Extraction of Food Consumption Systems by Nonnegative Matrix Factorization (NMF) for the Assessment of Food Choices

Advances in Nonnegative Matrix and Tensor Factorization

Compared with traditional remote sensing images, hyperspectral images have the advantages of high spectral resolution, combining images with spectrum, and continuous spectrum. The phenomenon of mixed pixels in hyperspectral images seriously affects the accuracy of distinguishing objects on the ground, and has always been an important problem that hinders the further development of this technology. The most effective way to solve the mixed pixel problem is to perform mixed pixel unmixing. The purpose of hyperspectral unmixing is to obtain pure spectrum (endmembers) and their corresponding proportions (abundance). The nonnegative matrix factorization (NMF) technique has been widely adopted in the hyperspectral images unmixing problem due to its own advantages. The NMF method based on sparsity constraint can achieve better unmixing effect because of fully using of the sparse characteristic of the data. However, the unmixing model based on the sparse NMF still has shortcomings. Hyperspectral images contain a large amount of geometric structural information, which is not considered by most existing sparse NMF methods. To address those shortcomings, new regularization terms and weights can be introduced into the NMF model to better promote the unmixing performance. To solve this problem, a novel unmixing algorithm named spatial-spectral graph regularized sparse non-negative matrix factorization (SSGNMF) algorithm is proposed in this paper. Most of the sparse constrained unmixing algorithms have the problem of insufficient prior representation of abundance sparsity and using of spatial information insufficiently. On the one hand, the model of SSGNMF introduces graph regularization to preserve high-dimensional spatial information in hyperspectral images. On the other hand, the spatial weighting factor enables more spatial information to be incorporated into the unmixing model, and the spectral weighting factor can promote row sparsity of abundance matrices. By comparing with other classical algorithms, simulated and real hyperspectral data experimental results demonstrate that the introduction of dual weights and graph regularization can improve the unmixing effect, which verifies the validity of this algorithm. In addition, the experimental results also show that the graph regularization term and dual weights introduced in the NMF model in this paper can indeed promote the hyperspectral image unmixing performance well.

Improved self-paced learning framework for nonnegative matrix factorization

Approaches for identifying PM2.5 source types and source areas at a remote background site of South China in spring.

Bayesian Estimators are very useful in speech enhancement and noise reduction. But, it is noted that the traditional estimators process only amplitudes and the phase is left unprocessed. Among the Bayesian estimators, Super- Gaussian based estimators provide improved noise reduction. Super-Gaussian Bayesian estimators, which uses processed phase information for estimation of amplitudes provides further improved results. In this work, the Complex speech coefficients given Uncertain Phase (CUP) based Bayesian estimators like CUP-GG (CUP Estimator with speech spectral coefficients assumed as Gamma and noise spectral coefficients as Generalized Gamma), CUP-NG (Speech as Nakagami) are compared under white noise, pink noise, Babble noise and Non-Stationary factory noise conditions. The statistical estimators show less effective results under completely non-stationary assumptions like non-stationary factory noise, babble noise etc. Non-negative Matrix Factorization (NMF) based algorithms show better performance for non stationary noises. The drawback of NMF is, it requires apriori knowledge about speech. This drawback can be overcome by taking the advantages of both statistical approaches and NMF approaches. NR-NMF and WR-NMF speech enhancement methods are developed by providing posteriori regularization based on statistical assumption of speech and noise DFT coefficients distribution. Also a speech enhancement method which uses CUP-GG estimator and NMF with online noise bases update are considered for comparison. The progress in neural network based approaches for speech enhancement further shown that with large dataset and better training, the speech enhancement algorithms results in improved results. In this work, the neural network approach for speech enhancement is implemented and compared the method with traditional estimators and NMF approaches. For generalization of unseen noise types the proposed neural network approach uses dropout. Also for training the network, the features obtained from apriori SNR and aposteriori SNR is used in this method. The objective of this paper is to analyze the performance of speech enhancement methods based on Neural Network, NMF and statistical based. The objective performance measures Perceptual Evaluation of Speech Quality (PESQ), Short-Time Objective Intelligibility (STOI), Signal to Noise Ratio (SNR), Segmental SNR (Seg SNR) are considered for comparison.

