Negative Matrix Factorization Research Articles

Identification of a prognosis‑associated signature associated with energy metabolism in triple‑negative breast cancer.

At present, a large number of exciting results have been found regarding energy metabolism within the triple-negative breast cancer (TNBC) field. Apart from aerobic glycolysis, a number of other catabolic pathways have also been demonstrated to participate in energy generation. However, the prognostic value of energy metabolism for TNBC currently remains unclear. In the present study, the association between gene expression profiles of energy metabolism and outcomes in patients with TNBC was examined using datasets obtained from the Gene Expression Omnibus and The Cancer Genome Atlas. In total, four robust TNBC subtypes were identified on the basis of negative matrix factorization clustering and gene expression patterns, which exhibited distinct immunological, molecular and prognostic (disease-free survival) features. The differentially expressed genes were subsequently identified from the subgroup that demonstrated the poorest prognosis compared with the remaining 3 subgroups, where their biological functions were assessed further by means of gene ontology enrichment analysis. Any signatures found to be associated with energy metabolism were then established using the Cox proportional hazards model to assess patient prognosis. According to results of Kaplan-Meier analysis, the constructed signature consisting of eight genes that were associated with energy metabolism distinguished patient outcomes into low- and high-risk groups. In addition, this signature, which was found to be markedly associated with the clinical characteristics of the patients, served as an independent factor in predicting TNBC patient prognosis. According to gene set enrichment analysis, the gene sets related to the high-risk group participated in the MAPK signal transduction pathway, focal adhesion and extracellular matrix receptor interaction, whilst those related to the low-risk group were revealed to be mainly associated with mismatch repair and propanoate metabolism. Findings from the present study shed new light on the role of energy metabolism within TNBC, where the eight-gene signature associated with energy metabolism constructed can be utilized as a new prognostic marker for predicting survival in patients with TNBC.

Image Analysis using Non Negative Matrix Factorization

Image analysis extracts the meaningful information from the images. This information is very much helpful to recognition and authentication. There are number of techniques available for image analysis. Image analysis can be used in analysis of the scene, image understanding and computer vision. Image analysis can be used in Medical image processing, Geology, optical character recognition and forensics. There are mainly four steps in the image analysis 1.image pre processing 2. Segmentation 3.feature extraction and 4. Classification and interpretation. Feature extraction is the main part for any image analysis. In this paper Multi modal biometric authentication system can be defined for security. In this process Non Negative Matrix Factorization (NMF) technique is used for feature extraction and for fusion Principle component analysis is used. After getting the features these can be encoding using Kronecker product. At the end Euclidean distance measure is used for authentication.

Negative Binomial Matrix Factorization

We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson factorization (PF) perturbed by a multiplicative term which models exposure. This term brings a degree of freedom for controlling the dispersion, making NBMF more robust to outliers. We describe a majorization-minimization (MM) algorithm for a maximum likelihood estimation of the parameters. We provide results on a recommendation task and demonstrate the ability of NBMF to efficiently exploit raw data.

A New Model of Identifying Differentially Expressed Genes via Weighted Network Analysis Based on Dimensionality Reduction Method

Background: As a method to identify Differentially Expressed Genes (DEGs), Non- Negative Matrix Factorization (NMF) has been widely praised in bioinformatics. Although NMF can make DEGs to be easily identified, it cannot provide more associated information for these DEGs. Objective: The methods of network analysis can be used to analyze the correlation of genes, but they caused more data redundancy and great complexity in gene association analysis of high dimensions. Dimensionality reduction is worth considering in this condition. Methods: In this paper, we provide a new framework by combining the merits of two: NMF is applied to select DEGs for dimensionality reduction, and then Weighted Gene Co-Expression Network Analysis (WGCNA) is introduced to cluster on DEGs into similar function modules. The combination of NMF and WGCNA as a novel model accomplishes the analysis of DEGs for cholangiocarcinoma (CHOL). Results: Some hub genes from DEGs are highlighted in the co-expression network. Candidate pathways and genes are also discovered in the most relevant module of CHOL. Conclusion: The experiments indicate that our framework is effective and the works also provide some useful clues to the reaches of CHOL.

Traditional Dimensionality Reduction Techniques using Deep Learning

From the analysis of big data, dimensionality reduction techniques play a significant role in various fields where the data is huge with multiple columns or classes. Data with high dimensions contains thousands of features where many of these features contain useful information. Along with this there contains a lot of redundant or irrelevant features which reduce the quality, performance of data and decrease the efficiency in computation. Procedures which are done mathematically for reducing dimensions are known as dimensionality reduction techniques. The main aim of the Dimensionality Reduction algorithms such as Principal Component Analysis (PCA), Random Projection (RP) and Non Negative Matrix Factorization (NMF) is used to decrease the inappropriate information from the data and moreover the features and attributes taken from these algorithms were not able to characterize data as different divisions. This paper gives a review about the traditional methods used in Machine algorithm for reducing the dimension and proposes a view, how deep learning can be used for dimensionality reduction.

