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.
SymNMF finds a simpler matrix approximating a given symmetric nonnegative matrix.
problem Finding a simpler matrix that approximates a given symmetric nonnegative matrix.
method Simple and efficient coordinate descent schemes.
result The methods effectively solve symNMF for large and sparse matrices.
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 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…
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.
NMF linked to clustering, reviewed and explained.
problem Linking NMF to clustering.
method Exploring NMF variants and their clustering interpretations.
result NMF variants can be used for clustering.
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.
Paper proposes monotonous NMF to handle scale and ordering ambiguities in nonnegative matrix factorization.
problem Scale and ordering ambiguities in nonnegative matrix factorization.
method Alternating least-squares algorithm for monotonous NMF, relaxed mixing matrix assumption.
result Monotonous NMF estimates monotonous signals better than standard NMF when sources are monotonous.
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.
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.
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.
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 D 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.
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 C or S 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.
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…
Nonnegative matrix factorization (NMF) has been shown recently to be tractable under the separability assumption, under which all the columns of the input data matrix belong to the convex cone generated by only a few of these columns. Bittorf, Recht, Ré and Tropp (`Factoring nonnegative matrices with linear programs', …
Unified Bayesian NMF models for binary data with automatic dimension selection.
problem Binary data analysis with nonnegative matrix factorization and link functions.
method Bayesian mean-parameterized nonnegative binary matrix factorization (NBMF) models with collapsed Gibbs and variational algorithms.
result Automatic detection of relevant components without manual tuning.
A new ranking model uses nonnegative matrix factorization for tennis players.
problem Modeling latent variables influencing tennis player performance.
method Combines Bradley-Terry-Luce model with nonnegative matrix factorization.
result Model identifies surface type as key determinant of male player performance.
Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being highly ill-posed, that is, there typically exist many different but equivalent facto…
Enhances NMF for better time series recovery and prediction using side information.
problem Reconstruct and predict electricity consumption time series.
method Extends NMF with side information, proposes HALSX algorithm.
result Improved recovery and prediction performance validated on various datasets.
L21 SNF compresses mixed-sign data robustly.
problem Compression of mixed-sign data with high fidelity.
method Regularized L21 Semi-NonNegative Matrix Factorization (L21 SNF).
result Rigorous proof of convergence and use-case advantages demonstrated.
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.