Given a symmetric nonnegative matrix , symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix , usually with much fewer columns than , such that . SymNMF can be used for data analysis and in particular for various clustering tasks. In this paper, we p…
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48 results for “Symmetric nonnegative matrix factorization”
We simplify symmetric NMF by transforming it into a nonsymmetric problem, enabling faster and more efficient solutions.
problem Efficiently solving symmetric nonnegative matrix factorization (NMF).
method Transforming symmetric NMF into a nonsymmetric problem, applying fast alternating algorithms, and rigorously proving convergence.
result Fast algorithms for symmetric NMF can converge to a critical point at least at a sublinear rate.
The SCMU algorithm computes cone factorizations for symmetric cones, improving upon existing methods.
problem Computing cone factorizations for symmetric cones in optimization.
method Introduces and analyzes the symmetric-cone multiplicative update (SCMU) algorithm.
result The SCMU algorithm non-decreases the squared loss objective.
A new method solves SymNMF problems faster and more efficiently.
problem Symmetric nonnegative matrix factorization (SymNMF) for data analytics.
method Nonconvex variable splitting method.
result The method converges to KKT points and has a global sublinear convergence rate.
New algorithm finds overlapping communities in networks.
problem Finding overlapping communities in networks.
method Linking NMF optimization to MMSB parameters, proposing GeoNMF.
result GeoNMF is provably optimal and consistent.
Paper proposes a Frank-Wolfe solver for symmetric NMF under simplicial constraint.
problem Optimizing symmetric nonnegative matrix factorization with simplicial constraint.
method Frank-Wolfe optimization algorithm for nonconvex problems.
result Proves convergence rate of for -approximate KKT points.
Paper checks SSC for matrix factorizations using Gurobi.
problem Checking the SSC for various matrix factorizations.
method Formulated as a non-convex quadratic optimization problem over a bounded set, solved with Gurobi.
result SSC can be checked in reasonable time for realistic scenarios.
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.
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.
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.
Two fast algorithms improve SNMF for clustering.
problem Improving clustering quality with SNMF.
method Variable splitting, APG, ADMM.
result New algorithms outperform state of the art.
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.
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.
The exact nonnegative matrix factorization (exact NMF) problem is the following: given an -by- nonnegative matrix and a factorization rank , find, if possible, an -by- nonnegative matrix and an -by- nonnegative matrix such that . In this paper, we propose two heuristics for exac…
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.
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.
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.
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.
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.
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.
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.
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.
Fast Convolutive Nonnegative Matrix Factorization Through Coordinate and Block Coordinate Updatescs.LG
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.
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.
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.
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.
New inequalities for matrix supermartingales converge under various conditions.
problem Convergence and maximal inequalities of supermartingales in positive semidefinite matrices.
method Developed new concentration inequalities for matrix supermartingales.
result New inequalities for matrix supermartingales under different tail conditions.
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.
We develop a method to factorize symmetric sparse Boolean matrices efficiently.
problem Finding a symmetric factorization of a given matrix into a sparse, Boolean matrix.
method Polynomial-time algorithm based on bootstrapping higher-order information and tensor decomposition.
result A matrix with full column rank can be recovered with high probability when the matrix size is sufficiently large.
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. …
Paper proves min-vol NMF robust to noise under expanded condition.
problem Robustness of min-vol NMF to noise.
method Proved robustness under expanded sufficiently scattered condition.
result Proves min-vol NMF identifies groundtruth factors in noise.
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 and algorithms outperform classic SNMF.
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.
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…
Alternating optimization method based on nonnegative matrix factorizations for deep neural networkscs.LG
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 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.
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.
Proposes a multilayer nonlinear semi-nonnegative matrix factorization for better recommendation.
problem Inaccurate user-item interaction modeling with classical matrix factorization.
method Multilayer nonlinear Semi-NMF approach for latent user and item representations.
result Proposed method achieves better generalization in prediction and comparable representation in clustering.
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.
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 or can be guaranteed under certain sparsity and algebraic conditions.
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.
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 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 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. …
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.
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.
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.