鄭明燕2006-07-262018-06-282006-07-262018-06-282000-09-30http://ntur.lib.ntu.edu.tw//handle/246246/20936我們介紹一種描述樣本點與點關係的 樹狀圖。我們的方法間接利用密度函數的 坡度估計值。樹狀圖中兩點相連對等於經 過此兩點，沿密度函數曲面，的最陡坡曲 線會合於同一聚點。這些最陡坡曲線在樣 本平面上的投影稱為陡坡樹狀圖。陡坡樹 狀圖有規律的結構而且由非參數密度函數 估計，若其能一致估計密度函數及其導 數，建造的它的類似體可對它一致估計。 此外，我們建議一種樹叢圖，其中樣本點 之間以與部分陡坡樹狀圖相近的線段連 接。一個樹叢圖是一個規律化的最小全距 圖。建構樹叢圖的密度曲面估計使用的帶 寬較建構最小全距圖的密度曲面估計使用 的帶寬大，所以樹叢圖具有遠較為規則的 形狀。We suggest new approaches to constructing tree diagrams that describe associations among points in a scatterplot. Our methods are based implicitly on gradient estimates. In our tree diagrams, two data points are associated with one another if and only if their respective curves of steepest ascent up the density or intensity surface lead toward the same mode. The representation, in the sample space, of the set of steepest ascent curves corresponding to the data, is called the gradient tree. It has a regular, octopus-like structure, and is consistently estimated by its analogue computed from a nonparametric estimator which gives consistent estimation of both the density surface and its derivatives. We also suggest `forests', in which data are linked by line segments which represent good approximations to portions of the population gradient tree. A forest is a regularization of a minimum spanning tree. However, forests use a larger bandwidth for constructing the density-surface estimate than is implicit in the MST, with the result that they are substantially more orderly and are more readily interpreted.application/pdf39391 bytesapplication/pdfzh-TW國立臺灣大學數學系暨研究所Density ascent linedensity estimationforestgradient treeminimum spanning treenearest neighbor methodsridge estimationtree diagramreporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/20936/1/892118M002007.pdf