KPCA和KFD的屬性解釋以及分類法則之研究
Attribute Interpretation and Classification Rules behind Kernel Principal Component Analysis and Kernel Fisher Discriminants
Date Issued
2005
Date
2005
Author(s)
Chen, Yi-Hung
DOI
en-US
Abstract
In general, classification methods can be divided into two categories: one is unsupervised classification and the other is supervised classification. PCA and FLD are linear multivariate analysis methods where PCA is an unsupervised classification method and FLD belongs to supervised classification methods. Because linear methods are not sufficient to analyze the data with nonlinear patterns, the nonlinear methods KPCA and KFD are hence extended from PCA and FLD, respectively. Both transform the instances from the original attribute space to the feature space which could be arbitrarily large, possibly an infinite dimensional space. The feature space is efficient for feature extraction and pattern recognition but we loss the meanings of the original attributes there. For attribute interpretation, we need to segment the instances with nonlinear patterns into several partitions where each partition has its own linear patterns. Then, we can apply linear methods in each partition respectively for attribute interpretation. For KPCA, the segmentation is manipulated in the feature space through the second and higher KPC score(s) and then come back to the original attribute space for attribute interpretation. For KFD, we segment the training instance by an appropriate second and higher KFD score(s) to construct a linear predictive model for future prediction. This segmentation turns KPCA to segmented PCA by minimizing the reconstruction error and transforms KFD to segmented FLD by maximizing the classification accuracy. To verify this method, simulated examples are first used to examine and compare the proposed methods against other conventional methods. Then, real-world data sets are used to validate the proposed methodologies.
Subjects
分類方法
以核函數為根基的主成分分析
以核函數為根基的費雪區別方法
Classification method
Kernel principal component analysis
Kernel Fisher discriminants
Type
thesis
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