We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an inpu…
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48 results for “Decomposition method”
The study examines how different interpolation methods affect the decomposition of life insurance surplus.
problem The impact of different interpolation methods on the decomposition of life insurance surplus.
method The study uses the IASU decomposition method to analyze the effects of different interpolation methods (Lee-Carter and linear) on the surplus decomposition.
result Lee-Carter and linear interpolation yield almost identical decompositions, while constant approximations result in different decompositions.
The Adomian decomposition method is shown to be equivalent to the Taylor series approach.
problem Incorrectly perceived complexity of the Adomian decomposition method.
method Demonstrates the Adomian decomposition method as equivalent to the Taylor series approach.
result The Adomian decomposition method is simpler and more straightforward.
IKD uses eigen-decomposition for nonlinear dimensionality reduction.
problem Lack of sophisticated and nonlinear dimensionality reduction methods.
method Inverse Kernel Decomposition (IKD) based on eigen-decomposition of sample covariance matrix.
result IKD achieves comparable performance to optimization-based methods with faster running speeds.
Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in practice, and no extensive comparisons have been made between available methods. Previo…
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.
New method uses random decompositions for high-dimensional Bayesian optimization.
problem Learning accurate decompositions for high-dimensional black-box functions.
method Data-independent random tree-based decomposition sampling.
result Random decomposition upper-confidence bound algorithm (RDUCB) yields significant empirical gains.
SRMD uses random features for efficient time-frequency analysis.
problem Efficiently analyzing time-series data with low computational cost.
method Sparse Random Mode Decomposition (SRMD) constructs a sparse approximation to the spectrogram.
result SRMD outperforms other methods in signal representation, outlier removal, and mode decomposition.
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.
The aim of this paper is to provide some new tools to aid the study of decomposition complexity, a notion introduced by Guentner, Tessera and Yu. In this paper, three equivalent definitions for decomposition complexity are established. We prove that metric spaces with finite hyperbolic dimension have finite (weak) deco…
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.
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize them, and in the past regularization has mostly been performed using bespoke modif…
New method models matrix time series using tensor CP-decomposition.
problem Modeling matrix time series with reduced complexity.
method One-pass estimation via generalized eigenanalysis and refined projection.
result Component coefficient vectors estimated consistently with certain rates.
This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the occurrence frequency of atoms of the dictionary over the data set. This criterion, wel…
Article presents QR and LQ decomposition algorithms for various matrix sizes and ranks.
problem Solving least squares problems in machine learning and computer vision.
method Developed novel matrix backpropagation algorithms for QR and LQ decompositions of different matrix sizes and ranks.
result Numerical stability and computational efficiency of the proposed methods.
NACT improves tensor regression predictions with regularization.
problem Improving tensor regression predictions with structural information.
method Noise-Augmented regularization on Tucker decomposition.
result Achieves exact regularization on core tensor in linear and generalized linear tensor regression.
We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family …
A new framework for efficient Bayesian network inference.
problem High-dimensional Bayesian networks are hard to infer due to computational scaling.
method Directed convex subgraphs and minimal d-decomposition tree for decomposition, enabling parallel computation.
result The method reduces computational cost and enables parallel computation.
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.
New method solves elliptic equations on manifolds without grids.
problem Solving elliptic equations on complex manifolds.
method Numerical domain decomposition method avoiding global grids.
result Method validated on specific 4D manifolds.
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.
The paper describes handle decompositions and Kirby diagrams for plane algebraic curves.
problem Understanding the topology of the complement of plane algebraic curves.
method Using braid monodromy to refine handle decompositions and Kirby diagrams.
result Explicit handle decompositions and Kirby diagrams for plane algebraic curves are provided.
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.
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.
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.
We present an approach for penalized tensor decomposition (PTD) that estimates smoothly varying latent factors in multi-way data. This generalizes existing work on sparse tensor decomposition and penalized matrix decompositions, in a manner parallel to the generalized lasso for regression and smoothing problems. Our ap…
Efficient algorithm for Hadamard decomposition of matrices.
problem Decomposing matrices into low-rank factors efficiently.
method Alternating optimization with SVD-inspired initialization and momentum.
result Significantly improved performance compared to existing methods.
