched. While tools for DNA methylation analysis have been developed, most of them have focused on intergroup comparative analysis within a dataset; therefore, it is difficult to conduct cross-dataset studies, such as rare disease studies or cross-institutional studies. This study describes a novel method for DNA methylation analysis, namely, methPLIER, which enables interdataset comparative analyses. methPLIER combines Pathway Level Information Extractor (PLIER), which is a non-negative matrix factorization (NMF) method, with regularization by a knowledge matrix and transfer learning. methPLIER can be used to perform intersample and interdataset comparative analysis based on latent feature matrices, which are obtained via matrix factorization of large-scale data, and factor-loading matrices, which are obtained through matrix factorization of the data to be analyzed. We used methPLIER to analyze a lung cancer dataset and confirmed that the data decomposition reflected sample characteristics for recurrence-free survival. Moreover, methPLIER can analyze data obtained via different preprocessing methods, thereby reducing distributional bias among datasets due to preprocessing. Furthermore, methPLIER can be employed for comparative analyses of methylation data obtained from different platforms, thereby reducing bias in data distribution due to platform differences. methPLIER is expected to facilitate cross-sectional DNA methylation data analysis and enhance DNA methylation data resources.

A Robust Method for the Unsupervised Scoring of Immunohistochemical Staining.

Immunohistochemistry is a powerful technique that is widely used in biomedical research and clinics; it allows one to determine the expression levels of some proteins of interest in tissue samples using color intensity due to the expression of biomarkers with specific antibodies. As such, immunohistochemical images are complex and their features are difficult to quantify. Recently, we proposed a novel method, including a first separation stage based on non-negative matrix factorization (NMF), that achieved good results. However, this method was highly dependent on the parameters that control sparseness and non-negativity, as well as on algorithm initialization. Furthermore, the previously proposed method required a reference image as a starting point for the NMF algorithm. In the present work, we propose a new, simpler and more robust method for the automated, unsupervised scoring of immunohistochemical images based on bright field. Our work is focused on images from tumor tissues marked with blue (nuclei) and brown (protein of interest) stains. The new proposed method represents a simpler approach that, on the one hand, avoids the use of NMF in the separation stage and, on the other hand, circumvents the need for a control image. This new approach determines the subspace spanned by the two colors of interest using principal component analysis (PCA) with dimension reduction. This subspace is a two-dimensional space, allowing for color vector determination by considering the point density peaks. A new scoring stage is also developed in our method that, again, avoids reference images, making the procedure more robust and less dependent on parameters. Semi-quantitative image scoring experiments using five categories exhibit promising and consistent results when compared to manual scoring carried out by experts.

Accurate image derived input function in [18F]SynVesT-1 mouse studies using isoflurane and ketamine/xylazine anesthesia

BackgroundKinetic modeling in positron emission tomography (PET) requires measurement of the tracer plasma activity in the absence of a suitable reference region. To avoid invasive blood sampling, the use of an image derived input function has been proposed. However, an accurate delineation of the blood pool region in the PET image is necessary to obtain unbiased blood activity. Here, to perform brain kinetic modeling in [18F]SynVesT-1 dynamic scans, we make use of non-negative matrix factorization (NMF) to unmix the activity signal from the different tissues that can contribute to the heart region activity, and extract only the left ventricle activity in an unbiased way. This method was implemented in dynamic [18F]SynVesT-1 scans of mice anesthetized with either isoflurane or ketamine–xylazine, two anesthestics that we showed to affect differently radiotracer kinetics. The left ventricle activity (NMF-IDIF) and a manually delineated cardiac activity (IDIF) were compared with arterial blood samples (ABS), and for isoflurane anesthetized mice, arteriovenous (AV) shunt blood data were compared as well. Finally, brain regional 2 tissue compartment modeling was performed using IDIF and NMF-IDIF, and the model fit accuracy (weighted symmetrical mean absolute percentage error, wsMAPE) as well as the total volume of distribution (VT) were compared.ResultsIn isoflurane anesthetized mice, the difference between ABS and NMF-IDIF activity (+ 12.8 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 11%, p = 0.0023) was smaller than with IDIF (+ 16.4 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 9.8%, p = 0.0008). For ketamine–xylazine anesthetized mice the reduction in difference was larger (NMF-IDIF: 16.9 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 10%, p = 0.0057, IDIF: 56.3 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 14%, p < 0.0001). Correlation coefficient between isoflurane AV-shunt time activity curves and NMF-IDIF (0.97 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 0.01) was higher than with IDIF (0.94 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 0.03). The brain regional 2TCM wsMAPE was improved using NMF-IDIF compared with IDIF, in isoflurane (NMF-IDIF: 1.24 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 0.24%, IDIF: 1.56 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 0.30%) and ketamine–xylazine (NMF-IDIF: 1.40 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 0.24, IDIF: 2.62 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 0.27) anesthetized mice. Finally, brain VT was significantly (p < 0.0001) higher using NMF-IDIF compared with IDIF, in isoflurane (3.97 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 0.13% higher) and ketamine–xylazine (32.7 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 2.4% higher) anesthetized mice.ConclusionsImage derived left ventricle blood activity calculated with NMF improves absolute activity quantification, and reduces the error in the kinetic modeling fit. These improvements are more pronounced in ketamine–xylazine than in isoflurane anesthetized mice.

