22 papers · ranked by Valyu relevance
Ren-Cang Li, Li Wang, Mei Yang
This paper is concerned with Partial Tensor Block-Diagonalization of a multiway tensor by orthonormal matrices so that the extracted block-diagonal part optimally represents the tensor. The basic idea is to maximize the block-diagonal part via the tensor's mode-multiplications by orthonormal matrices. For that reason…
Junjun Pan, Michael K. Ng
It is well-known that a complex circulant matrix can be diagonalized by a discrete Fourier matrix with imaginary unit i. The main aim of this paper is to demonstrate that a quaternion circulant matrix cannot be diagonalized by a discrete quaternion Fourier matrix with three imaginary units i, j and k. Instead, a…
Divyanshu Pandey, Adithya Venugopal, H. Leib
In the past few decades, multi-linear algebra also known as tensor algebra has been adapted and employed as a tool for various engineering applications. Recent developments in tensor algebra have indicated that several well-known concepts from Linear Algebra can be extended to a multi-linear setting with the help of a…
Alexandru V. Avram, Kadharbatcha S. Saleem, Peter J. Basser
Diffusion MRI studies with resolutions of a few hundred micrometers have consistently shown that in the cortex water diffusion occurs preferentially along radial and tangential orientations with respect to the cortical surface, in agreement with histology. These dominant orientations do not change significantly even if…
Malihe Nobakht Kooshkghazi, Salman Ahmadi-Asl, Andre L. F. de Almeida
This paper is devoted to studying the application of the block Krylov subspace method for approximation of the truncated tensor SVD (T-SVD). The theoretical results of the proposed randomized approach are presented. Several experimental experiments using synthetics and real-world data are conducted to verify the…
Genjiao Zhou, Shoushi Wang, Jinhong Huang, Kathiravan Srinivasan
Tensor eigenproblems have wide applications in blind source separation, magnetic resonance imaging, and molecular conformation. In this study, we explore an alternating direction method for computing the largest or smallest Z-eigenvalue and corresponding eigenvector of an even-order symmetric tensor. The method…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Alain Franc
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of the entries. The rank of a tensor extends to arrays with more than two entries the…
Bin Qi, Wensheng Zhang, Lei Zhang, Xingwang Li + 3 more
'Kefeng Guo'] The spectrum situation awareness problem in space-air-ground integrated networks (SAGINs) is studied from a tensor-computing perspective. Tensor and tensor computing, including tensor decomposition, tensor completion and tensor eigenvalues, can satisfy the application requirements of SAGINs. Tensors can…
Andor Menczer, Örs Legeza
State Algorithms on AI Accelerators Authors: ['Andor Menczer' 'Örs Legeza'] We introduce novel algorithmic solutions for hybrid CPU-multiGPU tensor network state algorithms utilizing non-Abelian symmetries building on AI-motivated state-of-the-art hardware and software technologies. The presented numerical simulations…
BEN GABRIELSON, HANLU YANG, TRUNG VU, VINCE CALHOUN + 1 more
Generalizations of matrix decompositions to multidimensional arrays, called tensor decompositions, are simple yet powerful methods for analyzing datasets in the form of tensors. These decompositions model a data tensor as a sum of rank-1 tensors, whose factors provide uses for a myriad of applications. Given the…
Tatsuya Yokota
Calculations, and Decompositions Authors: ['Tatsuya Yokota'] | 1 | Introduction | | 3 | | --- | --- | --- | --- | | 2 | Vectors, Matrices and Tensors | | 6 | | | 2.1 | Vectors | 6 | | | 2.2 | Matrices | 6 | | | 2.3 | Tensors | 8 | | | 2.4 | Modes of tensors | 9 | | | 2.5 | Tensor network diagrams | 10 | | 3 | |…
Jiahao Su, Jingling Li, Xiaoyu Liu, Teresa Ranadive + 3 more
'Christopher Coley' 'Tai-Ching Tuan' 'Furong Huang'] We propose a framework of tensorial neural networks (TNNs) extending existing linear layers on low-order tensors to multilinear operations on higher-order tensors. TNNs have three advantages over existing networks: First, TNNs naturally apply to higher-order data…
Authors not listed
We introduce localized active space state interaction singles (LASSIS), a multireference electronic structure method that uses two-step diagonalization to model systems characterized by multiple distinct localized centers of strong electron correlation, with weaker but not negligible electron correlation between the…
Kairong Hong, Yingying Ren, Fengyuan Li, Wentao Mao + 4 more
'Yongbo Li' 'Bing Li' 'Khandaker Noman'] Demand for spare parts, which is triggered by element failure, project schedule and reliability demand, etc., is a kind of sensing data to the aftermarket service of large manufacturing enterprises. Prediction of the demand for spare parts plays a crucial role in inventory…
Junhua Zeng, Yuning Qiu, Yumeng Ma, Andong Wang + 1 more
As a promising data analysis technique, sparse modeling has gained widespread traction in the field of image processing, particularly for image recovery. The matrix rank, served as a measure of data sparsity, quantifies the sparsity within the Kronecker basis representation of a given piece of data in the matrix…
Ethan C. Hung, Enio Hodzic, Zhixin Cyrillus Tan, Aaron S. Meyer
Tensor factorization is a dimensionality reduction method applied to multidimensional arrays. These methods are useful for identifying patterns within a variety of biomedical datasets due to their ability to preserve the organizational structure of experiments and therefore aid in generating meaningful insights.…
Dionysia Kaziki, Andreas K. Engel, Guido Nolte
Cross-bispectral measures provide a rich description of interactions in EEG signals, but their third-order tensor structure poses substantial challenges for interpretation and dimensionality reduction. We introduce a low-rank tensor decomposition framework specifically designed for cross-bispectral EEG data. The model…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…
Suguru Fujita, Yasuaki Karasawa, Ken-ichi Hironaka, Y-h. Taguchi + 1 more
High-throughput omics technologies have enabled the profiling of entire biological systems. For the biological interpretation of such omics data, two analyses, hypothesis- and data-driven analyses including tensor decomposition, have been used. Both analyses have their own advantages and disadvantages and are mutually…
Maxwell Venetos, Mingjian Wen, Kristin Persson
The nuclear magnetic resonance (NMR) chemical shift tensor is a highly sensitive probe of the electronic structure of an atom and furthermore its local structure. Re- cently, machine learning has been applied to NMR in the prediction of isotropic chemi- cal shifts from a structure. Current machine learning models…
Kevin De Azevedo, Florian Buettner
In recent years, the exponential growth of high-dimensional, multi-modal molecular data has created both opportunities and challenges in personalized medicine. While existing approaches like matrix decomposition and neural network-based embeddings have been used to analyze such data, they have limitations in…