Principal Component Analysis With Complex Kernel: The Widely Linear Model
File(s)
Accepted version
Author(s)
Papaioannou, A
Zafeiriou, S
Type
Journal Article
Abstract
Nonlinear complex representations, via the use of complex kernels, can be applied to model and capture the nonlinearities of complex data. Even though the theoretical tools of complex reproducing kernel Hilbert spaces (CRKHS) have been recently successfully applied to the design of digital filters and regression and classification frameworks, there is a limited research on component analysis and dimensionality reduction in CRKHS. The aim of this brief is to properly formulate the most popular component analysis methodology, i.e., Principal Component Analysis (PCA), in CRKHS. In particular, we define a general widely linear complex kernel PCA framework. Furthermore, we show how to efficiently perform widely linear PCA in small sample sized problems. Finally, we show the usefulness of the proposed framework in robust reconstruction using Euler data representation.
Date Issued
2014-09-01
Date Acceptance
2013-10-28
Citation
IEEE Transactions on Neural Networks and Learning Systems, 2014, 25 (9), pp.1719-1726
ISSN
2162-2388
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Start Page
1719
End Page
1726
Journal / Book Title
IEEE Transactions on Neural Networks and Learning Systems
Volume
25
Issue
9
Copyright Statement
© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Subjects
Science & Technology
Technology
Computer Science, Artificial Intelligence
Computer Science, Hardware & Architecture
Computer Science, Theory & Methods
Engineering, Electrical & Electronic
Computer Science
Engineering
Complex kernels
machine vision
pattern recognition
principal component analysis (PCA)
HILBERT-SPACES
RECOGNITION
EIGENFACES
PROJECTION
LMS
Publication Status
Published