Application of non-negative matrix factorization in oncology: one approach for establishing precision medicine.

The increase in the expectations of artificial intelligence (AI) technology has led to machine learning technology being actively used in the medical field. Non-negative matrix factorization (NMF) is a machine learning technique used for image analysis, speech recognition, and language processing; recently, it is being applied to medical research. Precision medicine, wherein important information is extracted from large-scale medical data to provide optimal medical care for every individual, is considered important in medical policies globally, and the application of machine learning techniques to this end is being handled in several ways. NMF is also introduced differently because of the characteristics of its algorithms. In this review, the importance of NMF in the field of medicine, with a focus on the field of oncology, is described by explaining the mathematical science of NMF and the characteristics of the algorithm, providing examples of how NMF can be used to establish precision medicine, and presenting the challenges of NMF. Finally, the direction regarding the effective use of NMF in the field of oncology is also discussed.

An automated approach for determining the number of components in non-negative matrix factorization with application to mutational signature learning

Non-negative matrix factorization (NMF) is a popular method for finding a low rank approximation of a matrix, thereby revealing the latent components behind it. In genomics, NMF is widely used to interpret mutation data and derive the underlying mutational processes and their activities. A key challenge in the use of NMF is determining the number of components, or rank of the factorization. Here we propose a novel method, CV2K, to choose this number automatically from data that is based on a detailed cross validation procedure combined with a parsimony consideration. We apply our method for mutational signature analysis and demonstrate its utility on both simulated and real data sets. In comparison to previous approaches, some of which involve human assessment, CV2K leads to improved predictions across a wide range of data sets.

Subject-specific EEG channel selection using non-negative matrix factorization for lower-limb motor imagery recognition

Objective. This study aims to propose and validate a subject-specific approach to recognize two different cognitive neural states (relax and pedaling motor imagery (MI)) by selecting the relevant electroencephalogram (EEG) channels. The main aims of the proposed work are: (i) to reduce the computational complexity of the BCI systems during MI detection by selecting the relevant EEG channels, (ii) to reduce the amount of data overfitting that may arise due to unnecessary channels and redundant features, and (iii) to reduce the classification time for real-time BCI applications. Approach. The proposed method selects subject-specific EEG channels and features based on their MI. In this work, we make use of non-negative matrix factorization to extract the weight of the EEG channels based on their contribution to MI detection. Further, the neighborhood component analysis is used for subject-specific feature selection. Main results. We executed the experiments using EEG signals recorded for MI where ten healthy subjects performed MI movement of the lower limb to generate motor commands. An average accuracy of 96.66%, average true positive rate (TPR) of 97.77%, average false positives rate of 4.44%, and average Kappa of 93.33% were obtained. The proposed subject-specific EEG channel selection based MI recognition system provides 13.20% improvement in detection accuracy, and 27% improvement in Kappa value with less number of EEG channels compared to the results obtained using all EEG channels. Significance. The proposed subject-specific BCI system has been found significantly advantageous compared to the typical approach of using a fixed channel configuration. This work shows that fewer EEG channels not only reduce computational complexity and processing time (two times faster) but also improve the MI detection performance. The proposed method selects EEG locations related to the foot movement, which may be relevant for neuro-rehabilitation using lower-limb movements that may provide a real-time and more natural interface between patient and robotic device.

