Dimension Reduction and Its Applications

Autor: Yi-Ren Yeh, 葉倚任
Rok vydání: 2010
Druh dokumentu: 學位論文 ; thesis
Popis: 98
In this dissertation, we develop a dimension reduction framework for learning tasks based on the nonlinear dimension reduction methods. We first focus on the kernel extension of sliced inverse regression (SIR) which is a supervised dimension reduction and its implementation. Based on these nonlinear dimension reduction methods, the main linear features are extracted in this embedded feature space and many linear algorithms can be applied to the images of input data in this feature effective dimension reduction subspace. Except for the kernel SIR, we also study the robustness issue of kernel principal component analysis (PCA). A class of new robust procedures is proposed based on eigenvalue decomposition of weighted covariance. The proposed procedures will place less weights to deviant patterns and thus behave more resistant to data contamination and model deviation. In the end of this dissertation, anomaly detection and bankruptcy prognosis via dimension reduction methods are presented. In the anomaly detection, we have explored the variation of principal directions in the leave one out scenario. The over-sampling PCA is also proposed to enlarge the outlierness of an outlier. In addition, the online estimating principal directions in LOO is used for reducing the computational loading and satisfying the on-line detecting demand. In the bankruptcy prognosis, we apply feature selection via 1-norm support vector machine (SVM) and incremental forward feature selection (IFFS). The results show the selection of accounting ratios via 1-norm SVM and IFFS can perform as well as the greedy search. Besides, an 2-D visualization scheme via different models is also proposed to bank officer to make the decision.
Databáze: Networked Digital Library of Theses & Dissertations