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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/78706

    Title: Isometric Sliced Inverse Regression for Nonlinear Manifolds Learning
    Authors: Yao, Wei-ting;Wu, Han-ming
    Contributors: 淡江大學數學學系
    Keywords: Hierarchical clustering;Isometric feature mapping (ISOMAP);Nonlinear dimension reduction;Nonlinear manifold;Rank-two ellipse seriation;Sliced inverse regression
    Date: 2013-09
    Issue Date: 2012-10-20 10:41:17 (UTC+8)
    Publisher: New York: Springer New York LLC
    Abstract: 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.
    Relation: Statistics and Computing 23(5), pp.563-576
    DOI: 10.1007/s11222-012-9330-z
    Appears in Collections:[Graduate Institute & Department of Mathematics] Journal Article

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