Monitor Ionizing Radiation-Induced Cellular Responses with Raman Spectroscopy, Non-Negative Matrix Factorization, and Non-Negative Least Squares

Radiation therapy (RT) is one of the most commonly prescribed cancer treatments. New tools that can accurately monitor and evaluate individual patient responses would be a major advantage and lend to the implementation of personalized treatment plans. In this study, Raman spectroscopy (RS) was applied to examine radiation-induced cellular responses in H460, MCF7, and LNCaP cancer cell lines across different dose levels and times post-irradiation. Previous Raman data analysis was conducted using principal component analysis (PCA), which showed the ability to extract biological information of glycogen. In the current studies, the use of non-negative matrix factorization (NMF) allowed for the discovery of multiplexed biological information, specifically uncovering glycogen-like and lipid-like component bases. The corresponding scores of glycogen and previously unidentified lipids revealed the content variations of these two chemicals in the cellular data. The NMF decomposed glycogen and lipid-like bases were able to separate the cancer cell lines into radiosensitive and radioresistant groups. A further lipid phenotype investigation was also attempted by applying non-negative least squares (NNLS) to the lipid-like bases decomposed individually from three cell lines. Qualitative differences found in lipid weights for each lipid-like basis suggest the lipid phenotype differences in the three tested cancer cell lines. Collectively, this study demonstrates that the application of NMF and NNLS on RS data analysis to monitor ionizing radiation-induced cellular responses can yield multiplexed biological information on bio-response to RT not revealed by conventional chemometric approaches.

Weakly Supervised Representation Learning for Audio-Visual Scene Analysis

Audio-visual (AV) representation learning is an important task from the perspective of designing machines with the ability to understand complex events. To this end, we propose a novel multimodal framework that instantiates multiple instance learning. Specifically, we develop methods that identify events and localize corresponding AV cues in unconstrained videos. Importantly, this is done using weak labels where only video-level event labels are known without any information about their location in time. We show that the learnt representations are useful for performing several tasks such as event/object classification, audio event detection, audio source separation and visual object localization. An important feature of our method is its capacity to learn from unsynchronized audio-visual events. We also demonstrate our framework's ability to separate out the audio source of interest through a novel use of nonnegative matrix factorization. State-of-the-art classification results, with a F1-score of 65.0, are achieved on DCASE 2017 smart cars challenge data with promising generalization to diverse object types such as musical instruments. Visualizations of localized visual regions and audio segments substantiate our system's efficacy, especially when dealing with noisy situations where modality-specific cues appear asynchronously.

Metabotypes Related to Meat and Vegetable Intake Reflect Microbial, Lipid and Amino Acid Metabolism in Healthy People.

The objective of this study is to develop a new methodology to identify the relationship between dietary patterns and metabolites indicative of food intake and metabolism. Plasma and urine samples from healthy Swiss subjects (n = 89) collected over two time points are analyzed for a panel of host-microbial metabolites using GC- and LC-MS. Dietary intake is evaluated using a validated food frequency questionnaire. Dietary pattern clusters and relationships with metabolites are determined using Non-Negative Matrix Factorization (NNMF) and Sparse Generalized Canonical Correlation Analysis (SGCCA). Use of NNMF allows detection of latent diet clusters in this population, which describes a high intake of meat or vegetables. SGCCA associates these clusters to i) diet-host microbial and lipid associated bile acid metabolism, and ii) essential amino acid metabolism. This novel application of NNMF and SGCCA allows detection of distinct metabotypes for meat and vegetable dietary patterns in a heterogeneous population. As many of the metabolites associated with meat or vegetable intake are the result of host-microbiota interactions, the findings support a role for microbiota mediating the metabolic imprinting of different dietary choices.

Bird sound spectrogram decomposition through Non-Negative Matrix Factorization for the acoustic classification of bird species.

Feature extraction for Acoustic Bird Species Classification (ABSC) tasks has traditionally been based on parametric representations that were specifically developed for speech signals, such as Mel Frequency Cepstral Coefficients (MFCC). However, the discrimination capabilities of these features for ABSC could be enhanced by accounting for the vocal production mechanisms of birds, and, in particular, the spectro-temporal structure of bird sounds. In this paper, a new front-end for ABSC is proposed that incorporates this specific information through the non-negative decomposition of bird sound spectrograms. It consists of the following two different stages: short-time feature extraction and temporal feature integration. In the first stage, which aims at providing a better spectral representation of bird sounds on a frame-by-frame basis, two methods are evaluated. In the first method, cepstral-like features (NMF_CC) are extracted by using a filter bank that is automatically learned by means of the application of Non-Negative Matrix Factorization (NMF) on bird audio spectrograms. In the second method, the features are directly derived from the activation coefficients of the spectrogram decomposition as performed through NMF (H_CC). The second stage summarizes the most relevant information contained in the short-time features by computing several statistical measures over long segments. The experiments show that the use of NMF_CC and H_CC in conjunction with temporal integration significantly improves the performance of a Support Vector Machine (SVM)-based ABSC system with respect to conventional MFCC.