A RANK-TWO NMF CLUSTERING: APPLICATION TO GLIOBLASTOMAS CHARACTERIZATION AND COMPARATIVE STUDY

This paper explores a novel clustering approach for multimodal Glioblastomas (GBM) characterization using the magnetic resonance image (MRI) modality. We define our segmentation problem as a linear mixture model (LMM). In every segmentation process, we generate a non-negative matrix with GLCM features from every MRI slice and a rank-two NMF (Non Negative Matrix Factorization) is applied. Our method process in four levels of segmentation. In the first one, the LMM matrix for the whole brain was generated from FLAIR modality to extract whole tumor region, which considered as the region of Interest (ROI). In the second level, we extract the ROI from T1c modality and the LMM matrix was generated from only this ROI to extract necrosis region. The principle will be the same for the other two levels to extract the enhanced and the non-enhanced region. Quantitative and qualitative assessment over the publicly dataset from MICCAI 2015 challenge (BRATS 2015) demonstrated that the proposed method could generate a competitive efficiency for high grade Glioblastomas characterization among several competing method. In order to highlight the performance of our method, we propose a comparative study with unsupervised segmentation methodologies (K-means, fuzzy C-means (FCM), gaussian mixture model (GMM) and hierarchical non-negative factorization (hNMF)) over the publicly BRATS 2015 dataset by computing validation metrics (the sensitivity, the dice and the specificity). The obtained results could attest the performance of the proposed algorithm compared to the unsupervised segmentation methodologies.

Improvement of surface-enhanced Raman scattering detection and imaging by multivariate curve resolution methods

Surface-enhanced Raman scattering (SERS) tags have been intensively applied in biological detection and imaging in recent years. However, both applications often suffer from high Raman background signals from containers such as 96-well plates or autofluorescence signals from biological tissues. Here, we greatly mitigate the influence of these high background Raman or fluorescent signals in both biological detection and imaging using two multivariate curve resolution (MCR) methods including negative matrix factorization and classical least squares. The limit of detection is lowered by one order of magnitude after applying MCR methods to detect target SERS tags in a 96-well plate. Additionally, in a multiplexed cell imaging assay, both false-negative and false-positive results were eliminated with the aid of MCR methods. Accordingly, we suggest a wider application of MCR methods during both biological detection and imaging of SERS tags with high background signals.

A fast and efficient count-based matrix factorization method for detecting cell types from single-cell RNAseq data

BackgroundSingle-cell RNA sequencing (scRNAseq) data always involves various unwanted variables, which would be able to mask the true signal to identify cell-types. More efficient way of dealing with this issue is to extract low dimension information from high dimensional gene expression data to represent cell-type structure. In the past two years, several powerful matrix factorization tools were developed for scRNAseq data, such as NMF, ZIFA, pCMF and ZINB-WaVE. But the existing approaches either are unable to directly model the raw count of scRNAseq data or are really time-consuming when handling a large number of cells (e.g. n>500).ResultsIn this paper, we developed a fast and efficient count-based matrix factorization method (single-cell negative binomial matrix factorization, scNBMF) based on the TensorFlow framework to infer the low dimensional structure of cell types. To make our method scalable, we conducted a series of experiments on three public scRNAseq data sets, brain, embryonic stem, and pancreatic islet. The experimental results show that scNBMF is more powerful to detect cell types and 10 - 100 folds faster than the scRNAseq bespoke tools.ConclusionsIn this paper, we proposed a fast and efficient count-based matrix factorization method, scNBMF, which is more powerful for detecting cell type purposes. A series of experiments were performed on three public scRNAseq data sets. The results show that scNBMF is a more powerful tool in large-scale scRNAseq data analysis. scNBMF was implemented in R and Python, and the source code are freely available at https://github.com/sqsun.

