47 citations · 105 across the 21 of their papers we have counts for
21 papers
Quantized Fourier and Polynomial Features for more Expressive Tensor Network Models
Frederiek Wesel, Kim Batselier
In the context of kernel machines, polynomial and Fourier features are commonly used to provide a nonlinear extension to linear models by mapping the data to a higher-dimensional s…
Large-Scale Learning with Fourier Features and Tensor Decompositions
Frederiek Wesel, Kim Batselier
Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of det…
MERACLE: Constructive layer-wise conversion of a Tensor Train into a MERA
Kim Batselier, Andrzej Cichocki, Ngai Wong
In this article two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglem…
Faster Tensor Train Decomposition for Sparse Data
Lingjie Li, Wenjian Yu, Kim Batselier
In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-ran…
Matrix Product Operator Restricted Boltzmann Machines
Cong Chen, Kim Batselier, Ching-Yun Ko +1
A restricted Boltzmann machine (RBM) learns a probability distribution over its input samples and has numerous uses like dimensionality reduction, classification and generative mod…
Deep Compression of Sum-Product Networks on Tensor Networks
Ching-Yun Ko, Cong Chen, Yuke Zhang +2
Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals…
The trouble with tensor ring decompositions
Kim Batselier
The tensor train decomposition decomposes a tensor into a "train" of 3-way tensors that are interconnected through the summation of auxiliary indices. The decomposition is stable,…
Multidimensional Realization Theory and Polynomial System Solving
Philippe Dreesen, Kim Batselier, Bart De Moor
Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of…
A Support Tensor Train Machine
Cong Chen, Kim Batselier, Ching-Yun Ko +1
There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms. An example is the support tensor machine (STM) that utilize…
Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains
Ching-Yun Ko, Kim Batselier, Wenjian Yu +1
We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their…
Tensor network subspace identification of polynomial state space models
Kim Batselier, Ching Yun Ko, Ngai Wong
This article introduces a tensor network subspace algorithm for the identification of specific polynomial state space models. The polynomial nonlinearity in the state space model i…
Matrix output extension of the tensor network Kalman filter with an application in MIMO Volterra system identification
Kim Batselier, Ngai Wong
This article extends the tensor network Kalman filter to matrix outputs with an application in recursive identification of discrete-time nonlinear multiple-input-multiple-output (M…
Computing low-rank approximations of large-scale matrices with the Tensor Network randomized SVD
Kim Batselier, Wenjian Yu, Luca Daniel +1
We propose a new algorithm for the computation of a singular value decomposition (SVD) low-rank approximation of a matrix in the Matrix Product Operator (MPO) format, also called t…
Parallelized Tensor Train Learning of Polynomial Classifiers
Zhongming Chen, Kim Batselier, Johan A. K. Suykens +1
In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polyn…
A Tensor Network Kalman filter with an application in recursive MIMO Volterra system identification
Kim Batselier, Zhongming Chen, Ngai Wong
This article introduces a Tensor Network Kalman filter, which can estimate state vectors that are exponentially large without ever having to explicitly construct them. The Tensor N…
Tensor Computation: A New Framework for High-Dimensional Problems in EDA
Zheng Zhang, Kim Batselier, Haotian Liu +2
Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables.…
Tensor Network alternating linear scheme for MIMO Volterra system identification
Kim Batselier, Zhongming Chen, Ngai Wong
This article introduces two Tensor Network-based iterative algorithms for the identification of high-order discrete-time nonlinear multiple-input multiple-output (MIMO) Volterra sy…
A constructive arbitrary-degree Kronecker product decomposition of tensors
Kim Batselier, Ngai Wong
We propose the tensor Kronecker product singular value decomposition~(TKPSVD) that decomposes a real -way tensor into a linear combination of tensor Kronecker prod…
A QR Algorithm for Symmetric Tensors
Kim Batselier, Ngai Wong
We extend the celebrated QR algorithm for matrices to symmetric tensors. The algorithm, named QR algorithm for symmetric tensors (QRST), exhibits similar properties to its matrix v…
Symmetric Tensor Decomposition by an Iterative Eigendecomposition Algorithm
Kim Batselier, Ngai Wong
We present an iterative algorithm, called the symmetric tensor eigen-rank-one iterative decomposition (STEROID), for decomposing a symmetric tensor into a real linear combination o…
A Constructive Algorithm for Decomposing a Tensor into a Finite Sum of Orthonormal Rank-1 Terms
Kim Batselier, Haotian Liu, Ngai Wong
We propose a constructive algorithm that decomposes an arbitrary real tensor into a finite sum of orthonormal rank-1 outer products. The algorithm, named TTr1SVD, works by converti…