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

In the digital world, the research papers are growing exponentially with time, and it is essential to cluster the documents under their respective categories for easier identification and access. However, researchers find it relatively challenging to recognize and categorize their favorite research articles. Though this task can be achieved by putting in the human work, it would be tedious and exhaustively time-consuming. Henceforth, much research has been done in the field of topic modelling to yield accurate results with a good computation time. The main objective of this paper is to compare the two distinct yet vastly used topic modelling approaches for research paper classification, which can further group the research papers into their respective classes. The two chosen topic modeling methodologies are Non-Negative Matrix Factorization (NMF) and Latent Dirichlet allocation (LDA). This paper introduces a comparison between LDA model's performance with a relatively efficient generative model (NMF) and analyzes its performance on the dataset that consists of 1740 papers extracted from the NYC university website. In comparison, the average coherence score for the LDA method was 0.5282, with its optimal choice of topics being 22, which was slightly higher than the NMF model as it yielded a coherence score of 0.4937 with its optimal topics being 9. To enhance the categorization of LDA, clustering the optimal topics of LDA from 22 to 10 using pyLDAvis has been done. On closely comparing both the models, LDA performs slightly better than NMF with a higher confidence score.

Along with the growth of the Internet, automatic recommender systems have become popular. Due to being intuitive and useful, factorization based models, including the Nonnegative Matrix Factorization (NMF) model, are one of the most common approachs for building recommender systems. In this study, we focus on how a recommender system can be built for online services and how the parameters of an NMF model should be selected in a recommender system setting. We first present a general system architecture in which any kind of factorization model can be used. Then, in order to see how accurate the NMF model fits the data, we randomly erase some parts of a real data set that is gathered from an online food ordering service, and we reconstruct the erased parts by using the NMF model. We report the mean squared errors for different parameter settings and different divergences.

Accuracy-optimized convolutional neural networks (CNNs) have emerged as highly effective models at predicting neural responses in brain areas along the primate ventral stream, but it is largely unknown whether they effectively model neurons in the complementary primate dorsal stream. We explored how well CNNs model the optic flow tuning properties of neurons in dorsal area MSTd and we compared our results with the Non-Negative Matrix Factorization (NNMF) model, which successfully models many tuning properties of MSTd neurons. To better understand the role of computational properties in the NNMF model that give rise to optic flow tuning that resembles that of MSTd neurons, we created additional CNN model variants that implement key NNMF constraints – non-negative weights and sparse coding of optic flow. While the CNNs and NNMF models both accurately estimate the observer's self-motion from purely translational or rotational optic flow, NNMF and the CNNs with nonnegative weights yield substantially less accurate estimates than the other CNNs when tested on more complex optic flow that combines observer translation and rotation. Despite its poor accuracy, NNMF gives rise to tuning properties that align more closely with those observed in primate MSTd than any of the accuracy-optimized CNNs. This work offers a step toward a deeper understanding of the computational properties and constraints that describe the optic flow tuning of primate area MSTd.

