We present a novel game-theoretic formulation of Non-Negative Matrix Factorization (NNMF), a popular data-analysis method with many scientific and engineering applications. The game-theoretic formulation is shown to have favorable scaling and parallelization properties, while retaining reconstruction and convergence performance comparable to the traditional Multiplicative Updates algorithm.
We propose a method for computing binary orthogonal non-negative matrix factorization (BONMF) for clustering and classification. The method is tested on several representative real-world data sets. The numerical results confirm that the method has improved accuracy compared to the related techniques. The proposed method is fast for training and classification and space efficient.
Non-Negative Matrix Factorization (NMF) is a valuable matrix factorization technique which produces a "parts-based" decomposition of data sets. Wi-Fi user counts are a privacy-preserving indicator of population movements in smart and connected urban environments. In this paper, we apply NMF with a novel matrix embedding to Wi-Fi user count data from the University of Colorado at Boulder Campus for the purpose of automatically identifying patterns of human movement in a Smart and Connected infrastructure environment.
Fox Chase Cancer Center, Temple University Health System（天普大学卫生系统福克斯·蔡斯癌症中心）
A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this framework and its convergence proven using the Expectation-Maximization algorithm. The proposed approach generalizes some existing methods for different noise structures and contrasts with the recently proposed quasi-likelihood approach, thus providing a useful alternative for non-negative matrix factorizations. A measure to evaluate the goodness-of-fit of the …
Columbia University（哥伦比亚大学）；Colorado State University（科罗拉多州立大学）；Stony Brook University（石溪大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）
We validate the use of matrix factorization for the automatic identification of relevant components from atomic pair distribution function (PDF) data. We also present a newly developed software infrastructure for analyzing the PDF data arriving in streaming manner. We then apply two matrix factorization techniques, Principal Component Analysis (PCA) and Non-negative Matrix Factorization (NMF), to study simulated and experiment datasets in the context of in situ experiment.
Sultan Qaboos University（苏丹卡布斯大学）；École de technologie supérieure（高等技术学院）
The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve the structure of data during matrix factorization. The idea is to add, to the NMF cost function, a penalty term to impose a scale relationship between the pairwise similarity matrices of the original and transformed data points. The solution of the new model involves deriving a new parametrized update scheme for the coefficient matrix, which makes it possibl…
IRIT, Université de Toulouse, CNRS（图卢兹大学 IRIT 研究所、法国国家科学研究中心）
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 matrix 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 show that NBMF allows to skip traditional pre-processing stages, such as binarization, which lead to loss of information. Two estimation approaches are presented: maximum likelihood and variational Bayes infere…
The paper discusses a pooling mechanism to induce subsampling in graph structured data and introduces it as a component of a graph convolutional neural network. The pooling mechanism builds on the Non-Negative Matrix Factorization (NMF) of a matrix representing node adjacency and node similarity as adaptively obtained through the vertices embedding learned by the model. Such mechanism is applied to obtain an incrementally coarser graph where nodes are adaptively pooled into communities based on the outcomes of the non-negative factorization. The empirical analysis on graph classification bench…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Classification and topic modeling are popular techniques in machine learning that extract information from large-scale datasets. By incorporating a priori information such as labels or important features, methods have been developed to perform classification and topic modeling tasks; however, most methods that can perform both do not allow for guidance of the topics or features. In this paper, we propose a method, namely Guided Semi-Supervised Non-negative Matrix Factorization (GSSNMF), that performs both classification and topic modeling by incorporating supervision from both pre-assigned doc…
Toronto Metropolitan University（多伦多都会大学）；University of Toronto（多伦多大学）
The selection of most informative and discriminative features from high-dimensional data has been noticed as an important topic in machine learning and data engineering. Using matrix factorization-based techniques such as nonnegative matrix factorization for feature selection has emerged as a hot topic in feature selection. The main goal of feature selection using matrix factorization is to extract a subspace which approximates the original space but in a lower dimension. In this study, rank revealing QR (RRQR) factorization, which is computationally cheaper than singular value decomposition (…
IRIT, Université de Toulouse, CNRS（图卢兹大学 IRIT 研究所、法国国家科学研究中心）；ISAE-SUPAERO, Université de Toulouse（图卢兹大学 ISAE-SUPAERO 高等航空与航天学院）
We introduce a new non-negative matrix factorization (NMF) method for ordinal data, called OrdNMF. Ordinal data are categorical data which exhibit a natural ordering between the categories. In particular, they can be found in recommender systems, either with explicit data (such as ratings) or implicit data (such as quantized play counts). OrdNMF is a probabilistic latent factor model that generalizes Bernoulli-Poisson factorization (BePoF) and Poisson factorization (PF) applied to binarized data. Contrary to these methods, OrdNMF circumvents binarization and can exploit a more informative repr…
