相关论文: DPar2: Fast and Scalable PARAFAC2 Decomposition fo…
A fast full-wave simulation technique is presented for the analysis of large irregular planar arrays of identical 3-D metallic antennas. The solution method relies on the Macro Basis Functions (MBF) approach and an interpolatory technique…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
This paper introduces a novel general-purpose algorithm for Pauli decomposition that employs matrix slicing and addition rather than expensive matrix multiplication, significantly accelerating the decomposition of multi-qubit matrices. In a…
The robust PCA of covariance matrices plays an essential role when isolating key explanatory features. The currently available methods for performing such a low-rank plus sparse decomposition are matrix specific, meaning, those algorithms…
Ultrasound Elastography aims to determine the mechanical properties of the tissue by monitoring tissue deformation due to internal or external forces. Tissue deformations are estimated from ultrasound radio frequency (RF) signals and are…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
In this work, we develop deterministic and random sketching-based algorithms for two types of tensor interpolative decompositions (ID): the core interpolative decomposition (CoreID, also known as the structure-preserving HOSVD) and the…
Tensor operations are surging as the computational building blocks for a variety of scientific simulations and the development of high-performance kernels for such operations is known to be a challenging task. While for operations on one-…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics.…
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…
We consider the line spectral estimation problem which aims to recover a mixture of complex sinusoids from a small number of randomly observed time domain samples. Compressed sensing methods formulates line spectral estimation as a sparse…
Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
In this paper, we develop software for decomposing sparse tensors that is portable to and performant on a variety of multicore, manycore, and GPU computing architectures. The result is a single code whose performance matches optimized…
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…
The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…