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    Title: 等軸距切片逆迴歸法之非線性流形學習
    Other Titles: Isometric Sliced Inverse Regression for Nonlinear Manifolds Learning
    Authors: 吳漢銘
    Contributors: 淡江大學數學系
    Keywords: 階層式群集分析;等軸距特徵映射;非線性維度縮減;非線性流形;秩二橢 圓排序;切片逆迴歸法
    Hierarchical clustering;isometric feature mapping (ISOMAP);nonlinear dimension reduction;nonlinear manifold;rank-two ellipse seriation;sliced inverse regression
    Date: 2010
    Issue Date: 2012-05-22 22:14:27 (UTC+8)
    Abstract: 運用切片逆迴歸法可以找出有效的維度縮減方向來探索高維度資料的內在結 構。在這一個計畫中,我們針對非線性維度縮減問題,提出利用幾何測地線距離逼近 法的一個混合型切片逆迴歸法,我們稱此方法為等軸距切片逆迴歸法。所提的方法 中,第一步是先計算兩兩資料點等軸距距離,然後根據群集分析(例如: 階層式群集分 析)或排序方法(例如: 秩二橢圓排序法)在這個距離矩陣上的分群結果,當成切片的依 據,使得傳統的切片逆迴歸演算法可以被應用。我們將說明等軸距切片逆迴歸法可以 重新找到非線性流形資料,例如瑞士捲和S 曲線資料,內隱的維度和幾何結構。進一 步,我們將應用所找到的特徵向量在分類問題上。說明的例子會有一般的實際資料及 微陣列基因表現資料。所提的方法也會和其它現存的幾個維度縮減方法相比較。
    Sliced inverse regression was introduced to find the effective dimension reduction directions for exploring the intrinsic structure of high-dimensional data. In this proposal, we plan to present a hybrid SIR method for nonlinear dimension reduction using the geodesic distance approximation which we call the isometric SIR. The proposed method firstly computes the isometric distance between data points. Then the distance matrix is sliced according to the results of the clustering such as the hierarchical clustering and/or the seriation algorithm such as the rank-two ellipse seriation so that the classical SIR algorithm can be applied. We will show that the isometric SIR can recover the embedded dimensionality and the geometric structure of the nonlinear manifolds data sets such as the Swiss-roll and S-curve. We will also illustrate how the features found with isometric SIR can further be used for the classification problems of the real world data and microarray gene expression data. The comparisons with those obtained with several existing dimension reduction techniques are also investigated.
    Appears in Collections:[數學學系暨研究所] 研究報告

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