23 papers · ranked by Valyu relevance
Petr Tichavský, Anh Huy Phan, Andrzej Cichocki
Tensor diagonalization means transforming a given tensor to an exactly or nearly diagonal form through multiplying the tensor by non-orthogonal invertible matrices along selected dimensions of the tensor. It is generalization of approximate joint diagonalization (AJD) of a set of matrices. In particular, we derive (1)…
Erna Begović, Ana Boksic
In this paper we develop a Jacobi-type algorithm for the approximate diagonalization of tensors of order d ≥ 3 via tensor trace maximization. For a general tensor this is an alternating least squares algorithm and the rotation matrices are chosen in each mode one-by-one to maximize the tensor trace. On the other hand…
Erna Begović
For a general third-order tensor A ∈ R n×n×n the paper studies two closely related problems, an SVD-like tensor decomposition and an (approximate) tensor diagonalization. We develop a Jacobi-type algorithm that works on 2 × 2 × 2 subtensors and, in each iteration, maximizes the sum of squares of its diagonal entries.…
Jianze Li, Konstantin Usevich, Pierre Comon
In this paper, we consider a family of Jacobi-type algorithms for simultaneous orthogonal diagonalization problem of symmetric tensors. For the Jacobi-based algorithm of [SIAM J. Matrix Anal. Appl., 2(34):651–672, 2013], we prove its global convergence for simultaneous orthogonal diagonalization of symmetric matrices…
Majid Janzamin, Rong Ge, Jean Kossaifi, Anima Anandkumar
| 1 | | Introduction | | | | | 3 | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | 1.1 | Method of Moments and Moment Tensors . | | . | . | . | 5 | . | . | . | . | | . | | | 1.2 | Warm-up: Learning a Simple Model with Tensors | | | | | 6 | . | . | . | . | | . | | |…
Yun Miao, Liqun Qi, Yimin Wei
In this paper, we investigate the tensor similar relationship and propose the T-Jordan canonical form and its properties. The concept of T-minimal polynomial and T-characteristic polynomial are proposed. As a special case, we present properties when two tensors commutes based on the tensor T-product. We prove that the…
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…
Andrew E Teschendorff, Jing Han, Dirk S Paul, Joni Virta + 1 more
There is an increased need for integrative analyses of multi-omic data. Although several algorithms for analysing multi-omic data exist, no study has yet performed a detailed comparison of these methods in biologically relevant contexts. Here we benchmark a novel tensorial independent component analysis (tICA)…
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…
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…
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…
Yann Garniron, Thomas Applencourt, Kevin Gasperich, Anouar Benali + 15 more
Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multi-reference second-order perturbation theory (PT2). The determinant-driven…
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…
Christian J. Burnham, Niall J. English
We present a novel derivation of the multipole interaction (energies, forces and fields) in spherical harmonics, which results in an expression that is able to exactly reproduce the results of earlier Cartesian formulations. Our method follows the derivations of Smith (W. Smith, CCP5 Newsletter 1998, 46, 18.) and Lin…
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…
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…
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…
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…
Suleiman A. Khan, Muhammad Ammad-ud-din
With recent advancements in measurement technologies, many multi-way and tensor datasets have started to emerge. Exploiting the natural tensor structure in the data has been shown to be advantageous for both explorative and predictive studies in several application areas of bioinformatics and computational biology.…
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…
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
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…
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…