基於貝氏循序切割之流形學習

Abstract

當使用越複雜的特徵來建立模型時，模型需要更多的資料來才能訓練。然而，此所需的資料個數對於特徵的維度呈現指數成長。為了能夠處理高維度的特徵，我們時常需要降維的技術。 在本篇論文中，基於貝氏循序切割，我們提出一個新的流形學習方法。其流程有兩部分。第一步，我們修改貝氏循序切割的分數計算方式，使其能夠將高維度資料切割成局部的群集。第二步，我們建立這些群集的關係，而這些資訊能夠協助我們決定群集的相關程度，進而循序地表示整體資料。有了這些資訊，我們可以將資料在低維度空間攤開，達到降維的作用。

The more complicated features used to construct a model, the more data we need for model learning. Unfortunately, the required amount of data grows exponentially as the feature space dimension grows. To deal with high-dimensional feature space, dimension reduction techniques are usually needed. In this thesis, we propose a new manifold learning method based on Bayesian Sequential Partitioning (BSP). Our framework has two parts. First, we modify the score function of BSP to make it suitable for the separation of high dimensional data into local data groups. Second, we build the relationship among those groups. The relationships can help us to decide the affinities among local groups and to represent the whole data set sequentially. Using the extracted relationships, we can unfold the data to find out their low-dimensional representation for dimension reduction.