The study examines non-negative curvature and conullity of curvature tensors.
problem Analyzing conullity conditions for curvature tensors and their compatibility with non-negative sectional curvature.
method Examined conullity two and three in specific dimensions, and used manifold properties to derive conditions.
result Finite volume manifolds with conullity 3 are locally products, and conditions are compatible with non-negative curvature only for specific manifold types.
We propose an algorithm for the non-negative factorization of an occurrence tensor built from heterogeneous networks. We use l0 norm to model sparse errors over discrete values (occurrences), and use decomposed factors to model the embedded groups of nodes. An efficient splitting method is developed to optimize the non…
Method detects multi-timescale consumer spending patterns from receipts.
problem Understanding and managing consumer behavior in high-dimensional data.
method Non-negative tensor factorization (NTF) to extract multi-timescale expenditure patterns.
result Consumption patterns are characterized based on spending behavior over different timescales.
Tensor factorization uncovers hidden patterns in student behavior data.
problem Discovering low-dimensional structure in high-dimensional behavioral data.
method Non-negative tensor factorization applied to wearable sensor data.
result Tensor factorization reveals clusters of students with different behaviors.
A new method for non-negative matrix factorization using generalized dual divergence.
problem Non-negative matrix factorization for various noise structures.
method Theoretical framework based on generalized dual Kullback-Leibler divergence, with algorithms developed and proven convergence using Expectation-Maximization.
result Generalizes existing methods and provides an alternative for non-negative matrix factorizations.
We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed counts as well as infer the rank of the decomposition. Moreover, leveraging a repa…
Unsupervised ML method reveals hidden features in reactive-diffusion simulations.
problem Automating interpretation of large model outputs in reactive-diffusion simulations.
method NTFk using Non-negative Tensor Factorization (NTF) coupled with k-means clustering.
result Identifies additive features characterizing mixing behavior.
Inertial methods solve non-convex non-smooth optimization problems efficiently.
problem Non-convex non-smooth optimization problems.
method Inertial block proximal methods for solving these problems.
result The methods converge globally under certain conditions and perform well in applications like NMF.
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country i took action a toward country j at time t"---known as dyadic events---in order to form an…
We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the alternating direction method of multipliers (ADMM): each matrix factor is updated in tur…
We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood, using a zero-truncated Poisson likelihood for binary data allows our model to scale …
A new method for decomposing non-negative tensors using energy-based modeling.
problem Challenges in traditional tensor decomposition methods, especially global optimization and rank selection.
method Energy-based modeling of tensors, considering interactions between modes for global optimization.
result Demonstrates effectiveness in tensor completion and approximation, revealing a relationship between many-body and low-rank approximations.
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections. We examine the approach of first performing factorization in the compressed dom…
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.
Efficiently reduces tensor ranks using mean-field approximation.
problem Low-rank approximation of non-negative tensors.
method Mean-field approximation of tensor rank reduction.
result Our algorithm achieves faster and competitive tensor rank reduction.
Paper proposes VAE-BPTF for better tensor factorization of sparse, imbalanced count data.
problem Inference of Bayesian Poisson-Gamma models for sparse and imbalanced count data is challenging.
method Variational auto-encoder framework with multi-layer perceptron networks for complex update information sharing and reweighting.
result VAE-BPTF outperforms current models in reconstruction errors and latent factor coherence across real-world datasets.
Tensor-networks enhance probabilistic modeling in physics and machine learning.
problem Understanding the expressive power of different tensor-network factorizations.
method Rigorous analysis of various tensor-network factorizations of discrete multivariate probability distributions.
result There are unbounded separations between the resource requirements of some tensor-network factorizations.
SOS programming verifies MTW tensor non-negativity for optimal transport maps.
problem Verifying MTW tensor non-negativity for general cost functions is difficult.
method Sum-of-Squares (SOS) programming for verifying and approximating MTW non-negativity.
result SOS programming provides certificates and approximations of MTW non-negativity.
TASTE combines static and temporal data for phenotyping EHRs.
problem Phenotyping EHRs with both static and temporal data.
method Jointly models static and temporal tensors using PARAFAC2 and non-negative matrix factorization, alternatingly solving sub-problems.
result TASTE outperforms existing methods in speed and clinical meaningfulness of phenotypes.
COPA models sparse, irregular tensors with constraints for interpretable temporal data.
problem Interpretable modeling of sparse, irregular tensors with constraints.
method COPA integrates optimization constraints like sparsity, non-negativity, and temporal smoothness into a hybrid optimization framework.
result COPA achieves significant speedups and interpretable results on large datasets.
Proposes a model to understand urban dynamics from mega-metropolises.
problem Understanding residents mobility patterns in mega-metropolises.
method Neighbor-Regularized and context-aware Non-negative Tensor Factorization (NR-cNTF).
result NR-cNTF accurately captures city rhythms and spatial communities.
We formulate and solve a tensor model using a latent-variable approach.
problem Parameter inference for Poisson canonical polyadic tensor models.
method Latent-variable formulation, Expectation-Maximization algorithms, Fisher information matrices.
result Derivation of Fisher information for PCP models, insights into model well-posedness.