Xidian University（西安电子科技大学）；Chongqing University of Posts and Telecommunications（重庆邮电大学）
Multi-view clustering (MVC) based on non-negative matrix factorization (NMF) and its variants have received a huge amount of attention in recent years due to their advantages in clustering interpretability. However, existing NMF-based multi-view clustering methods perform NMF on each view data respectively and ignore the impact of between-view. Thus, they can't well exploit the within-view spatial structure and between-view complementary information. To resolve this issue, we present semi-non-negative tensor factorization (Semi-NTF) and develop a novel multi-view clustering based on Semi-NTF w…
In this paper, we propose a new non-monotone conjugate gradient method for solving unconstrained nonlinear optimization problems. We first modify the non-monotone line search method by introducing a new trigonometric function to calculate the non-monotone parameter, which plays an essential role in the algorithm's efficiency. Then, we apply a convex combination of the Barzilai-Borwein method for calculating the value of step size in each iteration. Under some suitable assumptions, we prove that the new algorithm has the global convergence property. The efficiency and effectiveness of the propo…
University of Maryland（马里兰大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
We utilize a recently developed topic modeling method called SeNMFk, extending the standard Non-negative Matrix Factorization (NMF) methods by incorporating the semantic structure of the text, and adding a robust system for determining the number of topics. With SeNMFk, we were able to extract coherent topics validated by human experts. From these topics, a few are relatively general and cover broad concepts, while the majority can be precisely mapped to specific scientific effects or measurement techniques. The topics also differ by ubiquity, with only three topics prevalent in almost 40 perc…
Multi-view learning accomplishes the task objectives of classification by leverag-ing the relationships between different views of the same object. Most existing methods usually focus on consistency and complementarity between multiple views. But not all of this information is useful for classification tasks. Instead, it is the specific discriminating information that plays an important role. Zhong Zhang et al. explore the discriminative and non-discriminative information exist-ing in common and view-specific parts among different views via joint non-negative matrix factorization. In this pape…
University of Southern California（南加州大学）；Kobe University（神户大学）；CyberAgent, Inc.（CyberAgent 公司）；Information Sciences Institute, University of Southern California（南加州大学信息科学研究所）
Understanding consumer behavior is an important task, not only for developing marketing strategies but also for the management of economic policies. Detecting consumption patterns, however, is a high-dimensional problem in which various factors that would affect consumers' behavior need to be considered, such as consumers' demographics, circadian rhythm, seasonal cycles, etc. Here, we develop a method to extract multi-timescale expenditure patterns of consumers from a large dataset of scanned receipts. We use a non-negative tensor factorization (NTF) to detect intra- and inter-week consumption…
University of Applied Sciences and Arts, Northwestern Switzerland（瑞士西北应用科学与艺术大学）；University of Ljubljana（卢布尔雅那大学）
This article utilizes the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalise the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalised objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；University of Science and Technology of China（中国科学技术大学）；Shenzhen Research Institute of Big Data（深圳市大数据研究院）；Warshel Institute for Computational Biology, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）瓦谢尔计算生物研究院）
Non-negative matrix factorization (NMF) is a powerful tool for dimensionality reduction and clustering. Unfortunately, the interpretation of the clustering results from NMF is difficult, especially for the high-dimensional biological data without effective feature selection. In this paper, we first introduce a row-sparse NMF with $\ell_{2,0}$-norm constraint (NMF_$\ell_{20}$), where the basis matrix $W$ is constrained by the $\ell_{2,0}$-norm, such that $W$ has a row-sparsity pattern with feature selection. It is a challenge to solve the model, because the $\ell_{2,0}$-norm is non-convex and n…
Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including topic modeling, recommender systems and bioinformatics. Due to the compute-intensive nature of applications that must perform repeated NMF, several parallel implementations have been developed in the past. However, existing parallel NMF algorithms have not addressed data locality optimizations, which are critical for high performance since data movement costs greatly exceed the cost of arithmetic/logic operations on current computer systems. In this paper…
University of Maryland, Baltimore County（马里兰大学巴尔的摩郡分校）；LANL（洛斯阿拉莫斯国家实验室）
Non-negative matrix factorization (NMF) with missing-value completion is a well-known effective Collaborative Filtering (CF) method used to provide personalized user recommendations. However, traditional CF relies on the privacy-invasive collection of users' explicit and implicit feedback to build a central recommender model. One-shot federated learning has recently emerged as a method to mitigate the privacy problem while addressing the traditional communication bottleneck of federated learning. In this paper, we present the first unsupervised one-shot federated CF implementation, named FedSP…
Academy of Advanced Interdisciplinary Research, Xidian University（西安电子科技大学先进交叉学科研究院）；Center for OPTical Imagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University（西北工业大学光学图像分析与学习中心）；Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Xidian University（西安电子科技大学教育部智能感知与图像理解重点实验室、国际智能感知与计算研究中心）
