A new matrix factorization method that approximates data without requiring nonnegativity or convexity.
problem Approximating data matrices without the constraints of nonnegativity or convexity.
method A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix.
result The method allows for approximation of data sets without the usual constraints of nonnegativity or convexity.
New NMF algorithm uses Toeplitz matrix for facial recognition.
problem Facial recognition performance improvement.
method Proposes TNMF algorithm with Toeplitz penalty for NMF.
result TNMF outperforms ZNMF and other constrained NMF algorithms.
NIMFA is a Python library for nonnegative matrix factorization.
problem Efficiently factorizing nonnegative matrices for various applications.
method Unified interface, state-of-the-art methods, initialization approaches, quality scoring, supports dense and sparse matrices.
result Unified and efficient implementation of nonnegative matrix factorization methods.
New method reduces computational cost for nonnegative low rank matrix approximation.
problem Efficiently compute nonnegative low rank matrix approximation for nonnegative matrices.
method Alternating projections onto tangent spaces of fixed rank matrices manifold and nonnegative matrix manifold.
result Sequence converges linearly to optimal solutions, showing better performance in terms of computational time and accuracy.
Paper proposes a clustering algorithm for nonnegative data.
problem Clustering nonnegative data in disjoint subspaces.
method Simple algorithm to cluster nonnegative data.
result Matrix completion algorithm outperforms standard methods.
The exact nonnegative matrix factorization (exact NMF) problem is the following: given an m-by-n nonnegative matrix X and a factorization rank r, find, if possible, an m-by-r nonnegative matrix W and an r-by-n nonnegative matrix H such that X=WH. In this paper, we propose two heuristics for exac…
Randomized HALS for efficient NMF on big data.
problem Challenges in computing nonnegative matrix factorization for big data.
method Randomized hierarchical alternating least squares (HALS) algorithm.
result Efficient nonnegative decomposition for big data applications.
Graph neural networks speed up nonnegative matrix factorization.
problem Efficiently factorize nonnegative matrices for various applications.
method Developed a graph neural network that combines bipartite self-attention with ADMM updates.
result Significant acceleration achieved in nonnegative matrix factorization.
The paper compares inference methods for Bayesian nonnegative matrix factorisation.
problem Improving prediction accuracy and pattern discovery in nonnegative matrix factorisation.
method Compared non-probabilistic, Gibbs sampling, variational Bayesian, and maximum-a-posteriori approaches.
result Variational Bayesian inference is a new and efficient approach for Bayesian nonnegative models.
Given a symmetric nonnegative matrix A, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix H, usually with much fewer columns than A, such that A≈HHT. SymNMF can be used for data analysis and in particular for various clustering tasks. In this paper, we p…
Introduces NMF for hyperspectral imaging and discusses its geometry and complexity.
problem Constrained low-rank matrix approximation problems.
method NMF for hyperspectral imaging, geometry and uniqueness of NMF solutions, complexity, algorithms.
result Discussion on NMF's geometry and complexity.
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative coefficient matrix, and the coefficient matrix is used as the new representation. …
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.
New method learns local structure for better data representation.
problem Global structure learning ignores local structure in nonnegative matrix factorization.
method Proposes a new nonnegative matrix factorization method that learns local similarity and clustering.
result The new representation reveals inherent geometric property of the data more effectively.
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.
New algorithms improve NMF for extracting patterns from time series data.
problem Extracting short-lived temporal motifs from high-dimensional time series data.
method Extended HALS and ANLS algorithms for CNMF model.
result Improved performance on large-scale data compared to multiplicative updates.
ZNMF improves facial recognition performance using data-dependent penalties.
problem Facial recognition performance in the Cambridge ORL database.
method ZNMF uses data-dependent auxiliary constraints to modify NMF.
result ZNMF outperforms other constrained NMF algorithms in facial recognition.
New NMF method tackles nonnegative data with separability relaxed.
problem Nonnegative matrix factorization for nonnegative data.
method Generalized separability assumption, convex optimization model, gradient method, heuristic algorithm.
result Effective in synthetic, document, and image data sets.
Paper accelerates NMF algorithms using extrapolation.
problem Efficiently solving nonnegative matrix factorization problems.
method Inspired by convex optimization, uses extrapolation for two-block exact coordinate descent algorithms.
result Significantly accelerates NMF algorithms on various data sets.
Improved NMF using variance-reduced MU rule.
problem Slow convergence of multiplicative update in NMF.
method Introduces variance-reduced stochastic multiplicative update.
result Robustly outperforms state-of-the-art algorithms.
Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear representation in a low dimensional space by using the product of two nonnegative matrices. …
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.
New criterion ensures recovery of latent factors in NMF with mild conditions.
problem Identifying latent factors in nonnegative matrix factorization (NMF) under mild conditions.
method Proposed a new identification criterion based on the scatteredness of one factor's rows in the nonnegative orthant.
result Latent factors can be provably identified from the NMF model with minimal structural assumptions.
Paper proposes an effective mean-field inference method for NNBMs.
problem Inference in NNBMs is challenging due to their complex structure.
method Uses mean-field method and diagonal consistency method.
result Effective inference method for NNBMs is proposed.
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…
Reverse annealing boosts quantum matrix factorization performance.
problem Improving quantum matrix factorization performance.
method Combining forward and reverse annealing for nonnegative/binary matrix factorization.
result Combination of forward and reverse annealing significantly improves performance.
