NDLI: Fast orthogonal decomposition of Volterra cubic kernels using oblique unfolding

Content Provider	IEEE Xplore Digital Library
Author	Boyer, R. Badeau, R. Favier, G.
Copyright Year	2011
Description	Author affiliation: Université Paris XI (UPS), LSS-Supélec, CNRS, France (Boyer, R.) \|\| Télécom ParisTech, CNRS LTCI, France (Badeau, R.) \|\| Université Nice Sophia Antipolis, I3S, CNRS, France (Favier, G.)
Abstract	Discrete-time Volterra modeling is a central topic in many application areas and a large class of nonlinear systems can be modeled using high-order Volterra series. The problem with Volterra series is that the number of parameters grows very rapidly with the order of the nonlinearity and the memory in the system. In order to efficiently implement this model, kernel eigen-decomposition can be used in the context of a Parallel-Cascade realization of a Volterra system. So, using the multilinear SVD (HOSVD) for decomposing high-order Volterra kernels seems natural. In this paper, we propose to drastically reduce the computational cost of the HOSVD by (1) considering the symmetrized Volterra kernel and (2) exploiting the column-redundancy of the associated mode by using an oblique unfolding of the Volterra kernel. Keeping in mind that the complexity of the full HOSVD for a cubic (I × I × I) unstructured Volterra kernel needs $12I^{4}$ flops, our solution allows reducing the complexity to $2I^{4}$ flops, which leads to a gain equal to six for a sufficiently large size I.
Starting Page	4080
Ending Page	4083
File Size	140243
Page Count	4
File Format	PDF
ISBN	9781457705380
ISSN	15206149
e-ISBN	9781457705397
e-ISBN	9781457705373
DOI	10.1109/ICASSP.2011.5947249
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-05-22
Publisher Place	Czech Republic
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Kernel Tensile stress Matrix decomposition Complexity theory Symmetric matrices Signal processing Computational modeling oblique unfolding Volterra kernel fast HOSVD
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

FAST ORTHOGONAL DECOMPOSITION OF VOLTERRA CUBIC KERNELS USING OBLIQUE UNFOLDING

FAST ORTHOGONAL DECOMPOSITION OF VOLTERRA CUBIC KERNELS USING OBLIQUE UNFOLDING

FAST ORTHOGONAL DECOMPOSITION OF VOLTERRA CUBIC KERNELS USING OBLIQUE UNFOLDING (2011)

Identification of nonlinear stochastic systems described by a reduced complexity Volterra model using an ARGLS algorithm

Third-order Volterra kernels complexity reduction using PARAFAC

Efficient realization for symmetric orthogonal multiwavelet by simple scaling and rotation

Optimization of symmetric tensor computations

Decomposing tensors with structured matrix factors reduces to rank-1 approximations

Adaptive beamforming using fast low-rank covariance matrix approximations

Fast orthogonal decomposition of Volterra cubic kernels using oblique unfolding

Similar Documents

FAST ORTHOGONAL DECOMPOSITION OF VOLTERRA CUBIC KERNELS USING OBLIQUE UNFOLDING

FAST ORTHOGONAL DECOMPOSITION OF VOLTERRA CUBIC KERNELS USING OBLIQUE UNFOLDING

FAST ORTHOGONAL DECOMPOSITION OF VOLTERRA CUBIC KERNELS USING OBLIQUE UNFOLDING (2011)

Identification of nonlinear stochastic systems described by a reduced complexity Volterra model using an ARGLS algorithm

Third-order Volterra kernels complexity reduction using PARAFAC

Efficient realization for symmetric orthogonal multiwavelet by simple scaling and rotation

Optimization of symmetric tensor computations

Decomposing tensors with structured matrix factors reduces to rank-1 approximations

Adaptive beamforming using fast low-rank covariance matrix approximations

Fast orthogonal decomposition of Volterra cubic kernels using oblique unfolding