Bayesian tensor train method recovers streaming data with high accuracy.
problem Recovering high-order, incomplete, and noisy streaming data.
method Bayesian tensor train decomposition using streaming variational Bayes method.
result The proposed SPTT algorithm excels in recovering streaming data compared to state-of-the-art methods.
Paper detects and mitigates concept drift in streaming tensor decompositions.
problem Variability of latent concepts over time in dynamic data streams.
method SeekAndDestroy algorithm for detecting and mitigating concept drift.
result SeekAndDestroy effectively detects and mitigates concept drift in streaming tensor decompositions.
Efficiently factorize tensors in streaming data with coreset selection.
problem Efficiently factorize tensors in streaming data.
method Online filtering and kernelization techniques to select a coreset of vectors.
result CP decomposition of coreset approximates full data tensor decomposition.
Paper improves tensor approximation for streaming data.
problem Challenges in finding accurate low-tubal-rank tensor approximations in streaming settings.
method Extends Frequent Directions for efficient low-tubal-rank tensor approximation.
result The new algorithm achieves arbitrarily small approximation error with linear sketch size growth.
SPIDER uses deep neural networks for streaming tensor factorization.
problem Lack of effective approach for deep tensor factorization of streaming data.
method Bayesian neural networks with spike-and-slab prior, Taylor expansions, moment matching, and EPI framework.
result Effective incremental updates for latent factors and NN weights.
Online tensor subspace tracking algorithm for incomplete data.
problem Online subspace tracking of partially observed high-dimensional data.
method OLSTEC algorithm based on CP decomposition and recursive least squares.
result OLSTEC outperforms state-of-the-art algorithms in convergence rate.
New algorithm learns interpretable CP-basis from streaming tensor data under Markovian constraints.
problem Learning interpretable CP-basis from streaming tensor data under Markovian constraints.
method Online Tensor Factorization (OTF) with CANDECOMP/PARAFAC (CP) decomposition, proving convergence to stationary points.
result Algorithm converges almost surely to stationary points of the objective function under Markovian data generation.
Bayesian model identifies outliers and determines tensor rank in streaming data.
problem Outliers and over-fitting in streaming tensor factorization.
method Variational Bayesian Inference for robust tensor rank determination and outlier identification.
result Model accurately identifies sparse outliers and determines tensor rank.
Detects synchronized behavior in streaming data.
problem Tracking synchronized behavior in time-stamped tuples.
method AugSplicing algorithm for streaming dense block detection.
result Effective and robust in detecting anomalous behavior.
Method decomposes streaming data into sparse and low-rank components from compressive measurements.
problem Online decomposing compressive streaming data efficiently.
method Solves n-ℓ1 cluster-weighted minimization to decompose sparse and low-rank components. result Outperforms existing methods for numerical and video data.
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.
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for {\em real-time} processing of streaming data pose major challenge…
Efficiently decomposes large tensors using stochastic gradients.
problem Efficiently decomposing large tensors for multiway data analysis.
method Stochastic gradients computed via MTTKRP kernel for efficient computation.
result Advantages and scalability demonstrated for large-scale problems.
Tensor decomposition recovers Gaussian mixtures from moments.
problem Recovering Gaussian mixture models from datasets.
method Symmetric tensor decomposition of moment tensors built from empirical moments.
result Identifiable tensors with interpolation degree less than half their order.
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.
NA0CT2 improves tensor regression predictions with ℓ0 regularization.
problem Improving tensor regression predictions with structural information.
method Noise-Augmented ℓ0 regularization on Tucker decomposition. result Achieves exact ℓ0 regularization on core tensor in linear and generalized linear tensor regression. To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictiona…
Paper bounds tensor decomposition's RLCT, aiding Bayesian inference.
problem Unclear mathematical property of tensor decomposition.
method Algebraic geometrical method for upper bound derivation.
result Upper bound of real log canonical threshold (RLCT) derived.
Tensor decomposition improves robot control by modeling inverse dynamics.
problem Accurate modeling of inverse dynamics for robot control.
method Tensor decomposition of sparse tensors to approximate non-linear functions.
result Superior performance compared to state-of-the-art methods.
The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.
problem Understanding the training dynamics of gradient flow on tensor decomposition.
method Empirical observation and mathematical proof of gradient flow dynamics for orthogonally decomposable tensors.
result Gradient flow dynamics for orthogonally decomposable tensors follows a tensor deflation process, recovering all tensor components.
Paper tackles anomaly detection in e-commerce using Bayesian semi-supervised tensor decomposition.
problem Detecting anomalies in seller-reviewer data in e-commerce.
method Bayesian semi-supervised tensor decomposition with Polya-Gamma data augmentation and partial natural gradient learning.
result Semi-supervised approach outperforms state-of-the-art unsupervised baselines.
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
The paper uses tensor decompositions to improve neural network models for tree data.
problem Encoding structural knowledge from tree-structured data efficiently.
method Introduces new aggregation functions using Canonical and Tensor-Train decompositions.
result Proposed models outperform traditional methods on tree classification tasks.