Non-negative Matrix Factorization (NMF) is one of the most popular techniques for data representation and clustering, and has been widely used in machine learning and data analysis. NMF concentrates the features of each sample into a vector, and approximates it by the linear combination of basis vectors, such that the low-dimensional representations are achieved. However, in real-world applications, the features are usually with different importances. To exploit the discriminative features, some methods project the samples into the subspace with a transformation matrix, which disturbs the orig…
Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis of non-negative data. In particular, a lot of effort has been devoted to probabilistic NMF, namely estimation or inference tasks in probabilistic models describing the data, based for example on Poisson or exponential likelihoods. When dealing with time series data, several works have proposed to model the evolution of the activation coefficients as a non-negative Markov chain, most of the time in relation with the Gamma distribution, giving rise to so-called temporal NMF models. In this pap…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；City University of Hong Kong（香港城市大学）
Emergency Department (ED) crowding is a worldwide issue that affects the efficiency of hospital management and the quality of patient care. This occurs when the request for an admit ward-bed to receive a patient is delayed until an admission decision is made by a doctor. To reduce the overcrowding and waiting time of ED, we build a classifier to predict the disposition of patients using manually-typed nurse notes collected during triage, thereby allowing hospital staff to begin necessary preparation beforehand. However, these triage notes involve high dimensional, noisy, and also sparse text d…
Non-negative matrix factorization (NMF) is a dimensionality reduction technique which tends to produce a sparse representation of data. Commonly, the error between the actual and recreated matrices is used as an objective function, but this method may not produce the type of representation we desire as it allows for the complexity of the model to grow, constrained only by the size of the subspace and the non-negativity requirement. If additional constraints, such as sparsity, are imposed the question of parameter selection becomes critical. Instead of adding sparsity constraints in an ad-hoc m…
SUTD（新加坡科技设计大学(SUTD)（注：SUTD是Singapore University of Technology and Design的缩写，常见中文名新加坡科技设计大学））
Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive study, it is poorly understood whether or not there exist natural algorithms that can provably converge to a local minimum. Part of the reason is because the objective is heavily symmetric and its gradient is not Lipschitz. In this paper we define a multiplicative weight update type dynamics (modification of the seminal Lee-Seung algorithm) that runs concurre…
Urban areas provide us with a treasure trove of available data capturing almost every aspect of a population's life. This work focuses on mobility data and how it will help improve our understanding of urban mobility patterns. Readily available and sizable farecard data captures trips in a public transportation network. However, such data typically lacks temporal modalities and as such the task of inferring trip semantic, station function, and user profile is quite challenging. As existing approaches either focus on station-level or user-level signals, they are prone to overfitting and generat…
Non-negative matrix factorization (NMF) has become a popular method for representing meaningful data by extracting a non-negative basis feature from an observed non-negative data matrix. Some of the unique features of this method in identifying hidden data put this method amongst the powerful methods in the machine learning area. The NMF is a known non-convex optimization problem and the initial point has a significant effect on finding an efficient local solution. In this paper, we investigate the most popular initialization procedures proposed for NMF so far. We describe each method and pres…
Due to recent explosion of text data, researchers have been overwhelmed by ever-increasing volume of articles produced by different research communities. Various scholarly search websites, citation recommendation engines, and research databases have been created to simplify the text search tasks. However, it is still difficult for researchers to be able to identify potential research topics without doing intensive reviews on a tremendous number of articles published by journals, conferences, meetings, and workshops. In this paper, we consider a novel topic diffusion discovery technique that in…
Motivated by applications in hyperspectral imaging we investigate methods for approximating a high-dimensional non-negative matrix $\mathbf{\mathit{Y}}$ by a product of two lower-dimensional, non-negative matrices $\mathbf{\mathit{K}}$ and $\mathbf{\mathit{X}}.$ This so-called non-negative matrix factorization is based on defining suitable Tikhonov functionals, which combine a discrepancy measure for $\mathbf{\mathit{Y}}\approx\mathbf{\mathit{KX}}$ with penalty terms for enforcing additional properties of $\mathbf{\mathit{K}}$ and $\mathbf{\mathit{X}}$. The minimization is based on alternating…
Laurentian University（劳伦森大学）；Jaypee Institute of Information Technology（杰普信息技术学院）
Over the past few years, there has been a considerable spread of microarray technology in many biological patterns, particularly in those pertaining to cancer diseases like leukemia, prostate, colon cancer, etc. The primary bottleneck that one experiences in the proper understanding of such datasets lies in their dimensionality, and thus for an efficient and effective means of studying the same, a reduction in their dimension to a large extent is deemed necessary. This study is a bid to suggesting different algorithms and approaches for the reduction of dimensionality of such microarray datase…
