臺灣博碩士論文加值系統

本論文考量標準二元分類法的問題。在歐氏範數空間中，吾人將提出保證數據線性二元可分離之等價判別準則。針對線性二元可分離之數據，提供一個保證可正確分類之超平面。此外，我們提出一個簡易數值疊代方法來測試數據的線性二元可分離性。最後，吾人將提供一數值範例來說明主要定理之可行性。

The classical binary classification problem is considered in this thesis. Necessary and sufficient condition is proposed to guarantee the linear binary separability of the training data in the Euclidean normed space. A suitable hyperplane that correctly classifies the training data is also constructed provided that the necessary and sufficient condition is satisfied. Based on the main result, we present an easy-to-check criterion for the linear binary separability of the training set. Finally, two numerical examples are given to illustrate the use of the main result.

第一章 簡介 1
1-1 引言 1
1-2 論文架構 2
1-3 符號定義 3
第二章 定義與定理 4
2-1 非線性最佳化理論 [7] 4
2-1.1 非線性最佳化理論之原始問題 [7] 4
2-1.2 拉格朗日乘法元素（Lagrange Multiplier） 6
2-1.3 非線性最佳化理論之對偶問題 9
2-2 ROSENBLATT演算法 14
2-2.1 Rosenblatt感知機的原始型 14
2-2.2 Rosenblatt感知機之對偶型 18
2-2.3 修正Rosenblatt感知機原始型 20
2-3 超平面 24
2-4 線性分類 26
2-5 最大邊際分類 30
第三章 主要結論 37
3-1 系統描述 37
3-2 主要定理 43
第四章 範例模擬 45
4-1 範例一 45
4-2 範例二 47
第五章 結論與未來研究方向 49
5-1 結論 49
5-2 未來研究方向 49
參考文獻 50

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