軟充分維度縮簡法---理論與應用

淡江大學機構典藏 > 理學院 > 數學學系暨研究所 > 研究報告 > Item 987654321/46959

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题名:	軟充分維度縮簡法---理論與應用
其它题名:	Soft Sufficient Dimension Reduction: Theory and Application
作者:	吳漢銘
贡献者:	淡江大學數學學系
关键词:	群集分析;維度縮減;模糊c 均值法;微陣列基因表現資料;切片逆迴歸法;軟群集分析;Clustering;dimension reduction;fuzzy c-means;gene expression data;sliced inverseregression;soft clustering
日期:	2009
上传时间:	2010-04-15 15:40:53 (UTC+8)
摘要:	在這個計畫中的第一年，我們嘗試推導在逆迴歸問題中使用軟切片估計中央子空間的統計性質。我們會以切片逆迴歸法為原型來說明我們所提出的方法。而切片逆迴歸法是切片型充份維度縮減法家族中的一員。我們將証明此軟估計量在某些條件下具有漸近常態的分佈。其它的統計性質，例如有效性及最佳性也會一起探討。在實際的演算法裡，軟切片的起始值是從模糊c 均值法得到的群集組員。我們會比較這個軟估計量和其它的切片型充份維度縮減方法的正確性及穩定性。我們簡稱所提的方法為SSDR，代表軟充份維度縮減。其中軟切片逆迴歸法(SSIR)是SSDR 的特例。第二年，我們應用SSDR 法在微陣列資料基因分群，基序發現及醫學影像切割問題上。因為這些高維度的生物醫學資料具有雜訊的特性，一般的硬分群方法例如階層式群集法和K 均值法，對找出生物意義相關的基因群或醫學影像的不同組織分割，結果顯的很不穩定。我們提出以迭代方法來更新軟切片，這方法處理了「維度詛咒」的問題，並且我們期望會有較穩定的結果。我們又提出一個有加進集群組員資訊的二維投影圖，方便我們觀察資料的內含群集結構。另外，針對基因分群的應用，我們也發展了兩個生物效度指標，用來評量軟群集法在生物功能類別上的齊一性及穩定性。初步結果顯示，一些常用的軟群集法，用硬指標來評量，通常會高估軟群集法的表現。這事實告訴我們不僅要在群集法裡利用群集組員的必要性，而且在生物驗証指標上要考慮。我們會進一步採用這些指標來評量我們所提的軟群集法，並和其它的軟群集法相比較。同時我們也將研究了不同初始的群集組員對迭代軟充份維度縮減法的影響。 In the first year of this proposal, we plan to study the theoretical properties of the estimation of central subspace using a soft slicing method in the inverse regression (IR) problem. The sliced inverse regression (SIR) will be used as an illustrative prototype in the family of the slice-based sufficient dimension reduction (SDR) methods. We will show that the estimate using soft slicing has an asymptotic normal distribution under certain conditions. Other statistical properties such as efficiency and optimality will be elaborated as well. In practical implementation, the initial soft slices were obtained from the cluster memberships using fuzzy c-means. Then the soft estimates will be compared with other slice-based SDR methods in terms of accuracy and stability. We abbreviate the proposed method as SSDR for the soft sufficient dimension reduction. The soft sliced inverse regression (SSIR) is a special case for SSDR. In the second year, we will apply SSDR to gene clustering of microarray data, motif discovery, and medical image segmentation. Due to the noisy nature of the high-dimensional biomedical data, the conventional hard clustering methods such as hierarchical clustering and K-means are sensitive to reveal biologically relevant groups of genes or sensitive to detect different tissue segments of medical images. An iterative approach by updating soft slices is employed to prevent the curse of dimensionality and we expect to reach the stable results. A projected 2D plot with information of cluster membership is proposed for exploring the intrinsic data structure. For gene clustering, in particularly, we develop two new biological indices for evaluating soft clustering algorithms in terms of the biological homogeneity and the biological stability. The preliminary results of some existing soft clustering algorithms suggest that the hard biological indices usually over estimate the performance of the soft clustering algorithms. This indicates that one should not only consider the cluster memberships in clustering algorithms but also in the biological cluster validation. We will use these indices further for evaluating the proposed method with other soft clustering algorithms for gene clustering. At the same time, we will also investigate the effects of the different initial memberships for an iterative SSDR.
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