Isometric sliced inverse regression for nonlinear manifolds learning

• Main Authors: Wei-Ting Yao, 姚威廷
• Other Authors: 吳漢銘
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/24460542302146689830

碩士 === 淡江大學 === 數學學系碩士班 === 98 === Sliced inverse regression (SIR) was introduced to find an effective linear dimension-reduction direction to explore the intrinsic structure of high dimensional data. In this study, we present isometric SIR for nonlinear dimension reduction - 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 hierarchical clustering results with rank-two ellipse seriation, and the classical SIR algorithm is applied. We show that the isometric SIR can recover the embedded dimensionality and geometric structure of a nonlinear manifold dataset (e.g., the Swiss-roll). We illustrate how isometric SIR features can further be used for the classification problems. Finally, we report and discuss this novel method in comparison to several existing dimension-reduction techniques.