Performance Evaluation of Selected Cost Functions in Non Negative Matrix Factorization Based Decomposition of Acoustic Mixture

Interaction of acoustic signals when several audio sources are active simultaneously results in the disturbance of estimation of an individual source by co-occurring sounds. Data decomposition therefore constitutes one of the core tasks in monaural source separation. Particularly, in semi-supervised learning approach, viable means of achieving this is through the application of Non-negative Matrix Factorization (NMF). Owing to a paucity of information on the application of this method, especially in a speech system, evaluation of some cost functions in NMF-based monaural speech decomposition was investigated in this study. A generalized gradient descent algorithm is derived for the minimization while three cost functions: Euclidean Distance, Kullback-Leibler Divergence and Itakura-Saito divergences are applied to the derived separation NMF algorithm. These divergences are evaluated using experimental data while the performance of each of these is evaluated based on the cost values and convergence rate. Itakura-Saito divergence yields optimal performance over the other two divergences for given number of iterations and number of channels. Keywords— Cost functions, non-negative matrix factorization, speech separation, evaluation

Comparison of Three Un-mixing Based Hyperspectral Image Fusion Techniques

With the availability of multi sensor data in many fields, such as remote sensing, medical imaging or machine vision, sensor fusion has emerged as a new and promising research area. It is possible to have several images of the same scene providing different information although the scene is the same. This is because each image has been captured with a different sensor. A non-negative matrix factorization (NNMF) un mixing based fusion technique with vertex component analysis (VCA) based end member initialization and simple multiplicative update to improve the spatial resolution and to preserve the spectral resolution of the hyper spectral image is proposed. Its performance is analyzed with different number of iterations and end member initializations. A Constrained Non Negative Matrix Factorization unmixing based fusion technique is developed by adding a regularization term to the objective function to preserve the spectral resolution of the hyper spectral image, and its performance is analyzed with different number of iterations and end members. A rank two NNMF and hierarchical clustering based end member initialization and block principal pivoting algorithm based abundance estimation technique, for fusing hyper spectral image and simulated multispectral image is proposed and its performance is analyzed for different overlapping and non overlapping group of multispectral and hyper spectral bands. The performance of the above three methods are compared and analyzed. The obtained results show that the performance of rank two NNMF hierarchical clustering based fusion technique is better than the other two constrained and unconstrained NNMF un mixing based techniques. Also, the performance of these three proposed multi sensor image fusion techniques are compared with an existing image fusion technique.

Image Fusion in Remote Sensing Based on Spectral Unmixing and Improved Non - negative Matrix Factorization Algorithm

Image Fusion in Remote Sensing Based on Spectral Unmixing and Improved Non - negative Matrix Factorization Algorithm

Data Reduction Algorithm Using Nonnegative Matrix Factorization with Nonlinear Constraints

Processing ofdata with very large dimensions has been a hot topic in recent decades. Various techniques have been proposed in order to execute the desired information or structure. Non- Negative Matrix Factorization (NMF) based on non-negatives data has become one of the popular methods for shrinking dimensions. The main strength of this method is non-negative object, the object model by a combination of some basic non-negative parts, so as to provide a physical interpretation of the object construction. The NMF is a dimension reduction method thathasbeen used widely for numerous applications including computer vision,text mining, pattern recognitions,and bioinformatics. Mathematical formulation for NMF did not appear as a convex optimization problem and various types of algorithms have been proposed to solve the problem. The Framework of Alternative Nonnegative Least Square(ANLS) are the coordinates of the block formulation approaches that have been proven reliable theoretically and empirically efficient. This paper proposes a new algorithm to solve NMF problem based on the framework of ANLS.This algorithm inherits the convergenceproperty of the ANLS framework to nonlinear constraints NMF formulations.

Retrieving the Quantitative Chemical Information at Nanoscale from Scanning Electron Microscope Energy Dispersive X-ray Measurements by Machine Learning.

The quantitative composition of metal alloy nanowires on InSb semiconductor surface and gold nanostructures on germanium surface is determined by blind source separation (BSS) machine learning method using non-negative matrix factorization from energy dispersive X-ray spectroscopy (EDX) spectrum image maps measured in a scanning electron microscope (SEM). The BSS method blindly decomposes the collected EDX spectrum image into three source components, which correspond directly to the X-ray signals coming from the supported metal nanostructures, bulk semiconductor signal, and carbon background. The recovered quantitative composition is validated by detailed Monte Carlo simulations and is confirmed by separate cross-sectional transmission electron microscopy EDX measurements of the nanostructures. This shows that simple and achievable SEM EDX measurements together with machine learning non-negative matrix factorization-based blind source separation processing could be successfully used for the nanostructures quantitative chemical composition determination. Our finding can make the chemical quantification at the nanoscale much faster and cost efficient for many systems.

Multiple structure recovery via robust preference analysis

This paper address the extraction of multiple models from outlier-contaminated data by exploiting preference analysis and low rank approximation. First points are represented in the preference space, then Robust PCA (Principal Component Analysis) and Symmetric NMF (Non negative Matrix Factorization) are used to break the multi-model fitting problem into many single-model problems, which in turn are tackled with an approach inspired to MSAC (M-estimator SAmple Consensus) coupled with a model-specific scale estimate. Experimental validation on public, real data-sets demonstrates that our method compares favorably with the state of the art.