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns), which is equivalent to the hyperspectral unmixing problem under the linear mixing mo…
Paper introduces a novel matrix-wise sparse MNNLS formulation and algorithm.
problem Sparse nonnegative least squares with multiple right-hand sides.
method Matrix-wise sparsity constraint, two-step algorithm.
result More accurate results compared to state-of-the-art methods.
Algorithm recovers multiple time series from aggregated data.
problem Recovering multiple nonnegative time series from a few temporal aggregates.
method Extends NMF algorithms to use linear measurements as observations, incorporating individual autocorrelation.
result Effective recovery of multiple time series from aggregated data.
Nonnegative sectional curvature linked to matrix displacement convexity.
problem Nonnegative sectional curvature in Riemannian manifolds.
method Matrix displacement convexity as a criterion for nonnegative sectional curvature.
result Entropy functional matrix displacement convexity implies nonnegative sectional curvature.
New probabilistic model for semi-nonnegative matrix factorization using Skellam distribution.
problem Automatic clustering of semi-nonnegative data.
method Skellam-SNMF model with EM and VBEM algorithms.
result New divergence D and algorithms outperform classic SNMF. Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.
problem Identify nonnegative Tucker decomposition factors uniquely.
method Adapting NMF identifiability results, derive procedures using tensor unfoldings or slices.
result Nonnegative Tucker decomposition factors are identifiable under certain sparsity conditions.
Nonnegative low-rank matrix recovery can have spurious local minima.
problem Nonnegative low-rank matrix recovery problems can have spurious local minima.
method Investigated projected gradient methods for nonnegative low-rank recovery problems.
result Benign nonconvexity holds in the fully-observed case with RIP constant δ=0 but fails in the partially-observed case and higher-rank ground truths.
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.
The study examines how prior and likelihood choices affect Bayesian matrix factorisation on small datasets.
problem Improving predictive performance of Bayesian matrix factorisation on small datasets.
method Review and comparison of 16 Bayesian matrix factorisation models across four groups: Gaussian-likelihood with real-valued priors, nonnegative priors, semi-nonnegative models, and Poisson-likelihood approaches.
result Poisson models give poor predictions, and nonnegative models are more constrained than real-valued ones.
New insights into when NMF decompositions are not unique.
problem Non-identifiability of NMF decompositions.
method Characterization of non-identifiability conditions.
result Characterized when and how non-uniqueness can occur in NMF.
A new method for DNNs using NMFs without BP.
problem Difficulties in finding appropriate parameters for DNNs.
method Alternating optimization with semi-nonnegative matrix factorizations.
result Similar error rates to conventional DNNs with BP.
Paper introduces SMM for forecasting multiple time series with missing values.
problem Forecasting multiple time series with missing and noisy values.
method Sliding Mask Method (SMM) using Non-negative Matrix Factorization (NMF).
result The method outperforms state-of-the-art methods in time series forecasting.
Paper presents a provably correct algorithm for CNMF under separable conditions.
problem Convolutive nonnegative matrix factorization (CNMF) under separable assumptions.
method Algorithm exploiting NMF model and existing separable NMF algorithms.
result Guaranteed solution in low noise settings, runs in polynomial time.
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…
Although nonnegative matrix factorization (NMF) is NP-hard in general, it has been shown very recently that it is tractable under the assumption that the input nonnegative data matrix is close to being separable (separability requires that all columns of the input matrix belongs to the cone spanned by a small subset of…
Proposes CC-NMDF for analyzing manifold-valued data.
problem Nonlinear structure in manifold-valued data requires new analysis methods.
method Curvature-corrected nonnegative manifold data factorization (CC-NMDF) with an iterative algorithm.
result Demonstrates CC-NMDF on real-world diffusion tensor MRI data.
Unified framework for online nonnegative matrix factorization with outlier handling.
problem Performing nonnegative matrix factorization with outliers in large-scale data.
method Unified framework with two solvers based on gradient descent and ADMM, proving convergence.
result Sequence of objective values and learned dictionaries converge to optimal points.
Efficiently factorizes coupled matrix tensor data for better accuracy and speed.
problem Poor computation efficiency in existing N-CMTF algorithms.
method Column-wise element selection to prevent frequent gradient updates.
result More accurate and computationally efficient factorization.
The paper explores partial identifiability in nonnegative matrix factorization under specific conditions.
problem Identifying specific columns of the matrices in nonnegative matrix factorization.
method Mathematical rigor and geometric interpretation to analyze partial identifiability of columns in nonnegative matrix factorization.
result The partial uniqueness of a single column of C or S can be guaranteed under certain sparsity and algebraic conditions. Given a matrix M (not necessarily nonnegative) and a factorization rank r, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix U with r columns and a nonnegative matrix V with r rows such that UV is the best possible approximation of M according to some metric. In this paper, we study th…
Method uses NMF for clustering with partial distance measurements.
problem Proximity clustering with partial distance measurements.
method Nyström approximation with Nonnegative Matrix Factorization.
result Find nearly optimal clustering quality on synthetic and real-world data.
Method improves clarity in forecasting spatio-temporal data.
problem Forecasting spatio-temporal data with clarity and interpretability.
method Supervised semi-nonnegative matrix factorization with frequency regularization.
result Method offers clearer interpretability in forecasting spatio-temporal data.