SimTensor is a multi-platform, open-source software for generating artificial tensor data (either with CP/PARAFAC or Tucker structure) for reproducible research on tensor factorization algorithms. SimTensor is a stand-alone application based on MATALB. It provides a wide range of facilities for generating tensor data w…
The report analyzes Legendre decomposition for tensor data.
problem Finding effective lower dimensional representations of tensors.
method Theoretical analysis of dual parameters and dually flat manifold properties, followed by experimental verification and clustering.
result Parameters on submanifold cannot be directly used as low-rank representations.
A new framework improves tensor completion accuracy by considering numerical priors.
problem Tensor completion accuracy loss due to ignoring numerical priors.
method Generalized CP Decomposition Tensor Completion (GCDTC) framework incorporating numerical priors.
result GCDTC framework outperforms state-of-the-arts in non-negative tensor completion.
Alexandrov spaces with non-negative curvature are characterized by the matrix displacement convexity of an entropy tensor.
problem Characterizing non-negative curvature in Alexandrov spaces
method Constructing a parallel trivialization of the entropy tensor
result The entropy tensor is matrix displacement convex on Alexandrov spaces
In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold M and a symmetric 2-tensor r, construct a metric on M whose Ricci tensor equals r. In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita…
Paper proposes GSSNMF for legal document classification and topic modeling.
problem Lack of methods that can both classify and model topics with guidance.
method Guided Semi-Supervised Non-negative Matrix Factorization (GSSNMF).
result Improves both classification accuracy and topic coherence.
A new method for traffic data imputation considering spatiotemporal correlations.
problem Traffic data imputation, especially for high-level missing scenarios.
method Spatiotemporal regularized Tucker decomposition approach.
result The proposed method outperforms existing methods on real-world traffic datasets.
This paper reviews methods for discovering patient subgroups from EHR data.
problem Discovering subgroups of patients and co-occurring medical conditions from EHR data.
method Low-rank data approximation methods like matrix and tensor decompositions.
result These methods provide transparent and interpretable insights into patient phenotypes.
The paper introduces a pooling mechanism for graph CNNs using NMF.
problem Pooling in graph structured data for efficient computation.
method Non-negative matrix factorization for node pooling.
result The pooling mechanism improves graph classification performance.
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), K-means clustering, etc., rely on the factorization of a matrix obtained by concatenating high-dimensional vectors from a training collection. W…
This work proposes a new algorithm for automated and simultaneous phenotyping of multiple co-occurring medical conditions, also referred as comorbidities, using clinical notes from the electronic health records (EHRs). A basic latent factor estimation technique of non-negative matrix factorization (NMF) is augmented wi…
Method reveals multi-timescale trading dynamics in online financial markets.
problem Capturing and characterizing trading dynamics at different time scales.
method Non-negative tensor factorization (NTF) for multi-timescale activity patterns.
result NTF uncovers hidden activity patterns and crisis modalities in trading.
The paper surveys methods to approximate non-negative matrices using lower-dimensional factors.
problem Approximating high-dimensional non-negative matrices with lower-dimensional factors.
method Alternating minimization with surrogate functionals for Tikhonov functionals.
result Developed a general framework for adding penalty terms to surrogate functionals.
In this paper we study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Schouten tensor on compact Riemannian manifolds with boundary. We prove its solvability and the compactness of the solution set, provided the Ricci tensor is non-negative definite.
New method for inference on covariates in NMF with random effects.
problem Formal inference for covariate effects in NMF with non-negativity constraints.
method NMF-RE model with random effects, ridge updates, df-based cap, asymptotic linearization, wild bootstrap.
result Valid inference on covariates with non-negativity constraint, avoiding degeneracy.
New method for ordinal data improves recommendation systems.
problem Improving recommendation systems with ordinal data.
method Ordinal Non-negative Matrix Factorization (OrdNMF) for ordinal data.
result OrdNMF outperforms existing methods in recommendation experiments.
ALℓ0CORE tensor decomposition reduces computational cost for sparse count data.
problem Efficiently decompose sparse count data matrices.
method Probabilistic Tucker decomposition with ℓ0-norm constraint. result ALℓ0CORE achieves similar results to full Tucker decomposition at a fraction of the cost. Detects memorization in neural networks using non-negative factorization.
problem Identifying memorization in deep neural networks.
method Measures non-linearity using non-negative factorization of activation matrices.
result High non-linearity in deep layers indicates memorization.
The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods non-negative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general class of prior distributions and shows how the prior affects the rate of convergenc…
We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to arbitrary sets of tensors of any depth, including matrices, can be interpreted as u…
In this letter, we propose enhanced factored three way restricted Boltzmann machines (EFTW-RBMs) for speech detection. The proposed model incorporates conditional feature learning by multiplying the dynamical state of the third unit, which allows a modulation over the visible-hidden node pairs. Instead of stacking prev…
We find obstructions to the existence of Einstein metrics of non-negative sectional curvature on a smooth closed simply connected manifold of any dimension. The results are achieved by combining the classical Morse theory of the loop space with a new upper bound for the topological entropy of the geodesic flow in terms…
A1GM method improves efficiency in reconstructing missing data using KL divergence.
problem Efficiently reconstructing missing data in matrices.
method Fast non-gradient-based rank-1 NMF using KL divergence.
result A1GM outperforms gradient methods in efficiency with competitive reconstruction errors.
We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare i…
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.
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.