Generalized KPCA by adaptive rules in feature space

Authors:
Yanwei Pang;Lei Wang;Yuan Yuan
Affiliations:
School of Electronic Information Engineering, Tianjin University, Tianjin, China;Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei, China;School of Engineering and Applied Science, Aston University, Birmingham, UK
Venue:
International Journal of Computer Mathematics
Year:
2010

Citing 0
Cited 6

A New Incremental PCA Algorithm With Application to Visual Learning and Recognition

Neural Processing Letters
A new kernelization framework for Mahalanobis distance learning algorithms

Neurocomputing
Discriminant analysis via support vectors

Neurocomputing
An iterative algorithm for robust kernel principal component analysis

Neurocomputing
Dimensionality reduction by Mixed Kernel Canonical Correlation Analysis

Pattern Recognition
Adaptive kernel subspace method for speeding up feature extraction

Neurocomputing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA.