Study multiplicative tensors on Lie groupoids using infinitesimal data.
problem Understanding tensors on Lie groupoids with groupoid structure.
method Complete description through infinitesimal data.
result Unified description of multiplicative forms, multivector fields, and holomorphic structures.
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…
Proposes BHT-ARIMA for forecasting multiple short time series.
problem Forecasting multiple short time series with mutual correlations.
method Block Hankel tensors, Tucker decomposition, generalized tensor ARIMA.
result Improves forecasting accuracy and reduces computational cost.
Graphical notation simplifies tensor operations and decompositions.
problem Complex tensor operations are difficult to understand and represent.
method Introduces graphical notation to represent tensor operations.
result Simplified representation of tensor operations and decompositions.
MCCA extracts shared structure from multiple tensor datasets.
problem Extracting shared structure from multiple tensor datasets.
method Multilinear common component analysis (MCCA) using Kronecker products of mode-wise covariance matrices.
result MCCA constructs a common basis that retains information from multiple tensor datasets.
Study of curvature tensor algebra with nonstandard multiplications.
problem Understanding curvature tensor algebra structures.
method Investigates orthogonally invariant commutative nonassociative multiplications on curvature tensors.
result Characterizes curvature tensor algebras in low dimensions and proves their simplicity in higher dimensions.
In this work, we consider Corporate Governance (CG) ties among companies from a multiple network perspective. Such a structure naturally arises from the close interrelation between the Shareholding Network (SH) and the Board of Directors network (BD). In order to capture the simultaneous effects of both networks on CG,…
NNEinFact fits any nonnegative tensor factorization quickly and accurately.
problem Limited user-friendly tools for fitting tailored nonnegative tensor factorizations.
method NNEinFact is an einsum-based multiplicative update algorithm that fits any nonnegative tensor factorization.
result NNEinFact converges to a stationary point of the loss, supports missing data, and fits tensors with hundreds of millions of entries in seconds.
A new tensor decomposition method that minimizes KL divergence.
problem Tensor reconstruction accuracy.
method Legendre decomposition, based on information geometry.
result Minimizes KL divergence and improves tensor reconstruction accuracy.
Bayesian method for imputing missing values in tensor data.
problem Missing data in multi-way arrays (tensors) in biomedical studies.
method Flexible Bayesian framework with conjugate priors for CP factorization.
result Accurately captures uncertainty in microbiome profiles at missing timepoints.
Study proves conditions for Einstein-type manifolds with specific Weyl tensor properties.
problem Conditions for Einstein-type manifolds with specific Weyl tensor properties.
method Proved conditions for Einstein-type manifolds with fourth-order divergence-free Weyl tensor and zero radial Weyl curvature.
result Proved that a complete Einstein-type manifold with specific Weyl tensor properties is locally a warped product.
A Matlab toolbox for tensor operations based on t-product.
problem Extending matrix operations to tensors.
method Developed a Matlab toolbox implementing tensor operations based on t-product.
result Implemented several tensor operations including SVD, spectral norm, and nuclear norm.
The paper classifies Kähler manifolds with specific Killing tensors.
problem Classifying Kähler manifolds with certain Killing tensors.
method Analyzing manifolds with J-invariant Killing tensors having specific eigenvalues and eigendistributions.
result Classification of compact, simply connected Kähler manifolds with specified properties.
Paper predicts spatial variation data from few samples using tensor methods.
problem Predict spatial variation data from limited samples in high-dimensional data.
method Bayesian tensor completion exploiting hidden low-rank property.
result Predicts spatial variation data efficiently from few samples.
Develops a tensor decomposition method with side information.
problem Identifying the relationship between a high-dimensional tensor and side information.
method Supervised tensor decomposition incorporating multiple feature matrices.
result Captures effective dimension reduction of the data tensor in feature space.
A new method for analyzing multi-source, multi-way data reduces dimensionality and reveals shared and individual structures.
problem Analyzing multi-source, multi-way data from different high-throughput technologies.
method Multiple Linked Tensor Factorization (MULTIFAC) extending CP decomposition with L2 penalties and EM algorithm for incomplete data.
result MULTIFAC approximates underlying signal, identifies shared and unshared structures, and imputes missing data.
New algorithm detects tensor dependence structure alterations efficiently.
problem Detecting alterations in tensor dependence structures.
method Tensor-normal distributions, decorrelation, centralization, SERA (Sparsity-Exploited Reranking Algorithm).
result The proposed SERA algorithm controls false discovery rates effectively.
