89 citations · 289 across the 16 of their papers we have counts for
18 papers
Double Nonstationarity: Blind Extraction of Independent Nonstationary Vector/Component from Nonstationary Mixtures -- Algorithms
Zbyněk Koldovský, Václav Kautský, Petr Tichavský
In this article, nonstationary mixing and source models are combined for developing new fast and accurate algorithms for Independent Component or Vector Extraction (ICE/IVE), one o…
How to Train Unstable Looped Tensor Network
Anh-Huy Phan, Konstantin Sobolev, Dmitry Ermilov +4
A rising problem in the compression of Deep Neural Networks is how to reduce the number of parameters in convolutional kernels and the complexity of these layers by low-rank tensor…
Characterization of Decomposition of Matrix Multiplication Tensors
Petr Tichavsky
In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decom…
Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network
Anh-Huy Phan, Konstantin Sobolev, Konstantin Sozykin +6
Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kerne…
Dynamic Independent Component/Vector Analysis: Time-Variant Linear Mixtures Separable by Time-Invariant Beamformers
Zbyněk Koldovský, Václav Kautský, Petr Tichavský
A novel extension of Independent Component and Independent Vector Analysis for blind extraction/separation of one or several sources from time-varying mixtures is proposed. The mix…
Cramér-Rao Bounds for Complex-Valued Independent Component Extraction: Determined and Piecewise Determined Mixing Models
Václav Kautský, Zbyněk Koldovský, Petr Tichavský +1
This paper presents Cramér-Rao Lower Bound (CRLB) for the complex-valued Blind Source Extraction (BSE) problem based on the assumption that the target signal is independent of the…
Gradient Algorithms for Complex Non-Gaussian Independent Component/Vector Extraction, Question of Convergence
Zbyněk Koldovský, Petr Tichavský
We revise the problem of extracting one independent component from an instantaneous linear mixture of signals. The mixing matrix is parameterized by two vectors, one column of the…
Error Preserving Correction for CPD and Bounded-Norm CPD
Anh-Huy Phan, Petr Tichavský, Andrzej Cichocki
In CANDECOMP/PARAFAC tensor decomposition, degeneracy often occurs in some difficult scenarios, e.g., when the rank exceeds the tensor dimension, or when the loading components are…
Best Rank-One Tensor Approximation and Parallel Update Algorithm for CPD
Anh-Huy Phan, Petr Tichavský, Andrzej Cichocki
A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates…
Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition
Anh-Huy Phan, Andrzej Cichocki, Andre Uschmajew +3
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general ten…
Numerical CP Decomposition of Some Difficult Tensors
Petr Tichavsky, Anh Huy Phan, Andrzej Cichocki
In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to…
Tensor Deflation for CANDECOMP/PARAFAC. Part 3: Rank Splitting
Anh-Huy Phan, Petr Tichavsky, Andrzej Cichocki
CANDECOMP/PARAFAC (CPD) approximates multiway data by sum of rank-1 tensors. Our recent study has presented a method to rank-1 tensor deflation, i.e. sequential extraction of the r…
On tensor rank of conditional probability tables in Bayesian networks
Jiří Vomlel, Petr Tichavský
A difficult task in modeling with Bayesian networks is the elicitation of numerical parameters of Bayesian networks. A large number of parameters is needed to specify a conditional…
Non-Orthogonal Tensor Diagonalization
Petr Tichavsky, 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 d…
CANDECOMP/PARAFAC Decomposition of High-order Tensors Through Tensor Reshaping
Anh Huy Phan, Petr Tichavsky, Andrzej Cichocki
In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unf…
Cramer-Rao-Induced Bounds for CANDECOMP/PARAFAC tensor decomposition
Petr Tichavsky, Anh Huy Phan, Zbynek Koldovsky
This paper presents a Cramer-Rao lower bound (CRLB) on the variance of unbiased estimates of factor matrices in Canonical Polyadic (CP) or CANDECOMP/PARAFAC (CP) decompositions of…
Low Complexity Damped Gauss-Newton Algorithms for CANDECOMP/PARAFAC
Anh Huy Phan, Petr Tichavský, Andrzej Cichocki
The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of collinearity of factors and different magnitudes of factors; neverthel…
On Fast Computation of Gradients for CANDECOMP/PARAFAC Algorithms
Anh Huy Phan, Petr Tichavský, Andrzej Cichocki
Product between mode- unfolding $\bY_{(n)}$ of an -D tensor $\tY$ and Khatri-Rao products of factor matrices $\bA^{(m)}$, exists in algo…