Isometric Sliced Inverse Regression for Nonlinear Manifolds Learning

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題名:	Isometric Sliced Inverse Regression for Nonlinear Manifolds Learning
作者:	Yao, Wei-ting;Wu, Han-ming
貢獻者:	淡江大學數學學系
關鍵詞:	Hierarchical clustering;Isometric feature mapping (ISOMAP);Nonlinear dimension reduction;Nonlinear manifold;Rank-two ellipse seriation;Sliced inverse regression
日期:	2013-09
上傳時間:	2012-10-20 10:41:17 (UTC+8)
出版者:	New York: Springer New York LLC
摘要:	Sliced inverse regression (SIR) was developed to find effective linear dimension-reduction directions for exploring the intrinsic structure of the high-dimensional data. In this study, we present isometric SIR for nonlinear dimension reduction, which is a hybrid of the SIR method using the geodesic distance approximation. First, the proposed method computes the isometric distance between data points; the resulting distance matrix is then sliced according to K-means clustering results, and the classical SIR algorithm is applied. We show that the isometric SIR (ISOSIR) can reveal the geometric structure of a nonlinear manifold dataset (e.g., the Swiss roll). We report and discuss this novel method in comparison to several existing dimension-reduction techniques for data visualization and classification problems. The results show that ISOSIR is a promising nonlinear feature extractor for classification applications.
關聯:	Statistics and Computing 23(5), pp.563-576
DOI:	10.1007/s11222-012-9330-z
顯示於類別:	[數學學系暨研究所] 期刊論文

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