Paper proposes C-STM for multimodal neuroimaging data classification.
problem Multimodal neuroimaging data fusion for better classification.
method Coupled Support Tensor Machine (C-STM) using latent factors from ACMTF.
result C-STM achieves better classification performance than single-mode classifiers.
New hierarchical tensor decomposition model for complex data.
problem Lack of natural generalization of hierarchical NMF to tensors.
method Proposes a new hierarchical nonnegative tensor decomposition (HNTF) model.
result Model more naturally illuminates topic hierarchy.
This paper uses probability tensors for efficient path planning in complex scenarios.
problem Efficient path planning in complex environments with obstacles and multiple goals.
method Probability tensors are used to model agent motion and decision-making, incorporating past and future information.
result The model finds solutions in complex scenarios, demonstrating realistic emergent behaviors.
Bayesian tensor network reduces conditional probability calculation to polynomial time.
problem Exponential cost of calculating conditional probabilities for multiple events.
method Bayesian tensor network (BTN) with polynomial complexity.
result Competitive performance in image recognition with simple tree structures.
A new tensor-based method for multi-view clustering.
problem Lack of explicit correlations between features across multiple views.
method Introduces a tensor-based approach to explore higher-order interactions among multiple views.
result Our MMC algorithm outperforms other methods on real-world datasets.
A new method combines multiple node embeddings using tensor decomposition.
problem Generating accurate node embeddings for complex networks.
method TenSemble2Vec: combines multiple embeddings via tensor decomposition.
result Improves node embeddings by leveraging complementary information from different methods.
A Riemannian manifold is called Weyl homogeneous, if its Weyl tensors at any two points are "the same", up to a positive multiple. A Weyl homogeneous manifold is modeled on a homogeneous space M0, if its Weyl tensor at every point is "the same" as the Weyl tensor of M0, up to a positive multiple. We prove that a …
New tensor approach models global fixed income risks across maturities and economies.
problem Lack of models capturing multi-dimensional data in global fixed income markets.
method Introduces tensor-valued approach to model shared risks among multiple interest rate curves.
result Estimates risk factors decomposable into maturity and country domains, enabling tailored portfolio management.
Paper develops federated tensor factorization for phenotyping without sharing patient data.
problem Deriving phenotypes across multiple hospitals without patient-level data sharing.
method Secure data harmonization and federated computation using ADMM.
result Method generates phenotypes similar to centralized training while respecting privacy.
TEC combines multiple RPSTMs to classify big tensors efficiently.
problem Tensor classification for big data applications.
method Tensor Ensemble Classifier (TEC) using Random Projection-based Support Tensor Machine (RPSTM).
result TEC provides statistically consistent predictions with reduced computational cost.
Weakly Einstein Kähler surfaces are characterized and classified.
problem Characterizing and classifying weakly Einstein Kähler surfaces.
method Several conditions and constructions to characterize and classify weakly Einstein Kähler surfaces.
result Classification of weakly Einstein Kähler surfaces with specific properties and construction of new examples.
New concept of metric Lie algebras helps classify Lie groups.
problem Classifying Lie groups based on conformal Killing symmetric tensors.
method Introducing metric Lie algebras of Killing type and proving conditions for these algebras.
result Conditions for Lie algebras to be of Killing type with respect to any positive definite metric.
The study describes AC^{\perp} manifolds with specific Ricci eigenvalues.
problem Characterizing AC^{\perp} manifolds with particular Ricci tensor properties.
method Analyzes Gray AC^{\perp} manifolds with specific Ricci eigenvalues.
result Identifies Gray AC^{\perp} manifolds with Ricci tensors having two eigenvalues of multiplicity 1 and dim M-1.
SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.
problem High-dimensional and incomplete tensor completion.
method Spectra-Guided Neural Tucker Factorization (SG-NTF) with Spatio-Temporal Co-Gating (STCG).
result Maintains competitive completion accuracy with parameter efficiency.
Unified approach to tensor PCA and related problems using tensor cumulants.
problem Statistical inference on invariant distributions, particularly tensor PCA.
method Definition and analysis of tensor cumulants to unify and extend previous results.
result Unified explanation of hardness and subexponential-time algorithms for tensor PCA.
Paper predicts multiple types of miRNA-disease associations using tensor decomposition.
problem Predicting miRNA-disease associations, especially multi-type ones.
method Represented miRNA-disease-type triplets as a tensor and used Tensor Decomposition methods.
result Tensor Decomposition methods improve a recent baseline by up to 38% in top-1 F1.
In Lorentzian manifolds of any dimension the concept of causal tensors is introduced. Causal tensors have positivity properties analogous to the so-called ``dominant energy condition''. Further, it is shown how to build, from ANY given tensor A, a new tensor quadratic in A and ``positive'', in the sense that it is …
Unified algorithm for tensor decomposition supports multiple loss functions and models.
problem Efficient tensor decomposition for various models and loss functions.
method Hierarchical combination of ADMM and MM for optimization.
result Wide-range applications can be solved by the proposed algorithm.
Study on hypersurfaces with specific curvature conditions.
problem Characterizing hypersurfaces with certain curvature properties.
method Defined and analyzed the Opozda-Verstraelen affine curvature tensor for hypersurfaces.
result Conditions for pseudosymmetry types of hypersurfaces with specific curvature properties.
Bayesian model improves image completion accuracy by automatically learning low rank structure.
problem Improving image completion accuracy with limited data and avoiding overfitting.
method Developed a Bayesian low rank tensor ring model with multiplicative interaction and Student-T distribution for sparse core factors.
result The proposed method outperforms state-of-the-art image completion techniques, especially in recovery accuracy.
Study vacuum static spaces with vanishing Bach and Weyl tensors, proving harmonicity and rigidity results.
problem Characterizing vacuum static spaces with specific tensor properties.
method Analyzing the complete divergence of Bach and Weyl tensors, proving conditions for harmonicity and rigidity.
result Proves the vanishing of complete divergence of Bach and Weyl tensors implies harmonicity of the metric.
GETF efficiently decomposes large-scale Boolean tensors.
problem Efficiently factorizing large-scale Boolean tensors.
method Geometric Expansion for all-order Tensor Factorization (GETF).
result GETF significantly improves reconstruction accuracy and efficiency.
DTCCA learns nonlinear transformations of multi-view data for high-order correlation.
problem Learning complex nonlinear transformations of multiple data views.
method Maximizes high-order canonical correlation by jointly learning transformations of each view using a reformulated tensor decomposition.
result DTCCA efficiently handles high-dimensional and large number of views, overcoming scalability issues.
Bayesian Tensor Ring factorization improved for scalability and handling of discrete data.
problem Scalability issues and handling of discrete data in Bayesian Tensor Ring factorization.
method Proposes a novel Bayesian Tensor Ring model with a nonparametric Multiplicative Gamma Process prior and Pólya-Gamma augmentation for discrete data. Developed efficient Gibbs sampler and online EM algorithm for scalability.
result Significantly improved scalability and handling of discrete data compared to previous methods.
Bayesian model predicts phenotype effects from multi-environmental factors.
problem Predict phenotype effects from multi-environmental trials.
method Bayesian tensor regression with spike-and-slab structure.
result Model outperforms previous methods in simulation and real-world data.
Develops a new tensor PCA method for analyzing multiple network data.
problem Analyzing multiple large networks for dimensionality reduction.
method Semi-Symmetric Tensor PCA (SS-TPCA) for principal components analysis.
result SS-TPCA achieves the same estimation accuracy as classical matrix PCA, with error proportional to the square root of the number of vertices.
This paper introduces tensors and their applications in machine learning.
problem No specific problem stated; focuses on tensor concepts and applications.
method Overview of tensor concepts, decomposition algorithms, and applications.
result Introduction to tensor decompositions and their use in machine learning.
The paper provides recovery guarantees for CNNs with multiple kernels under polynomial sample and computational complexities.
problem Parameter recovery for non-overlapping CNNs with multiple kernels.
method Showed local strong convexity of squared loss for most popular activations, used tensor methods for initialization, and proved convergence of gradient descent.
result Gradient descent following tensor initialization converges to the global optimal with polynomial time complexity.
Study covariant derivatives of eigenfunctions on curved spaces, proving they are scalar multiples of the functions.
problem Understanding covariant derivatives of eigenfunctions on curved spaces.
method Analyzing the Laplace-Beltrami operator on Riemannian manifolds with constant curvature.
result Covariant derivatives of eigenfunctions are scalar multiples of the functions, and these scalars are polynomials in the eigenvalue.
PREMA recovers detailed data from aggregated views.
problem Reconstructing detailed data from aggregated views.
method Low-rank tensor factorization.
result Recovery guarantees under certain conditions.
A new tensor completion method using tensor networks with Tucker wrapper.
problem Low-rank tensor completion in various applications.
method Solving LRTC as a system of nonlinear equations using a two-level alternative least squares method.
result The method converges to the exact solution at a linear rate with high probability.