Finding imaging patterns of structural covariance via Non-Negative Matrix Factorization

In this paper, we investigate the use of Non-Negative Matrix Factorization (NNMF) for the analysis of structural neuroimaging data. The goal is to identify the brain regions that co-vary across individuals in a consistent way, hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies. NNMF offers a directly data-driven way of extracting relatively localized co-varying structural regions, thereby transcending limitations of Principal Component Analysis (PCA), Independent Component Analysis (ICA) and other related methods that tend to produce dispersed components of positive and negative loadings. In particular, leveraging upon the well known ability of NNMF to produce parts-based representations of image data, we derive decompositions that partition the brain into regions that vary in consistent ways across individuals. Importantly, these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split-sample experiments. We empirically validate NNMF in two data sets: i) a Diffusion Tensor (DT) mouse brain development study, and ii) a structural Magnetic Resonance (sMR) study of human brain aging. We demonstrate the ability of NNMF to produce sparse parts-based representations of the data at various resolutions. These representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes. Moreover, we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like PCA and ICA.

Impurity Profiling of a Chemical Weapon Precursor for Possible Forensic Signatures by Comprehensive Two-Dimensional Gas Chromatography/Mass Spectrometry and Chemometrics

In this report we present the feasibility of using analytical and chemometric methodologies to reveal and exploit the chemical impurity profiles from commercial dimethyl methylphosphonate (DMMP) samples to illustrate the type of forensic information that may be obtained from chemical-attack evidence. Using DMMP as a model compound of a toxicant that may be used in a chemical attack, we used comprehensive two-dimensional gas chromatography/time-of-flight mass spectrometry (GC x GC/TOF-MS) to detect and identify trace organic impurities in six samples of commercially acquired DMMP. The GC x GC/TOF-MS data was analyzed to produce impurity profiles for all six DMMP samples using 29 analyte impurities. The use of PARAFAC for the mathematical resolution of overlapped GC x GC peaks ensured clean spectra for the identification of many of the detected analytes by spectral library matching. The use of statistical pairwise comparison revealed that there were trace impurities that were quantitatively similar and different among five of the six DMMP samples. Two of the DMMP samples were revealed to have identical impurity profiles by this approach. The use of nonnegative matrix factorization indicated that there were five distinct DMMP sample types as illustrated by the clustering of the multiple DMMP analyses into five distinct clusters in the scores plots. The two indistinguishable DMMP samples were confirmed by their chemical supplier to be from the same bulk source. Sample information from the other chemical suppliers supported the idea that the other four DMMP samples were likely from different bulk sources. These results demonstrate that the matching of synthesized products from the same source is possible using impurity profiling. In addition, the identified impurities common to all six DMMP samples provide strong evidence that basic route information can be obtained from impurity profiles. Finally, impurities that may be unique to the sole bulk manufacturer of DMMP were found in some of the DMMP samples.

Rapid identification of structural phases in combinatorial thin-film libraries using x-ray diffraction and non-negative matrix factorization

In this work we apply a technique called non-negative matrix factorization (NMF) to the problem of analyzing hundreds of x-ray microdiffraction (microXRD) patterns from a combinatorial materials library. An in-house scanning x-ray microdiffractometer is used to obtain microXRD patterns from 273 different compositions on a single composition spread library. NMF is then used to identify the unique microXRD patterns present in the system and quantify the contribution of each of these basis patterns to each experimental diffraction pattern. As a baseline, the results of NMF are compared to the results obtained using principle component analysis. The basis patterns found using NMF are then compared to reference patterns from a database of known structural patterns in order to identify known structures. As an example system, we explore a region of the Fe-Ga-Pd ternary system. The use of NMF in this case reduces the arduous task of analyzing hundreds of microXRD patterns to the much smaller task of identifying only nine microXRD patterns.

Considerations on Parallelizing Nonnegative Matrix Factorization for Hyperspectral Data Unmixing

Nonnegative matrix factorization (NMF) is a recently developed linear unmixing technique that assumes that the original sources and transform were positively defined. Given that the linear mixing model (LMM) for hyperspectral data requires positive endmembers and abundances, with only minor modifications, NMF can be used to solve LMM. Traditionally, NMF solutions include an iterative process resulting in considerable execution times. In this letter, we provide two novel algorithms aimed at speeding the NMF through parallel processing: the first based on the traditional multiplicative solution and the second modifying an adaptive projected gradient technique known to provide better convergence. The algorithms' implementations were tested on various data sets; the results suggest that a significant speedup can be achieved without decrease in accuracy. This supports the further use of NMF for linear unmixing.