The paper explores tensor decompositions in deep learning models.
problem Compressing parameter space and creating richer representations.
method Tensor decompositions applied to deep learning models.
result Tensor methods can yield richer adaptive representations of complex data.
New algorithms solve tensor problems with random components using SDP.
problem Exact tensor nuclear norm, decomposition, and completion for random tensors.
method Degree-4 Sum of Squares (SOS) semidefinite programs.
result Exact solutions for tensor nuclear norm, decomposition, and completion with random asymmetric components.
VecHGrad solves complex tensor decomposition problems more accurately and efficiently.
problem Complex tensor decomposition with multiple matrices and diagonal tensors.
method VecHGrad algorithm using gradient, Hessian-vector product, and adaptive line search.
result VecHGrad converges faster and more accurately than existing methods.
SaMbaTen efficiently maintains tensor decompositions for growing datasets.
problem Maintaining tensor decompositions for dynamic, growing datasets.
method Sampling-based batch incremental tensor decomposition algorithm.
result SaMbaTen achieves comparable accuracy to state-of-the-art techniques but is significantly faster and scalable.
A new algorithm speeds up CP decomposition for large tensors.
problem Efficiently processing large-scale tensors in real-time.
method Randomized online CP decomposition (ROCP) algorithm.
result ROCP reduces computing time and memory usage significantly.
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.
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.
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.
Scalable and robust TR decomposition for large-scale data with missing entries and outliers.
problem Handling large-scale tensor data with missing entries and outliers.
method Auto-weighted steepest descent method for missing entries and outliers identification, FGMC and RStS strategies.
result Outperforms existing TR decomposition methods in the presence of outliers and runs faster than robust tensor completion algorithms.
MARS automatically selects tensor decomposition ranks, improving performance in neural network tasks.
problem Determining optimal decomposition ranks in tensor decompositions.
method MARS uses binary masks to learn optimal tensor structure during training via relaxed MAP estimation.
result MARS achieves better results than previous methods in various tasks.
Develops SymGCP for tensor decompositions with general symmetry.
problem Handling symmetry in tensor decompositions for better model accuracy.
method Introduces SymGCP, a generalized CP decomposition that accounts for any subset of tensor modes' symmetry.
result SymGCP enables efficient and scalable tensor decomposition with improved model robustness and accuracy.
Paper addresses statistical efficiency and scalability in tensor train decomposition.
problem Statistical inefficiency and scalability issues in tensor train decomposition.
method Introduces a convex relaxation and alternating optimization method with randomization.
result Derives error bounds and demonstrates method's performance on real data.
Two methods preserve tensor structure for reduced dimensionality in tensor regression.
problem Reducing dimensionality of tensor predictors for improved interpretation and accuracy.
method Developed two tensor dimension reduction methods using Tucker and CP decompositions.
result Substantial improvement in accuracy over existing methods in simulations and applications.
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
A novel approach to improve knowledge base completion using tensor decomposition.
problem Knowledge Base Completion (KBC) as a tensor completion problem.
method Canonical Tensor Decomposition (CP) with novel regularizers and reformulation.
result Improved KBC results using CP decomposition and ComplEx model.
The paper formalizes incidence tensors and their decomposition for geometric deep learning.
problem Representing structured data like graphs and simplicial complexes.
method Formalizes incidence tensors, analyzes their structure, and presents equivariant networks.
result Incidence tensors decompose into invariant subsets, leading to efficient linear map implementations.
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.
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. TATD predicts missing entries in time-evolving tensors by exploiting temporal dependency and sparsity.
problem Predict missing entries in time-evolving tensors with temporal dependency and sparsity issues.
method TATD (Time-Aware Tensor Decomposition) integrates temporal dependency and time-varying sparsity through a smoothing regularization with Gaussian kernel and alternating optimization.
result TATD achieves state-of-the-art accuracy for decomposing temporal tensors.
This work improves tensor decomposition methods, especially for large datasets.
problem Lack of efficient methods for estimating Tucker decompositions.
method Applies Johnson-Lindenstrauss type guarantees to Tucker decompositions with random embeddings.
result Effective dimension reduction with minimal error for large tensors.
Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are un…
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.
Efficient tensor completion method using rank minimization on TR latent space.
problem High model sensitivity and exponential model possibilities in TR decomposition.
method Nuclear norm regularization on latent TR factors, ADMM scheme.
result Superior performance and efficiency compared to state-of-the-art algorithms.
Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.
problem Identify nonnegative Tucker decomposition factors uniquely.
method Adapting NMF identifiability results, derive procedures using tensor unfoldings or slices.
result Nonnegative Tucker decomposition factors are identifiable under certain sparsity conditions.
New tensor network decompositions improve CNN performance.
problem Limited exploration of tensor network decompositions for CNNs.
method Characterized a new class of CNN modules and experimentally compared various decompositions.
result Some nonlinear decompositions outperform existing ones in terms of accuracy and efficiency.