NONLINEAR FEATURE EXTRACTION AND DIMENSION REDUCTION BY POLYGONAL PRINCIPAL CURVES

2006 ◽  
Vol 20 (01) ◽  
pp. 63-78 ◽  
Author(s):  
FENG ZHANG
Keyword(s):  
Feature Extraction ◽  
Principal Component ◽  
Polygonal Line ◽  
Principal Curves ◽  
Redundancy Elimination ◽  
Feature Extraction Method ◽  
Principal Curve ◽  
Nonlinear Feature Extraction ◽  
Nonlinear Feature ◽  
Nonlinear Pattern

In this article we propose a polygonal principal curve based nonlinear feature extraction method, which achieves statistical redundancy elimination without loss of information and provides more robust nonlinear pattern identification for high-dimensional data. Recognizing the limitations of linear statistical methods, this article integrates local principal component analysis (PCA) with a polygonal line algorithm to approximate the complicated nonlinear data structure. Experimental results demonstrate that the proposed algorithm can be implemented to reduce the computation complexity for nonlinear feature extraction in multivariate cases.

Simulation Research of Feature Extraction Method Based on Nonlinear Manifold Learning

2014 ◽  
Vol 533 ◽  
pp. 247-251
Author(s):  
Hai Bing Xiao ◽  
Xiao Peng Xie
Keyword(s):  
Feature Extraction ◽  
Manifold Learning ◽  
Extraction Method ◽  
Classification Performance ◽  
Locally Linear Embedding ◽  
Simulation Research ◽  
Feature Extraction Method ◽  
Linear Embedding ◽  
Nonlinear Feature Extraction ◽  
Nonlinear Feature

This paper deals with the study of Locally Linear Embedding (LLE) and Hessian LLE nonlinear feature extraction for high dimensional data dimension reduction. LLE and Hessian LLE algorithm which reveals the characteristics of nonlinear manifold learning were analyzed. LLE and Hessian LLE algorithm simulation research was studied through different kinds of sample for dimensionality reduction. LLE and Hessian LLE algorithm’s classification performance was compared in accordance with MDS. The simulation experimental results show that LLE and Hessian LLE are very effective feature extraction method for nonlinear manifold learning.

Training Data Reduction and Classification Based on Greedy Kernel Principal Component Analysis and Fuzzy C-Means Algorithm

2013 ◽  
Vol 347-350 ◽  
pp. 2390-2394
Author(s):  
Xiao Fang Liu ◽  
Chun Yang
Keyword(s):  
Principal Component Analysis ◽  
Feature Extraction ◽  
Computational Complexity ◽  
Principal Component ◽  
Large Data ◽  
Component Analysis ◽  
Training Data ◽  
Kernel Principal Component Analysis ◽  
Nonlinear Feature Extraction ◽  
Nonlinear Feature

Nonlinear feature extraction used standard Kernel Principal Component Analysis (KPCA) method has large memories and high computational complexity in large datasets. A Greedy Kernel Principal Component Analysis (GKPCA) method is applied to reduce training data and deal with the nonlinear feature extraction problem for training data of large data in classification. First, a subset, which approximates to the original training data, is selected from the full training data using the greedy technique of the GKPCA method. Then, the feature extraction model is trained by the subset instead of the full training data. Finally, FCM algorithm classifies feature extraction data of the GKPCA, KPCA and PCA methods, respectively. The simulation results indicate that the feature extraction performance of both the GKPCA, and KPCA methods outperform the PCA method. In addition of retaining the performance of the KPCA method, the GKPCA method reduces computational complexity due to the reduced training set in classification.

Kernel Orthogonal Neighborhood Preserving Discriminant Analysis

2011 ◽  
Vol 339 ◽  
pp. 571-574
Author(s):  
Xing Zhu Liang ◽  
Jing Zhao Li ◽  
Yu E Lin
Keyword(s):  
Feature Extraction ◽  
Discriminant Analysis ◽  
Extraction Method ◽  
Learning Algorithms ◽  
Recognition Rate ◽  
Kernel Matrix ◽  
Feature Extraction Method ◽  
Nonlinear Features ◽  
Nonlinear Feature Extraction ◽  
Nonlinear Feature

Several orthogonal feature extraction algorithms based on local preserving projection have recently been proposed. However, these methods still are linear techniques in nature. In this paper, we present nonlinear feature extraction method called Kernel Orthogonal Neighborhood Preserving Discriminant Analysis (KONPDA). A major advantage of the proposed method is that it is regarded every column of the kernel matrix as a corresponding sample. Then running KONPDA in kernel matrix, nonlinear features can be extracted. Experimental results on ORL database indicate that the proposed KONPDA method achieves higher recognition rate than the ONPDA method and other kernel-based learning algorithms.

scholarly journals NONLINEAR FEATURE EXTRACTION USING FISHER CRITERION

2008 ◽  
Vol 22 (06) ◽  
pp. 1089-1119 ◽  
Author(s):  
MATÍAS A. BUSTOS ◽  
MANUEL A. DUARTE-MERMOUD ◽  
NICOLÁS H. BELTRÁN
Keyword(s):  
Feature Extraction ◽  
Closed Form Solution ◽  
Numerical Algorithms ◽  
Form Solution ◽  
Distribution Functions ◽  
Fisher Criterion ◽  
Standard Pattern ◽  
Feature Extraction Method ◽  
Nonlinear Feature Extraction ◽  
Nonlinear Feature

In this paper the problem of nonlinear feature extraction based on the optimization of the Fisher criterion is analyzed. A new nonlinear feature extraction method is proposed. The method does not make use of numerical algorithms and it has an analytical (closed-form) solution. Moreover, no assumptions on the class probability distribution functions are imposed. The proposed method is applied to some standard pattern recognition problems and compared with other classical methodologies already proposed in the literature. The performance of the proposed method turned out to be superior when compared with the other methods studied.

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