針對單標籤分類、多標籤分類與回歸預測的問題，我們提出了一個演算法來解決這些問題，這個演算法主要可以分成四個步驟，分別是旋轉相似度計算、加權關聯性計算、混合式學習與門檻值檢測。
一開始，我們將訓練樣本輸入演算法中進行旋轉群相似度計算，它會將每筆訓練樣本都轉換成一表示各旋轉群的相似度的向量，而旋轉群是一種更妥善描述資料分佈的方法，尤其是當資料分佈的形狀越接近超球體、超橢圓體或是斜角超橢圓體。我們會將轉換過後的相似度進行加權合併整合，以得到此樣本與每種類別標籤或是輸出目標值的關聯性；之後，運用混合式學習演算法來修正演算法中的參數，以提升系統的效能，讓預測的結果更加的準確；我們會依照不同的問題類型而設定不同的門檻值函數，最後透過門檻值檢測取得演算法的預測輸出結果。
使用者並不需要預先設定旋轉群的數量，而是在訓練階段時，每個群將會自動建立與形成。最後我們透過一些實驗可以得知我們的方法的效能。

We propose an algorithm for single label classification, multi-label classification, and regression estimation which incorporates a rotating similarity, weighted relevance, hybrid learning, and threshold checking.
Firstly, the rotating cluster similarity is more suitable of the distribution of the data set with hyper-spherical, hyper-ellipsoidal, or oblique hyper-ellipsoidal shapes and it is used to transform each input instance into a rotating cluster similarity. Then, the similarity of the input instance will be combined to obtain the weighted relevance of the input instance to each particular category or output value. Next, we use the hybrid learning method to refine the parameters which is in this algorithm to get better performance. Finally, the threshold checking is used to obtain the output. We will set different kind of threshold functions to determine the output due to the kind of problems.
The number of rotating clusters do not need to be specified in advance. Each cluster will self-construct during the training phase. A number of experimental results are shown the effectiveness of our proposed method.

致謝 i
摘要 ii
Abstract iii
圖目錄 vi
表目錄 vii
第一章 導論 1
1.1. 研究動機與文獻回顧 1
1.2. 問題描述 4
1.3. 論文架構 4
第二章 文獻探討 5
2.1. 主成分分析(PCA) 5
2.2. Versatile elliptic basis function neural network (VEBF) 7
2.2.1. VEBF架構與概述 7
2.2.2. Geometrical Growth Criterion 8
2.2.3. Merging Strategy 10
2.3. LO Method 11
2.3.1. Structure Identification 13
2.3.2. Parameter Identification 15
第三章 研究方法 18
3.1. 系統流程與架構 18
3.2. 旋轉群相似度計算(Rotating Cluster Similarity) 20
3.2.1. 自構性規範(Self-Constructing Criterion) 21
3.3. 加權關聯性計算(Weighted Relevance) 25
3.4. 混合式學習法(Hybrid Learning) 27
3.5. 門檻值檢測(Threshold Checking) 29
3.6. 演算法與時間複雜度分析(Time Complexity Analysis) 30
3.7. 範例說明 32
第四章 實驗結果與分析 38
4.1. 單標籤分類 38
4.2. 多標籤分類 41
4.3. 回歸預測 43
第五章 結論與未來研究方向 47
參考文獻 49

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