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Danilo P Mandic - One of the best experts on this subject based on the ideXlab platform.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
IEEE Transactions on Neural Networks, 2020Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadiasl, Danilo P MandicAbstract:The canonical polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher order Tensors, it often exhibits high computational cost and permutation of tensor entries, and these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigor, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD and an iterative algorithm of low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the proposed approach.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
arXiv: Numerical Analysis, 2018Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadi Asl, Danilo P MandicAbstract:The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order Tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher-order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigour, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD, and an iterative algorithm with low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the approach.
Anh Huy Phan - One of the best experts on this subject based on the ideXlab platform.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
IEEE Transactions on Neural Networks, 2020Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadiasl, Danilo P MandicAbstract:The canonical polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher order Tensors, it often exhibits high computational cost and permutation of tensor entries, and these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigor, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD and an iterative algorithm of low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the proposed approach.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
arXiv: Numerical Analysis, 2018Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadi Asl, Danilo P MandicAbstract:The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order Tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher-order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigour, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD, and an iterative algorithm with low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the approach.
Giuseppe G Calvi - One of the best experts on this subject based on the ideXlab platform.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
IEEE Transactions on Neural Networks, 2020Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadiasl, Danilo P MandicAbstract:The canonical polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher order Tensors, it often exhibits high computational cost and permutation of tensor entries, and these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigor, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD and an iterative algorithm of low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the proposed approach.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
arXiv: Numerical Analysis, 2018Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadi Asl, Danilo P MandicAbstract:The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order Tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher-order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigour, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD, and an iterative algorithm with low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the approach.
Ivan V Oseledets - One of the best experts on this subject based on the ideXlab platform.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
IEEE Transactions on Neural Networks, 2020Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadiasl, Danilo P MandicAbstract:The canonical polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher order Tensors, it often exhibits high computational cost and permutation of tensor entries, and these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigor, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD and an iterative algorithm of low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the proposed approach.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
arXiv: Numerical Analysis, 2018Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadi Asl, Danilo P MandicAbstract:The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order Tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher-order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigour, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD, and an iterative algorithm with low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the approach.
Andrzej Cichocki - One of the best experts on this subject based on the ideXlab platform.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
IEEE Transactions on Neural Networks, 2020Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadiasl, Danilo P MandicAbstract:The canonical polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher order Tensors, it often exhibits high computational cost and permutation of tensor entries, and these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigor, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD and an iterative algorithm of low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the proposed approach.
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tensor networks for latent variable analysis higher order canonical polyadic decomposition
arXiv: Numerical Analysis, 2018Co-Authors: Anh Huy Phan, Andrzej Cichocki, Ivan V Oseledets, Giuseppe G Calvi, Salman Ahmadi Asl, Danilo P MandicAbstract:The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order Tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable effects grow exponentially with the tensor order. Prior compression of tensor in-hand can reduce the computational cost of CPD, but this is only applicable when the rank $R$ of the decomposition does not exceed the tensor dimensions. To resolve these issues, we present a novel method for CPD of higher-order Tensors, which rests upon a simple tensor network of representative inter-connected core Tensors of orders not higher than 3. For rigour, we develop an exact conversion scheme from the core Tensors to the factor matrices in CPD, and an iterative algorithm with low complexity to estimate these factor matrices for the inexact case. Comprehensive simulations over a variety of scenarios support the approach.