Robust and Secure Image Hashing via Non-Negative Matrix Factorizations

In this paper, we propose the use of non-negative matrix factorization (NMF) for image hashing. In particular, we view images as matrices and the goal of hashing as a randomized dimensionality reduction that retains the essence of the original image matrix while preventing intentional attacks of guessing and forgery. Our work is motivated by the fact that standard-rank reduction techniques, such as QR and singular value decomposition, produce low-rank bases which do not respect the structure (i.e., non-negativity for images) of the original data. We observe that NMFs have two very desirable properties for secure image hashing applications: 1) The additivity property resulting from the non-negativity constraints results in bases that capture local components of the image, thereby significantly reducing misclassification and 2) the effect of geometric attacks on images in the spatial domain manifests (approximately) as independent identically distributed noise on NMF vectors, allowing the design of detectors that are both computationally simple and, at the same time, optimal in the sense of minimizing error probabilities. Receiver operating characteristics analysis over a large image database reveals that the proposed algorithms significantly outperform existing approaches for image hashing.

NONNEGATIVE TENSOR FACTORIZATION FOR CONTINUOUS EEG CLASSIFICATION

In this paper we present a method for continuous EEG classification, where we employ nonnegative tensor factorization (NTF) to determine discriminative spectral features and use the Viterbi algorithm to continuously classify multiple mental tasks. This is an extension of our previous work on the use of nonnegative matrix factorization (NMF) for EEG classification. Numerical experiments with two data sets in BCI competition, confirm the useful behavior of the method for continuous EEG classification.

Non-Negative Matrix Factorization for Detection and Diagnosis of Plantwide Oscillations

In this paper, we propose the use of non-negative matrix factorization (NMF) of multivariate spectra for plantwide oscillation detection. One of the key features of NMF is that it provides a parts-based representation that allows us to retain the causal basis spectral shapes or parts that constitute the spectra of measurements, unlike the popular principal component analysis (PCA)-based methods. The contributions of this paper are as follows: (i) a novel measure known as the pseudo-singular value (PSV) to assess the order of the basis space (the PSV is also useful in determining the most dominant features of a data set); (ii) a power decomposition plot that contains the total power (defined in this work) and its decomposition by NMF (the power plot is a useful and compact visual tool that provides overall spectral characteristics of the plant and shows the decomposition of these characteristics into well-localized frequency components); and (iii) a novel measure defined as the strength factor (SF) to ass...

Nonnegative matrix factorization and its applications in pattern recognition

Matrix factorization is an effective tool for large-scale data processing and analysis. Nonnegative matrix factorization (NMF) method, which decomposes the nonnegative matrix into two nonnegative factor matrices, provides a new way for matrix factorization. NMF is significant in intelligent information processing and pattern recognition. This paper firstly introduces the basic idea of NMF and some new relevant methods. Then we discuss the loss functions and relevant algorithms of NMF in the framework of probabilistic models based on our researches, and the relationship between NMF and information processing of perceptual process. Finally, we make use of NMF to deal with some practical questions of pattern recognition and point out some open problems for NMF.

Determining Patterns in Neural Activity for Reaching Movements Using Nonnegative Matrix Factorization

We propose the use of nonnegative matrix factorization (NMF) as a model-independent methodology to analyze neural activity. We demonstrate that, using this technique, it is possible to identify local spatiotemporal patterns of neural activity in the form of sparse basis vectors. In addition, the sparseness of these bases can help infer correlations between cortical firing patterns and behavior. We demonstrate the utility of this approach using neural recordings collected in a brain-machine interface (BMI) setting. The results indicate that, using the NMF analysis, it is possible to improve the performance of BMI models through appropriate pruning of inputs.

Metagenes and molecular pattern discovery using matrix factorization.

We describe here the use of nonnegative matrix factorization (NMF), an algorithm based on decomposition by parts that can reduce the dimension of expression data from thousands of genes to a handful of metagenes. Coupled with a model selection mechanism, adapted to work for any stochastic clustering algorithm, NMF is an efficient method for identification of distinct molecular patterns and provides a powerful method for class discovery. We demonstrate the ability of NMF to recover meaningful biological information from cancer-related microarray data. NMF appears to have advantages over other methods such as hierarchical clustering or self-organizing maps. We found it less sensitive to a priori selection of genes or initial conditions and able to detect alternative or context-dependent patterns of gene expression in complex biological systems. This ability, similar to semantic polysemy in text, provides a general method for robust molecular pattern discovery.