Nonnegative matrix factorization (NMF) is an unsupervised learning method for decomposing high-dimensional nonnegative data matrices and extracting basic and intrinsic features. Since image data are described and stored as nonnegative matrices, the mining and analysis process usually involves the use of various NMF strategies. NMF methods have well-known applications in face recognition, image reconstruction, handwritten digit recognition, image denoising and feature extraction. Recently, several projective NMF (P-NMF) methods based on positively constrained projections have been proposed and were found to perform better than the standard NMF approach in some aspects. However, some drawbacks still affect the existing NMF and P-NMF algorithms; these include dense factors, slow convergence, learning poor local features, and low reconstruction accuracy. The aim of this paper is to design algorithms that address the aforementioned issues. In particular, we propose two embedded P-NMF algorithms: the first method combines the alternating least squares (ALS) algorithm with the P-NMF update rules of the Frobenius norm and the second one embeds ALS with the P-NMF update rule of the Kullback–Leibler divergence. To assess the performances of the proposed methods, we conducted various experiments on four well-known data sets of faces. The experimental results reveal that the proposed algorithms outperform other related methods by providing very sparse factors and extracting better localized features. In addition, the empirical studies show that the new methods provide highly orthogonal factors that possess small entropy values.

Clustering is a machine learning technique that seeks to uncover the intrinsic patterns from a dataset by grouping related objects together. While clustering has gained significant attention as a critical challenge over the years, multi-view clustering have only a few publications in the literature. Non-negative matrix factorization (NMF) is a data mining technique which decompose huge data matrices by placing constraints on the elements’ non-negativity. This technique has garnered considerable interest as a serious problem with numerous applications in a variety of fields, including language modeling, text mining, clustering, music transcribing, and neuroscience (gene separation). This lack of negative simplifies the interpretation of the generated matrices. Two different matrices are used: one is used to represent the cluster prototypes of a dataset, and the other is used to represent data partitions. The investigated datasets are frequently non-negative, and they occasionally contain sparse representations. Ding et al. [5] demonstrated that the orthogonal NMF and K-means hard clustering are equivalent. Kim and Park addressed this similarity and suggested a sparse non-negative matrix factorization (NMF) technique for data clustering. Their technique outperforms both K-means and NMF in terms of result consistency. We propose a research of multi-view clustering algorithms in this chapter and provide a novel methodology called multi-view non-negative matrix factorization, in which we investigate the collaboration between several NMF models. This strategy was evaluated using a variety of datasets, and the experimental findings demonstrate the suggested approach’s usefulness.KeywordsMulti-view clusteringCollaborative clusteringNon-negative matrix factorizationProjection

Matrix factorization is a useful technique for data representation in many data mining and machine learning tasks. Particularly, for data sets with all nonnegative entries, matrix factorization often requires that factor matrices be nonnegative, leading to nonnegative matrix factorization (NMF). One important application of NMF is for clustering with reduced dimensions of the data represented in the new feature space. In this paper, we propose a new graph regularized NMF method capable of feature learning and apply it to clustering. Unlike existing NMF methods that treat all features in the original feature space equally, our method distinguishes features by incorporating a feature-wise sparse approximation error matrix in the formulation. It enables important features to be more closely approximated by the factor matrices. Meanwhile, the graph of the data is constructed using cleaner features in the feature learning process, which integrates feature learning and manifold learning procedures into a unified NMF model. This distinctly differs from applying the existing graph-based NMF models after feature selection in that, when these two procedures are independently used, they often fail to align themselves toward obtaining a compact and most expressive data representation. Comprehensive experimental results demonstrate the effectiveness of the proposed method, which outperforms state-of-the-art algorithms when applied to clustering.

Nonnegative matrix factorization (NMF) is a widely used hyperspectral unmixing model which decomposes a known hyperspectral data matrix into two unknown matrices, i.e., endmember matrix and abundance matrix. Due to the use of least-squares loss, the NMF model is usually sensitive to noise or outliers. To improve its robustness, we introduce a general robust loss function to replace the traditional least-squares loss and propose a general loss-based NMF (GLNMF) model for hyperspectral unmixing in this letter. The general loss function is a superset of many common robust loss functions and is suitable for handling different types of noise. Experimental results on simulated and real hyperspectral data sets demonstrate that our GLNMF model is more accurate and robust than existing NMF methods.

Multiple graph regularized semi-supervised nonnegative matrix factorization with adaptive weights for clustering

Validation of an efficient non-negative matrix factorization method and its preliminary application in Central California