Efficient KLMS and KRLS algorithms: A random fourier feature perspective

Pantelis Bouboulis; Spyridon Pougkakiotis; S. Theodoridis

doi:10.1109/SSP.2016.7551811

Efficient KLMS and KRLS algorithms: A random fourier feature perspective

Pantelis Bouboulis, Spyridon Pougkakiotis, S. Theodoridis

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

34 Citations (Scopus)

Abstract

We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space, using random features of the kernel's Fourier transform. The advantage is that, the inner product of the mapped data approximates the kernel function. The resulting 'linear' algorithm does not require any form of sparsification, since, in contrast to all existing algorithms, the solution's size remains fixed and does not increase with the iteration steps. As a result, the obtained algorithms are computationally significantly more efficient compared to previously derived variants, while, at the same time, they converge at similar speeds and to similar error floors.

Original language	English
Title of host publication	2016 IEEE Statistical Signal Processing Workshop (SSP)
Publisher	IEEE
ISBN (Electronic)	9781467378031, 9781467378024
ISBN (Print)	9781467378048
DOIs	https://doi.org/10.1109/SSP.2016.7551811
Publication status	Published - 25 Aug 2016
Event	19th IEEE Statistical Signal Processing Workshop - Palma de Mallorca, Spain Duration: 25 Jun 2016 → 29 Jun 2016 https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7551702

Conference

Conference	19th IEEE Statistical Signal Processing Workshop
Abbreviated title	SSP 2016
Country/Territory	Spain
City	Palma de Mallorca
Period	25/06/16 → 29/06/16
Internet address	https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7551702

Keywords

Kernel Adaptive filter
Kernel Least Mean Squares
Kernel LMS
Kernel RLS
KLMS
Random Fourier Features

ASJC Scopus subject areas

Electrical and Electronic Engineering
Applied Mathematics
Signal Processing
Computer Science Applications

Access to Document

10.1109/SSP.2016.7551811

Cite this

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title = "Efficient KLMS and KRLS algorithms: A random fourier feature perspective",

abstract = "We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space, using random features of the kernel's Fourier transform. The advantage is that, the inner product of the mapped data approximates the kernel function. The resulting 'linear' algorithm does not require any form of sparsification, since, in contrast to all existing algorithms, the solution's size remains fixed and does not increase with the iteration steps. As a result, the obtained algorithms are computationally significantly more efficient compared to previously derived variants, while, at the same time, they converge at similar speeds and to similar error floors.",

keywords = "Kernel Adaptive filter, Kernel Least Mean Squares, Kernel LMS, Kernel RLS, KLMS, Random Fourier Features",

author = "Pantelis Bouboulis and Spyridon Pougkakiotis and S. Theodoridis",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 19th IEEE Statistical Signal Processing Workshop, SSP 2016 ; Conference date: 25-06-2016 Through 29-06-2016",

year = "2016",

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doi = "10.1109/SSP.2016.7551811",

language = "English",

isbn = "9781467378048",

booktitle = "2016 IEEE Statistical Signal Processing Workshop (SSP)",

publisher = "IEEE",

url = "https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7551702",

}

TY - GEN

T1 - Efficient KLMS and KRLS algorithms

T2 - 19th IEEE Statistical Signal Processing Workshop

AU - Bouboulis, Pantelis

AU - Pougkakiotis, Spyridon

AU - Theodoridis, S.

PY - 2016/8/25

Y1 - 2016/8/25

N2 - We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space, using random features of the kernel's Fourier transform. The advantage is that, the inner product of the mapped data approximates the kernel function. The resulting 'linear' algorithm does not require any form of sparsification, since, in contrast to all existing algorithms, the solution's size remains fixed and does not increase with the iteration steps. As a result, the obtained algorithms are computationally significantly more efficient compared to previously derived variants, while, at the same time, they converge at similar speeds and to similar error floors.

AB - We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space, using random features of the kernel's Fourier transform. The advantage is that, the inner product of the mapped data approximates the kernel function. The resulting 'linear' algorithm does not require any form of sparsification, since, in contrast to all existing algorithms, the solution's size remains fixed and does not increase with the iteration steps. As a result, the obtained algorithms are computationally significantly more efficient compared to previously derived variants, while, at the same time, they converge at similar speeds and to similar error floors.

KW - Kernel Adaptive filter

KW - Kernel Least Mean Squares

KW - Kernel LMS

KW - Kernel RLS

KW - KLMS

KW - Random Fourier Features

UR - http://www.scopus.com/inward/record.url?scp=84987920111&partnerID=8YFLogxK

U2 - 10.1109/SSP.2016.7551811

DO - 10.1109/SSP.2016.7551811

M3 - Conference contribution

AN - SCOPUS:84987920111

SN - 9781467378048

BT - 2016 IEEE Statistical Signal Processing Workshop (SSP)

PB - IEEE

Y2 - 25 June 2016 through 29 June 2016

ER -

Efficient KLMS and KRLS algorithms: A random fourier feature perspective

Abstract

Conference

Keywords

ASJC Scopus subject areas

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