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 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.
MaxVol NMF maximizes the volume of H 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 H. result MaxVol NMF solutions correspond to clustering columns in disjoint clusters.
DR-NMF uses unfolded ISTA for speech separation, offering interpretability and speed.
problem Speech separation in noisy environments.
method DR-NMF is a recurrent neural network that unfolds ISTA iterations for NMF of spectrograms.
result DR-NMF outperforms NMF and LSTM networks in speech separation.
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…
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…
Sparse NMF with archetypal regularization aims to robustly represent data points.
problem Representing data points as sparse linear combinations of archetypes.
method Sparse NMF with archetypal regularization, introducing strong and weak robustness.
result Theoretical robustness guarantees hold under minimal assumptions.
Adapts PALM to solve NMF with smooth and sparse solutions.
problem Non-negative matrix factorization for dimensionality reduction and source separation.
method Adapted PALM for convex minimization with non-differentiable constraints.
result Solves NMF with smooth and/or sparse solutions.
Non-negative blind source separation (non-negative BSS), which is also referred to as non-negative matrix factorization (NMF), is a very active field in domains as different as astrophysics, audio processing or biomedical signal processing. In this context, the efficient retrieval of the sources requires the use of sig…
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 quasi-Newton method tackles NMF with transform learning on orthogonal manifolds.
problem Efficiently learning transforms for NMF in non-convex optimization on orthogonal manifolds.
method Derives a quasi-Newton method on the orthogonal matrix manifold using sparse approximations of the Hessian.
result Outperforms state-of-the-art methods by orders of magnitude in experiments on synthetic and real audio data.
Efficient sparse GP model improves audio source separation.
problem Sparse Gaussian Process (GP) inference is computationally expensive for long audio frames.
method Used GP regression, spectral mixture kernels, and variational sparse GPs.
result Proposed method outperforms LD-PSDTF, KL-NMF, and IS-NMF.
Improved SVD-based NMF initialization reduces initial error and is faster.
problem Improving NMF initialization to reduce convergence error and computational cost.
method Nonnegative SVD with low-rank correction (NNSVD-LRC) that considers discarded SVD factors.
result Significantly reduces initial error with negligible additional computational cost.
The paper introduces MU for NMF with β-divergences and disjoint constraints.
problem Nonnegative matrix factorization with constraints.
method Design multiplicative updates for NMF based on β-divergences with disjoint constraints. result Multiplicative updates satisfy constraints and decrease the objective function.
We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework for S-NNLS based on a rectified power exponential scale mixture prior on the spars…
Nonnegative matrix factorization (NMF) with group sparsity constraints is formulated as a probabilistic graphical model and, assuming some observed data have been generated by the model, a feasible variational Bayesian algorithm is derived for learning model parameters. When used in a supervised learning scenario, NMF …
NCL improves interpretability of deep features by enforcing non-negativity.
problem Lack of interpretability in deep representations.
method Non-negative Contrastive Learning (NCL) using non-negativity constraints.
result NCL outperforms standard contrastive learning in feature disentanglement and selection.
A new method STMF improves missing value prediction using tropical semiring.
problem Limited capability of linear models to model complex relations.
method Sparse Tropical Matrix Factorization (STMF) using tropical semiring.
result STMF outperforms NMF on real data, especially in handling extreme values.
Brain networks in fMRI are typically identified using spatial independent component analysis (ICA), yet mathematical constraints such as sparse coding and positivity both provide alternate biologically-plausible frameworks for generating brain networks. Non-negative Matrix Factorization (NMF) would suppress negative BO…
New method sets explicit sparsity for groups of vectors in deep learning and NMF.
problem Tackles the challenge of achieving a desired average sparsity level in vector groups.
method Designs a new sparse projection method that sets the sparsity level for the whole set explicitly and automatically tunes the sparsity of each vector.
result Shows significant improvements in accuracy and reconstruction errors compared to existing methods in deep learning and NMF.
Non-negative matrix factorization (NMF) approximates a non-negative matrix X by a product of two non-negative low-rank factor matrices W and H. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between X and WTH to model the Poisson noise or the Gaussian noise.…
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.
Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors W and H, for the given input matrix A, such that A≈WH. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, …
New method enforces encoder sparsity in HPF for more interpretable feature selection.
problem Lack of encoder sparsity in HPF leads to lack of column-clustering property.
method Enforces encoder sparsity using a generalized additive model (GAM).
result Gains ability to perform feature selection and relates each representation to original features.
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…
A new objective function for NMF reduces model complexity and improves accuracy.
problem NMF's error-based objective function can lead to overly complex models.
method MDL-NMF uses minimum description length to balance model complexity and accuracy.
result MDL-NMF outperforms traditional NMF on various datasets.
Paper proposes DR-NMF for robust NMF with unknown noise model.
problem Robust NMF for unknown noise model.
method Multi-objective NMF with weighted-sum approach, DR-NMF via Frank-Wolfe algorithm.
result DR-NMF is robust to unknown noise model.
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.
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 paper analyzes the error in variational Bayesian NMF compared to Bayesian NMF.
problem Analyzing the variational approximation error in Bayesian NMF.
method Using algebraic geometrical methods, the paper derives an upper bound for the learning coefficient and a lower bound for the approximation error.
result The paper finds a lower bound for the approximation error, showing how well VBNMF approximates Bayesian NMF.
The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with a nonlinear formulation of the NMF. Within the framework of kernel machines, the mod…
A new particle-based method improves Bayesian NMF for better uncertainty estimates.
problem Lack of principled uncertainty understanding in traditional NMF.
method Particle-based variational approach to Bayesian NMF.
result Better particle approximations to Bayesian NMF posterior in less time.
New updates for β-divergence in convolutional NMF are stable and consistent.
problem Improving the stability and consistency of NMF updates for convolutional data.
method Presented multiplicative updates for β-divergence in closed form. result The new updates are stable and consistent across common β values. PL-NMF improves parallel NMF by optimizing data locality.
problem Data movement costs dominate in parallel NMF applications.
method Developed a parallel NMF algorithm based on HALS with data locality optimizations.
result Significant performance improvement over existing parallel NMF algorithms.
Test evaluates NMF-based topic models for document corpora.
problem Violation of likelihood assumptions in NMF topic models.
method Double parametric bootstrap test based on KL divergence and Poisson ML.
result Correctly identifies reliable NMF-based topic models.
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.
Near-convex archetypal analysis improves interpretability and fitting error in NMF.
problem High data fitting error in traditional archetypal analysis.
method Introduces near-convex archetypal analysis (NCAA) that combines AA and NMF.
result NCAA achieves lower data fitting error than state-of-the-art methods.
A new state-space approach improves NMF for dynamic data.
problem Modeling time series with strong temporal dependencies.
method Probabilistic framework with state-space approach and multi-lag N-VAR model.
result D-NMF outperforms static NMF and other state-of-the-art methods.
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.
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 …
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.
Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices appropriate for the intended applications. The method has been widely used for unsupervised learning tasks, including recommender systems (rating matrix of users by items) and document clustering (weighting matrix …
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 …
New method clusters data subspaces more accurately.
problem Improving subspace clustering for nonlinear data.
method Introduces nonlinear orthogonal NMF with kernel-based updates.
result Enhanced clustering performance compared to existing methods.
This paper explores NMF identifiability and its applications.
problem Understanding NMF identifiability for better interpretability and applications.
method Comprehensive tutorial on NMF identifiability, connections to algorithms and applications.
result Significant progress in NMF identifiability research since the 2010s.