Nonlinear dimension reduction based on the cumulative slicing mean estimation

機構典藏 > College of Sciences > Department of Applied Mathematics and Data Science > Thesis > Item 987654321/114269

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Title:	Nonlinear dimension reduction based on the cumulative slicing mean estimation
Other Titles:	基於累積切片平均估計的非線性維度縮減法
Authors:	王子豪;Wang, Tzu-Hao
Contributors:	淡江大學數學學系碩士班吳漢銘;Wu, Han-Ming
Keywords:	累積切片估計;等距特徵映射;流形學習;非線性維度縮減;切片逆迴歸;Cumulative slicing estimation;isometric feature mapping;manifold learning;Nonlinear dimension reduction;Sliced inverse regression
Date:	2017
Issue Date:	2018-08-03 14:47:08 (UTC+8)
Abstract:	文獻中，對於流形學習的非線性維度縮減已有不少研究。其中，迴歸等軸距切片逆迴歸法(ISOSIR)，是屬於一種半監督式的學習演算法，已被提出並証明它可以有效地探索非線性流形資料隱含的幾何結構，例如瑞士捲資料。ISOSIR 是採用均值法做為一個基礎的群集分析，應用到預先計算好的資料集等距距離矩陣。然而，反應變數在群內及群間的順序訊息在群集之後會被忽略，而順序結構是非線性資料很重要的特徵之一。另一方面，假設資料的具有類別資訊，等距離矩陣的計算並沒有考慮到這個資訊。在本研究中，我們擴展 ISOSIR 和等軸距累積切片平均估計法，提出一監督式演算法，用以解決上述這兩個問題。我們進行了模擬研究和實際資料分析，結果顯示所提出的方法可以揭示非線性流形資料的幾何結構，同時與監督式的ISOSIR 表現相當。我們更進一步研究，應用所找出的低維度資料特徵於實際資料的分類及回歸問題。 A number of studies have been conducted on the nonlinear dimension reduction for manifold learning in the literature. Among them, the isometric sliced inverse regression (ISOSIR), a semi-supervised learning algorithm, has been proposed and shown to be useful for exploring the embedded geometric structure of the nonlinear manifold data set such as the Swiss roll. ISOSIR applied K-means as a base clustering method to the pre-calculated isometric distance matrix of the data set. However, the ordering information of response both within and between the resulting clusters was ignored where the ordering structure was one of the most important characteristics of a nonlinear manifold data set. On the other hand, the construction of the isometric distance matrix did not consider the class labels of data if they were available. In this study, we are motivated to settle these two defects and propose the supervised extensions of ISOSIR and isometric cumulative slicing mean estimation. We conducted the simulation studies and real data analysis and shown that the proposed method can reveal the geometric structure of a nonlinear manifold data set and the results were comparable to the supervised ISOSIR. We further investigated the applications of the found features for the classification and regression problems to the real world data sets.
Appears in Collections:	[Department of Applied Mathematics and Data Science] Thesis

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