Related papers: Shape Constrained Tensor Decompositions using Spar…

Seasonal time series exhibit intricate long-term dependencies, posing a significant challenge for accurate future prediction. This paper introduces the Multi-scale Seasonal Decomposition Model (MSSD) for seasonal time-series forecasting.…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…

Learned video compression (LVC) has witnessed remarkable advancements in recent years. Similar as the traditional video coding, LVC inherits motion estimation/compensation, residual coding and other modules, all of which are implemented…

In this paper, we define a semi-tensor product for third-order tensors. Based on this definition, we present a new type of tensor decomposition strategy and give the specific algorithm. This decomposition strategy actually generalizes the…

Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…

Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To…

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…

Tensor data with rich structural information becomes increasingly important in process modeling, monitoring, and diagnosis. Here structural information is referred to structural properties such as sparsity, smoothness, low-rank, and…

There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…

We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the…

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary…

We present a new computational approach to approximating a large, noisy data table by a low-rank matrix with sparse singular vectors. The approximation is obtained from thresholded subspace iterations that produce the singular vectors…

In scientific fields such as quantum computing, physics, chemistry, and machine learning, high dimensional data are typically represented using sparse tensors. Tensor contraction is a popular operation on tensors to exploit meaning or alter…

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this…

This work considers the problem of computing the canonical polyadic decomposition (CPD) of large tensors. Prior works mostly leverage data sparsity to handle this problem, which is not suitable for handling dense tensors that often arise in…

Solving large-scale multistage stochastic programming (MSP) problems poses a significant challenge as commonly used stagewise decomposition algorithms, including stochastic dual dynamic programming (SDDP), face growing time complexity as…

Markov Decision Process (MDP) is the underlying model for optimal planning for decision-theoretic agents in stochastic environments. Although much research focuses on solving MDP problems both in tabular form or using factored…

Sparse Tucker Decomposition (STD) algorithms learn a core tensor and a group of factor matrices to obtain an optimal low-rank representation feature for the \underline{H}igh-\underline{O}rder, \underline{H}igh-\underline{D}imension, and…