25 papers · ranked by Valyu relevance
Andrzej Cichocki, Namgil Lee, Ivan Oseledets, Anh Huy Phan + 2 more
'Qibin Zhao' 'Danilo P. Mandic'] Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi–modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore timely and valuable for the multidisciplinary…
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…
Alhussein Fawzi, Matej Balog, Aja Huang, Thomas Hubert + 9 more
'Bernardino Romera-Paredes' 'Mohammadamin Barekatain' 'Alexander Novikov' 'Francisco J. R. Ruiz' 'Julian Schrittwieser' 'Grzegorz Swirszcz' 'David Silver' 'Demis Hassabis' 'Pushmeet Kohli'] Improving the efficiency of algorithms for fundamental computations can have a widespread impact, as it can affect the overall…
Davide Bacciu, Danilo P. Mandic
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way data analysis, we consider the use of tensor decompositions in compressing the…
Beheshteh T. Rakhshan, Guillaume Rabusseau
High-dimensional data arise naturally in many areas of science and engineering, including machine learning, signal processing, computational physics, and statistics. Such data are often represented as tensors, multi-dimensional generalizations of matrices. While tensors provide a natural representation for multi-modal…
Sangjun Son, Yong-chan Park, Minyong Cho, U. Kang + 1 more
How can we accurately and efficiently decompose a tensor stream? Tensor decomposition is a crucial task in a wide range of applications and plays a significant role in latent feature extraction and estimation of unobserved entries of data. The problem of efficiently decomposing tensor streams has been of great interest…
Hannah Korevaar, C. Jessica Metcalf, Bryan T. Grenfell, Robert Freckleton
'Robert Freckleton'] Title: Abstract 1. Many demographic and ecological processes generate seasonal and other periodicities. Seasonality in infectious disease transmission can result from climatic forces such as temperature and humidity; variation in contact rates as a result of migration or school calendar; or…
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 | |…
Alex H. Williams
Recordings from large neural populations are becoming an increasingly popular and accessible method in experimental neuroscience. While the activity of individual neurons is often too stochastic to interrogate circuit function on a moment-by-moment basis, multi-neuronal recordings enable us to do so by pooling…
Mostafa Elhoushi, Ye Tian, Zihao Chen, Farhan Shafiq + 1 more
Tensor decomposition is one of the well-known approaches to reduce the latency time and number of parameters of a pretrained convolutional neural network (CNN) model. However, in this paper, we propose an approach to use tensor decomposition to reduce training time of training a model from scratch. In our approach, we…
Claudio Turchetti
The aim of this paper is to present a mathematical framework for tensor PCA. The proposed approach is able to overcome the limitations of previous methods that extract a low dimensional subspace by iteratively solving an optimization problem. The core of the proposed approach is the derivation of a basis in tensor…
Ken Takiyama, Hikaru Yokoyama, Naotsugu Kaneko, Kimitaka Nakazawa
How the central nervous system (CNS) controls many joints and muscles is a fundamental question in motor neuroscience and related research areas. An attractive hypothesis is the module hypothesis: the CNS controls groups of joints or muscles (i.e., spatial modules) while providing time-varying motor commands (i.e.…
Claudio Turchetti
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a lowdimensional subspace by solving an optimization problem and assuming the…
Adam S. Jermyn
Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is actually set not by the rank but by the mutual information amongst the variables…
Wei Fang, Dongxu Wei, Ran Zhang
The rapid development of sensor technology gives rise to the emergence of huge amounts of tensor (i.e., multi-dimensional array) data. For various reasons such as sensor failures and communication loss, the tensor data may be corrupted by not only small noises but also gross corruptions. This paper studies the Stable…
Farzane Yahyanejad
This study advances our understanding of inter- and intra-pathways higher order signaling in the cellular system and it leads to new discovery of multiple intracellular structures in signal transduction pathways in yeast Saccharomyces. We present a new tensor decomposition algorithm in reconstructing the pathways based…
Christopher C. Gill, Jonathan Marchini
Disease etiology may be better understood through the study of gene expression in four dimensional (4D) experiments that consist of measurements on multiple individuals, genes, tissues and under multiple conditions or through time. We have developed a sparse Bayesian four dimensional tensor decomposition method aimed…
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…
Dazhou Li, Bo Zhou, Chuan Lin, Jian Gao + 3 more
'Qichun Zhang'] Background During the COVID-19 pandemic, the accurate forecasting and profiling of the supply of fresh commodities in urban supermarket chains may help the city government make better economic decisions, support activities of daily living, and optimize transportation to support social governance. In…
Authors not listed
Elucidating Collective Variables (CVs) for biomolecular dynamics is crucial for understanding numerous biological processes. By leveraging the tensor-train data structure, a multilinear version of the AMUSE (Algorithm for Multiple Unknown Signals) algorithm for Koopman approximation (AMUSEt) was recently developed to…
Xu Kong, Jicheng Li, Xiaolong Wang
Using the orthogonal rank of the tensor, a new estimation method for the upper bounds on the nuclear norms is presented and some new tight upper bounds on the nuclear norms are established. Taking into account the structure information of the tensor, an important factor affecting the upper bounds is discussed and some…
Angela F Harper, Simone S Köcher, Karsten Reuter, Christoph Scheurer
Machine learning (ML) surrogate modeling is a powerful approach to reduce the computational cost of first-principles calculations. While well established for the prediction of scalar observables like energetics or band gaps, performance metrics for the learning of tensor-based observables have not yet been formalized.…
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…
Ty Balduf, Marco Caricato
Optical rotation (OR) is a sensitive electronic property for which there are no clear structureproperty relations. We proposed an approach to decompose the OR tensor in terms of one-electron transitions between occupied-virtual molecular orbital pairs, called the Sia method. This method allows to select the transitions…
Charles Eads
This report describes and illustrates a set of automatable multicomponent exponential relaxation analysis protocols that are model-agnostic and suited to extracting information under circumstances when little prior knowledge about the underlying system is used. Methods are illustrated and mathematical and physical…