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.
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48 results for “nonlinear NMF”
Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this…
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.
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.
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…
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.
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…
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.
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…
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.
Proposes TS-NMF for 2D clustering, preserving spatial info.
problem Loss of spatial information in 2D data.
method Semi-Nonnegative Matrix Factorization with manifold learning.
result Improves clustering performance compared to state-of-the-art.
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.
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.
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.
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…
New updates for -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 -divergence in closed form.
result The new updates are stable and consistent across common values.
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.
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.
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.
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 …
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.
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 …
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.
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.
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.
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.
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.
VAE enhances NMF for probabilistic non-negative matrix factorisation.
problem Non-negative matrix factorisation with probabilistic coefficients.
method Design a VAE network with non-negative weights and non-negative Weibull distribution.
result Effective probabilistic NMF for generating new data and linking latent and input variables.
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.
NMF and PCC linked, improving data denoising and feature stability.
problem Improving NMF's rank estimation and feature stability.
method Combining NMF and PCC for robust rank estimation and feature stability.
result NMF features are stable against noise and optimization seeds.
New R package for NMF evaluated on real-world data.
problem Limited comprehensive evaluations of NMF packages under real-world conditions.
method Systematic performance comparison of three NMF packages using real-world data.
result New package outperforms existing ones in computational efficiency and reconstruction accuracy.
The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the ext…
Develops deep NMF models using β-divergences for feature extraction.
problem Inadequate evaluation metrics for deep NMF on diverse datasets.
method Introduces new deep NMF models using Kullback-Leibler divergence.
result Improves feature extraction quality across different types of data.
Topic models have been extensively used to organize and interpret the contents of large, unstructured corpora of text documents. Although topic models often perform well on traditional training vs. test set evaluations, it is often the case that the results of a topic model do not align with human interpretation. This …
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.