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.
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.
In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximatio…
Fast Bayesian NMF and Tri-Factorisation with improved convergence.
problem Difficult convergence in matrix tri-factorisation.
method Variational Bayesian algorithm for non-negative matrix factorisation and tri-factorisation.
result Faster convergence per iteration and wall-clock time than Gibbs sampling and non-probabilistic approaches.
A new method for Boolean matrix factorisation outperforms existing approaches.
problem Decomposing binary data matrices into meaningful patterns and quantifying their combinations.
method Probabilistic generative model with Metropolised Gibbs sampler for efficient posterior inference.
result The method outperforms all existing approaches on real and simulated data.
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation algorithm. Using the probabilistic model, we derive a matrix factorisation algorithm …
Bayesian HMF integrates multiple datasets for in/out-of-matrix prediction.
problem Data integration across different entity types and sparsity levels.
method Bayesian hybrid matrix factorisation model combining multiple methods.
result Consistently better in-matrix and out-of-matrix predictions compared to state-of-the-art methods.
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.
Unified framework for non-negative matrices and tensors using Wasserstein loss.
problem Finding low-dimensional representations of high-dimensional datasets with non-negative constraints.
method Unified mathematical framework with a smoothed Wasserstein loss, convex dual formulation for efficient computation.
result Efficient solution for non-negative matrix and tensor factorisations with Wasserstein loss.
New methods for hyperspectral unmixing handle intra-class variability.
problem Intra-class variability in hyperspectral images.
method Inertia-constrained Pixel-by-pixel NMF (IP-NMF) for handling variability.
result IP-NMF outperforms state-of-the-art methods in real data.
The paper shows how to recover true node positions from a graph or similarity matrix.
problem Recovering true distances and positions from a graph or similarity matrix.
method Two steps: matrix factorisation followed by nonlinear dimension reduction.
result Nonlinear dimension reduction can recover latent positions close to a manifold where geodesic distance is encoded.
New framework reduces factorisation model run time by exploiting sparse vector geometry.
problem Inefficient inner product computations over large sparse vectors in real-time applications.
method Geometry-aware permutation maps on a tessellated unit sphere for sparse vector embeddings.
result Significant reduction in run time with minimal accuracy loss.
TGP enhances collaborative filtering with side information using Gaussian Processes.
problem Improving collaborative filtering with side information.
method Formulated a Tucker Gaussian Process (TGP) that incorporates low-rank matrix factorisation and side information.
result Enhanced predictive performance for collaborative filtering problems.
Paper develops a decoder for sparse codes without encoder matrix, achieving optimal recovery.
problem Designing a decoder for sparse codes from linear measurements alone.
method Matrix factorization to recover encoder and sparse coding matrices from measurements.
result Decoder-Expander Based Factorisation recovers encoder and sparse coding matrix at optimal measurement rate with high probability.
The paper reformulates clustering as matrix factorization on the Stiefel manifold.
problem Clustering high-dimensional data like images and gene expression.
method Reformulates clustering as low-rank matrix estimation, using Burer-Monteiro factorization on the Stiefel manifold.
result Proves novel prediction bounds for clustering and proposes a componentwise Langevin sampler.
We propose a new approach for Collaborative Filtering which is based on Boolean Matrix Factorisation (BMF) and Formal Concept Analysis. In a series of experiments on real data (Movielens dataset) we compare the approach with the SVD- and NMF-based algorithms in terms of Mean Average Error (MAE). One of the experimental…
Identifying overlapping communities in networks is a challenging task. In this work we present a novel approach to community detection that utilises the Bayesian non-negative matrix factorisation (NMF) model to produce a probabilistic output for node memberships. The scheme has the advantage of computational efficiency…
A new algorithm MBMF improves recommendation accuracy and speed for sparse datasets.
problem Sparse and fluctuating predictions in recommender systems.
method MBMF uses magnitude constraints and Spherical coordinates to optimize faster than existing methods.
result MBMF outperforms existing algorithms in accuracy and speed on synthetic and real datasets.
End-to-end probabilistic inference improves audio signal processing.
problem Efficiently processing large audio signals with varying characteristics.
method Formulated a spectral mixture Gaussian process model with nonstationary priors, enabling infinite-horizon Gaussian process regression.
result The method outperforms standard techniques in processing audio signals with hundreds of thousands of data points.
For large matrix factorisation problems, we develop a distributed Markov Chain Monte Carlo (MCMC) method based on stochastic gradient Langevin dynamics (SGLD) that we call Parallel SGLD (PSGLD). PSGLD has very favourable scaling properties with increasing data size and is comparable in terms of computational requiremen…
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.
Simpler method for separating and manipulating latent attributes in autoencoders.
problem Separating and manipulating latent attributes in autoencoders.
method Matrix subspace projection
result Our method allows for changing selected attributes while preserving other information.
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.
Study uses NMF to analyze multimorbidity patterns in large EHR dataset.
problem Understanding and quantifying multimorbidity patterns over time.
method Non-negative Matrix Factorisation (NMF) for temporal phenotyping.
result Temporal characteristics of disease clusters reveal new multimorbidity patterns.
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.
Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determin…
Interpretable text-response modelling for structured outcomes
problem Predicting structured responses alongside textual data
method Joint non-negative matrix factorisation and binomial regression
result Recovering stable response-relevant textual signals
Generative model improves sound synthesis realism.
problem Synthesize natural sounds with realistic perception.
method Latent force modelling with physical knowledge incorporated.
result Generated sounds perceived as more realistic.
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.
We compute the categorified sl(N) link invariants as defined by Khovanov and Rozansky, for various links and values of N. This is made tractable by an algorithm for reducing tensor products of matrix factorisations to finite rank, which we implement in the computer algebra package Singular.
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.