Extractive multi-document summarization using population-based multicriteria optimization

Abstract Multi-document summarization is the process of extracting salient information from a set of source texts and present that information to the user in a condensed form. In this paper, we propose a multi-document summarization system which generates an extractive generic summary with maximum relevance and minimum redundancy by representing each sentence of the input document as a vector of words in Proper Noun, Noun, Verb and Adjective set. Five features, such as TF_ISF, Aggregate Cross Sentence Similarity, Title Similarity, Proper Noun and Sentence Length associated with the sentences, are extracted, and scores are assigned to sentences based on these features. Weights that can be assigned to different features may vary depending upon the nature of the document, and it is hard to discover the most appropriate weight for each feature, and this makes generation of a good summary a very tough task without human intelligence. Multi-document summarization problem is having large number of decision parameters and number of possible solutions from which most optimal summary is to be generated. Summary generated may not guarantee the essential quality and may be far from the ideal human generated summary. To address this issue, we propose a population-based multicriteria optimization method with multiple objective functions. Three objective functions are selected to determine an optimal summary, with maximum relevance, diversity, and novelty, from a global population of summaries by considering both the statistical and semantic aspects of the documents. Semantic aspects are considered by Latent Semantic Analysis (LSA) and Non Negative Matrix Factorization (NMF) techniques. Experiments have been performed on DUC 2002, DUC 2004 and DUC 2006 datasets using ROUGE tool kit. Experimental results show that our system outperforms the state of the art works in terms of Recall and Precision.

Discovering Perturbation of Modular Structure in HIV Progression by Integrating Multiple Data Sources Through Non-Negative Matrix Factorization.

Detecting perturbation in modular structure during HIV-1 disease progression is an important step to understand stage specific infection pattern of HIV-1 virus in human cell. In this article, we proposed a novel methodology on integration of multiple biological information to identify such disruption in human gene module during different stages of HIV-1 infection. We integrate three different biological information: gene expression information, protein-protein interaction information, and gene ontology information in single gene meta-module, through non negative matrix factorization (NMF). As the identified meta-modules inherit those information so, detecting perturbation of these, reflects the changes in expression pattern, in PPI structure and in functional similarity of genes during the infection progression. To integrate modules of different data sources into strong meta-modules, NMF based clustering is utilized here. Perturbation in meta-modular structure is identified by investigating the topological and intramodular properties and putting rank to those meta-modules using a rank aggregation algorithm. We have also analyzed the preservation structure of significant GO terms in which the human proteins of the meta-modules participate. Moreover, we have performed an analysis to show the change of coregulation pattern of identified transcription factors (TFs) over the HIV progression stages.

Itakura-Saito Divergence Non Negative Matrix Factorization with Application to Monaural Speech Separation

Itakura-Saito Divergence Non Negative Matrix Factorization with Application to Monaural Speech Separation

A NMF based approach for integrating multiple data sources to predict HIV-1-human PPIs.

BackgroundPredicting novel interactions between HIV-1 and human proteins contributes most promising area in HIV research. Prediction is generally guided by some classification and inference based methods using single biological source of information.ResultsIn this article we have proposed a novel framework to predict protein-protein interactions (PPIs) between HIV-1 and human proteins by integrating multiple biological sources of information through non negative matrix factorization (NMF). For this purpose, the multiple data sets are converted to biological networks, which are then utilized to predict modules. These modules are subsequently combined into meta-modules by using NMF based clustering method. The integrated meta-modules are used to predict novel interactions between HIV-1 and human proteins. We have analyzed the significant GO terms and KEGG pathways in which the human proteins of the meta-modules participate. Moreover, the topological properties of human proteins involved in the meta modules are investigated. We have also performed statistical significance test to evaluate the predictions.ConclusionsHere, we propose a novel approach based on integration of different biological data sources, for predicting PPIs between HIV-1 and human proteins. Here, the integration is achieved through non negative matrix factorization (NMF) technique. Most of the predicted interactions are found to be well supported by the existing literature in PUBMED. Moreover, human proteins in the predicted set emerge as ‘hubs’ and ‘bottlenecks’ in the analysis. Low p-value in the significance test also suggests that the predictions are statistically significant.

A non negative matrix factorization for collaborative filtering recommender systems based on a Bayesian probabilistic model

In this paper we present a novel technique for predicting the tastes of users in recommender systems based on collaborative filtering. Our technique is based on factorizing the rating matrix into two non negative matrices whose components lie within the range [0, 1] with an understandable probabilistic meaning. Thanks to this decomposition we can accurately predict the ratings of users, find out some groups of users with the same tastes, as well as justify and understand the recommendations our technique provides.

Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models

American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs.