In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximatio…
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48 results for “online NMF”
Predicts COVID-19 spread using dictionary learning and online NMF.
problem Limited daily case data for accurate prediction.
method Joint dictionary learning and online NMF for short evolution instances.
result Learned dictionary patterns improve predictions over time.
Nonnegative matrix factorization (NMF) is now a common tool for audio source separation. When learning NMF on large audio databases, one major drawback is that the complexity in time is O(FKN) when updating the dictionary (where (F;N) is the dimension of the input power spectrograms, and K the number of basis spectra),…
Non-negative Matrix Factorization (NMF) is a popular tool for data exploration. Bayesian NMF promises to also characterize uncertainty in the factorization. Unfortunately, current inference approaches such as MCMC mix slowly and tend to get stuck on single modes. We introduce a novel approach using rapidly-exploring ra…
Proposes a new NMF method incorporating neighborhood structure for better anomaly detection.
problem NMF's inability to incorporate neighborhood structure information limits its performance in nonlinear manifold structures.
method Integrates neighborhood structure information using Minimum Spanning Tree (MST) within NMF framework.
result Empirical results show superior performance in anomaly detection using the proposed method.
Nonnegative matrix factorization (NMF) is a popular method for audio spectral unmixing. While NMF is traditionally applied to off-the-shelf time-frequency representations based on the short-time Fourier or Cosine transforms, the ability to learn transforms from raw data attracts increasing attention. However, this adds…
Hierarchical NMF organizes COVID-19 literature into a searchable tree.
problem Organizing and searching for relevant COVID-19 research.
method Hierarchical nonnegative matrix factorization.
result Identified 8 major and 52 subtopics related to COVID-19.
Ensemble Kalman Filter improves GPSSM inference for online learning.
problem Non-mean-field variational inference issues in GPSSM.
method Combining EnKF with NMF variational inference.
result Improved online learning performance and data-fitting accuracy.
MaxVol NMF maximizes the volume of in NMF for better sparse and interpretable solutions.
problem Finding interpretable and unique NMF solutions.
method Dual approach to MinVol NMF, maximizing the volume of .
result MaxVol NMF solutions correspond to clustering columns in disjoint clusters.
Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors and , for the given input matrix , such that . NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, …
Nonnegative Matrix Factorization (NMF) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first, it was shown that they are closely linked. In this report, we provide a gentle introduction to clu…
A new NMF model for co-clustering and data approximation.
problem Finding a low rank approximation for nonnegative data.
method Generalizes separability assumption for NMF, proposing Co-Separable NMF (CoS-NMF).
result CoS-NMF outperforms state-of-the-art methods in co-clustering and data approximation.
In this paper, we propose a novel recurrent neural network architecture for speech separation. This architecture is constructed by unfolding the iterations of a sequential iterative soft-thresholding algorithm (ISTA) that solves the optimization problem for sparse nonnegative matrix factorization (NMF) of spectrograms.…
Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals can be monotonous in nature. For example, in source separation problem, the source…
SON-NMF estimates nonnegative rank on-the-fly for NMF.
problem Estimating the nonnegative rank of data in NMF.
method Sum-of-norms (SON) regularization to reduce rank, combined with a first-order BCD algorithm.
result SON-NMF can automatically estimate the rank from data without prior knowledge.
Neural NMF discovers hierarchical topics in multilayer data.
problem Detecting latent hierarchical structure in multilayer data.
method Recursive application of nonnegative matrix factorization (NMF) in layers with backpropagation optimization.
result Neural NMF outperforms other hierarchical NMF methods in synthetic and real-world datasets.
New method for sparse data using L1-NMF with improved sparsity control.
problem Sparse data with false zeros and heavy-tailed noise.
method Component-wise L1-NMF with weighted penalization and coordinate descent.
result Effective in handling sparse data with false zeros.
In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to dictionary matrix. We derive the algorithm by defining a simple objective funct…
Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this property of NMF on three applications, in image processing, text mining and hyperspe…
A new NMF variant tackles underdetermined problems with sparse and separable assumptions.
problem Underdetermined blind source separation, especially multispectral image unmixing.
method Sparse Separable Nonnegative Matrix Factorization (SSNMF) combining separability and sparsity assumptions. Algorithm based on SNPA and sparse nonnegative least squares.
result In noiseless settings, the algorithm recovers true underlying sources.
The paper introduces MU for NMF with -divergences and disjoint constraints.
problem Nonnegative matrix factorization with constraints.
method Design multiplicative updates for NMF based on -divergences with disjoint constraints.
result Multiplicative updates satisfy constraints and decrease the objective function.
Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for Symmetric NMF is not as easy as for the nonsymmetric counterpart, the latter adm…
Bayesian Non-negative Matrix Factorization (NMF) is a promising approach for understanding uncertainty and structure in matrix data. However, a large volume of applied work optimizes traditional non-Bayesian NMF objectives that fail to provide a principled understanding of the non-identifiability inherent in NMF-- an i…
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise) assumed on the data. In many applications, the noise model is unknown and difficu…
Unified NMF models for various noise distributions, improving feature extraction.
problem Inadequate assumptions for NMF under complex data distributions.
method Unified framework using MM-algorithms for traditional and convex NMF under Tweedie and Negative Binomial models.
result Unified multiplicative update rules for all models, including novel updates for convex NMF.
In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions, complexity, algorithms, and its link with extended formulations of polyhedra. In order to …
A new convex model tackles noisy separable NMF with provable correctness.
problem Noisy separable NMF with multiple data points near basis vectors.
method Smooth separability assumption, convex model, fast gradient method.
result The convex model provably recovers factors in the presence of noise.
We develop a unified and systematic framework for performing online nonnegative matrix factorization under a wide variety of important divergences. The online nature of our algorithm makes it particularly amenable to large-scale data. We prove that the sequence of learned dictionaries converges almost surely to the set…
Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA), also referred to as convex NMF, is a well-known NMF variant imposing that the bas…
Nonnegative matrix factorization (NMF) has been actively investigated and used in a wide range of problems in the past decade. A significant amount of attention has been given to develop NMF algorithms that are suitable to model time series with strong temporal dependencies. In this paper, we propose a novel state-spac…
Rank-One NMF-Based Initialization for NMF and Relative Error Bounds under a Geometric Assumptionstat.ML
We propose a geometric assumption on nonnegative data matrices such that under this assumption, we are able to provide upper bounds (both deterministic and probabilistic) on the relative error of nonnegative matrix factorization (NMF). The algorithm we propose first uses the geometric assumption to obtain an exact clus…
Improved clustering of extra-financial data using NMF with data separation.
problem High correlations and complex data structure in extra-financial datasets.
method Applying non-negative matrix factorization (NMF) with an initial data separation step.
result Enhanced clustering quality compared to PCA.
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 b…
Paper accelerates and secures distributed NMF.
problem Efficiently processing large NMF matrices and maintaining data privacy.
method Proposes DSANLS framework with matrix sketching for acceleration and secure adaptation.
result DSANLS framework and secure adaptations for distributed NMF.
Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is little guarantee on how well these methods work. Recently a surge of research have …
In this letter, we generalize the convolutional NMF by taking the -divergence as the contrast function and present the correct multiplicative updates for its factors in closed form. The new updates unify the -NMF and the convolutional NMF. We state why almost all of the existing updates are inexact and approximat…
The paper develops new algorithms for KL-divergence NMF, proving convergence and performance.
problem Improving NMF for nonnegative data with KL divergence.
method Collect and analyze properties of KL objective function, propose and test new algorithms.
result Guaranteed non-increasing objective function for one proposed algorithm, global convergence.
New methods improve analysis of single cell RNA sequencing data.
problem High dimensionality and complexity of scRNA-seq data.
method Topological Nonnegative Matrix Factorization (TNMF) and Robust Topological NMF (rTNMF).
result TNMF and rTNMF significantly outperform other NMF-based methods.
A new model BGAR(1) improves temporal NMF for time series data.
problem Temporal NMF models lack a well-defined stationary distribution.
method Introduced a new Gamma Markov chain model BGAR(1) to overcome the limitation of previous models.
result BGAR(1) model has a well-defined stationary distribution.
Nonnegative matrix factorization (NMF) has become a workhorse for signal and data analytics, triggered by its model parsimony and interpretability. Perhaps a bit surprisingly, the understanding to its model identifiability---the major reason behind the interpretability in many applications such as topic mining and hype…
Non-negative matrix factorization (NMF) is a technique for finding latent representations of data. The method has been applied to corpora to construct topic models. However, NMF has likelihood assumptions which are often violated by real document corpora. We present a double parametric bootstrap test for evaluating the…
A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernel-based orthogonal m…
A new portfolio method uses NMF for risk budgeting, outperforming classical methods.
problem Portfolio diversification and risk management in crypto and traditional assets.
method Risk factor budgeting using convex Non-negative Matrix Factorization (NMF).
result Our method outperforms classical portfolio allocations in diversification and risk profile.
Non-negative matrix factorization (NMF) is a knowledge discovery method that is used in many fields. Variational inference and Gibbs sampling methods for it are also wellknown. However, the variational approximation error has not been clarified yet, because NMF is not statistically regular and the prior distribution us…
Bayesian NMF model improves predictions and avoids overfitting.
problem Predicting missing values and finding hidden patterns in nonnegative data.
method Flexible and hierarchical prior for Bayesian NMF with Gibbs sampling.
result The proposed model leads to better predictions and avoids overfitting.
Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix and a factorization rank , NMF looks for a nonnegative matrix with columns and a …
Blind source separation is a common processing tool to analyse the constitution of pixels of hyperspectral images. Such methods usually suppose that pure pixel spectra (endmembers) are the same in all the image for each class of materials. In the framework of remote sensing, such an assumption is no more valid in the p…
Extracts factors from Treasury yields using ML techniques.
problem Understanding factors underlying Treasury yields.
method Nonnegative Matrix Factorization (NMF) and clustering.
result Factors identified through NMF and clustering.