This study proposes methods for multi-step-ahead stock price prediction using decomposition and neural networks.
problem Inaccurate one-step-ahead forecasting limits stock market decision-making.
method Two novel methods: DCT-MFRFNN and VMD-MFRFNN.
result VMD-MFRFNN outperforms other methods in multi-step-ahead stock price prediction.
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…
D-CDLF: Decomposition of Common and Distinctive Latent Factors for Multi-view High-dimensional Datastat.ML
Proposes D-CDLF for multi-view data decomposition.
problem Uncorrelatedness between common and distinctive latent factors.
method Decomposes data into common, distinctive, and noise components.
result Effective uncorrelatedness between distinctive latent factors from different views.
As a type of pseudoinverse learning, extreme learning machine (ELM) is able to achieve high performances in a rapid pace on benchmark datasets. However, when it is applied to real life large data, decline related to low-convergence of singular value decomposition (SVD) method occurs. Our study aims to resolve this issu…
The paper studies batch decompositions of random datasets with probabilistic similarity constraints.
problem Understanding how to optimally split large datasets into batches for better model learning.
method Assumes independent data points from a space, defines similarity, and uses probabilistic and martingale methods to find bounds on batch sizes.
result Demonstrates an inherent tradeoff between relaxing similarity constraints and batch size, and provides bounds for maximum similarity subsets.
MicroRNAs (miRNAs) play crucial roles in multifarious biological processes associated with human diseases. Identifying potential miRNA-disease associations contributes to understanding the molecular mechanisms of miRNA-related diseases. Most of the existing computational methods mainly focus on predicting whether a miR…
Sparse Tucker Decomposition and Graph Regularization for High-Dimensional Time Series Forecastingmath.ST
Sparse Tucker decomposition with graph regularization improves time series forecasting accuracy.
problem High-dimensional time series forecasting with over-parameterization issue.
method Sparse Tucker decomposition and graph regularization for tensor-based model.
result Non-asymptotic error bound and superior performance in numerical experiments.
Shape Constrained Tensor Decompositions using Sparse Representations in Over-Complete Librariesstat.ML
We consider -way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is based upon the CANDECOMP/PARAFAC (CP) decomposition which produces -rank appr…
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlik…
Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.
problem Understanding and modeling nonlinear dynamical systems.
method Trains neural networks to minimize forecast error based on spectral decomposition in the lifted space.
result Demonstrates effectiveness in eigenvalue estimation and forecast performance.
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically…
High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data…
Tensor decompositions are powerful tools for large data analytics as they jointly model multiple aspects of data into one framework and enable the discovery of the latent structures and higher-order correlations within the data. One of the most widely studied and used decompositions, especially in data mining and machi…
We provide a unified view of additive explanations for dependent inputs.
problem Challenges in obtaining a tractable representation and estimating the decomposition for dependent inputs.
method Combining Hilbert space methods with generalized functional ANOVA, we build an explicit decomposition Riesz Basis.
result Proposed a simple yet powerful algorithm to estimate the decomposition from data.
For n-bridge decompositions of links in S^3, we propose a practical method to ensure that the Hempel distance is at least two.
Paper tackles tensor decomposition for unaligned observations using RKHS and novel loss functions.
problem Tackles tensor decomposition for unaligned observations.
method Uses functions in RKHS to represent mode with unaligned observations, introduces versatile loss function, proposes optimization algorithm and stochastic gradient method.
result Demonstrates improved tensor decomposition efficiency and effectiveness with synthetic and real data.
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated using regression techniques. We propose as regression method a tensor decompositi…
Proposes a Gaussian process for Koopman mode decomposition.
problem Estimating Koopman mode decomposition quantities and latent variables.
method Unsupervised Gaussian process for simultaneous estimation.
result Efficient parameter estimation through low-rank approximations.
Review of algorithms for linear system approximations.
problem Linear approximation of high-dimensional dynamical systems.
method State-of-the-art algorithms for low-rank DMD.
result Provides additional details for comprehensive understanding.
New DDMs use neural networks for solving equations on manifold shapes.
problem Solving equations on complex, high-dimensional shapes.
method Physics-informed neural networks combined with domain decomposition methods.
result Validated methods work well on various shapes in high dimensions.