基於模糊線性區別分析之模糊分群法與結合空間資訊之支撐向量機

Abstract

統計學習演算法自動利用觀察資料來辨識複雜的樣本並進行決策。統計學習領域中有兩大主要議題：叢集分析與分類器設計。叢集分析演算法會將相似的樣本組織成同一個叢集；分類器則會利用現有的訓練樣本來決定新的未知樣本之類別。在本論文中，將提出模糊的分群演算法與融合空間資訊的分類器。在分群演算法方面，本文提出模糊線性區別分析之組間與組內分散矩陣，再搭配Fisher準則進行分群，此方法同時最小化群內資訊與最大化組間資訊。針對分類器的部分，透過空間資訊來調整支撐向量機的決策函數與限制式。利用真實資料的實驗結果顯示，本論文提出的方法可以有效地增加分群與分類的效能。

Statistical learning is trying to develop computer algorithms to recognize complex patterns and make decisions based on empirical data automatically. Two major issues are clustering and classification. Clustering organizes patterns into sensible clusters for patterns in the same cluster to be similar in a sense, whereas classification identifies the categories to which new patterns belong based on an available training set of data containing patterns of known categories. This thesis introduces a fuzzy-based clustering and a spatial-contextual classifier. Fuzzy-based clustering defines within- and between-cluster scatter matrices of a fuzzy-type linear discriminant analysis, and the clustering results are based on the Fisher criterion. The proposed clustering algorithm minimizes the within-cluster information and simultaneously maximizes the between-cluster information. For the classification part, a spatial-contextual term was used to modify the decision function and constraints of a support vector machine. Experimental results show that the proposed methods achieve good clustering and classification performance on famous real data sets.