Anisotropic Gaussian kernel adaptive filtering by Lie-group dictionary learning

The present paper proposes a novel kernel adaptive filtering algorithm, where each Gaussian kernel is parameterized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of scalar width parameter. In fact, different from conventional kerne...

Full description

Saved in:
Bibliographic Details
Published in:PloS one Vol. 15; no. 8; p. e0237654
Main Authors: Wada, Tomoya, Fukumori, Kosuke, Tanaka, Toshihisa, Fiori, Simone
Format: Journal Article
Language:English
Published: United States Public Library of Science 14.08.2020
Public Library of Science (PLoS)
Subjects:
Adaptation
Adaptive algorithms
Adaptive filters
Adaptive systems
Algorithms
Anisotropy
Computer and Information Sciences
Criteria
Dictionaries
Digital filters
Engineering and Technology
Engineering research
Isotropy
Kernels
Lie groups
Machine Learning
Mathematical analysis
Matrix methods
Nonlinear Dynamics
Normal Distribution
Parameters
Physical Sciences
Regularization
Research and Analysis Methods
Signal processing
Software
Symmetry
Teaching methods
Technology application
Italy
Japan
ISSN:1932-6203, 1932-6203
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The present paper proposes a novel kernel adaptive filtering algorithm, where each Gaussian kernel is parameterized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of scalar width parameter. In fact, different from conventional kernel adaptive systems, the proposed filter is structured as a superposition of non-isotropic Gaussian kernels, whose non-isotropy makes the filter more flexible. The adaptation algorithm will search for optimal parameters in a wider parameter space. This generalization brings the need of special treatment of parameters that have a geometric structure. In fact, the main contribution of this paper is to establish update rules for precision matrices on the Lie group of SPD matrices in order to ensure their symmetry and positive-definiteness. The parameters of this filter are adapted on the basis of a least-squares criterion to minimize the filtering error, together with an ℓ1-type regularization criterion to avoid overfitting and to prevent the increase of dimensionality of the dictionary. Experimental results confirm the validity of the proposed method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
Competing Interests: The authors have declared that no competing interests exist.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0237654