在近百年裡，人類發明了許許多多便利的工具，以追求更美好、舒適的生活環境，其中電腦為最重要的發明之一，其運算能力是人類無法比擬的；由於電腦能快速且準確地處理大量的資料，人們進而希望利用這項優勢來模擬人類的思維，而人工智慧就此堀起，舉凡類神經網路、資料探勘、模糊邏輯…等方法源源不絕的提出，應用到指紋辨識、影像壓縮、天線設計…等各方領域，在此我們將根據決策樹及模糊分群法對於資料的預測技術方面進行探討。模糊決策樹使用模糊分群的方法達到將資料分類的效果，進而建構決策樹以對資料做預測的動作；然而，在距離函數方面，由於設計輸出值的影響力將隨著輸入向量維度大小成反比，將導致在某些資料集的分類上產生問題，除此之外，每個葉節點的輸出模式僅以一個常數的代表輸出值，忽略了以此節點中資料的分佈狀況來描繪輸出結果的方法；我們將提出對距離函數更合理的定義來同時考慮具有權重因子的輸入及輸出空間的測量，且利用局部線性函數更廣泛的定義每個葉節點的輸出模式，並根據遞迴式奇異值分解的最小平方估算法求得此函數之各項係數；實驗結果顯示我們改良的方法在分類及迴歸問題上，都能具有較高的辨視效果及較小的均方差值。

In the last one hundred years, the mankind has invented a lot of convenient tools for pursuing beautiful and comfortable living environment. Computer is one of the most important inventions, and its operation ability is incomparable with the mankind. Because computer can deal with a large amount of data fast and accurately, people use this advantage to imitate human thinking. Artificial intelligence is developed extensively. Methods, such as all kinds of neural networks, data mining, fuzzy logic, etc., apply to each side fields (ex: fingerprint distinguishing, image compressing, antennal designing, etc.). We will probe into to prediction technology according to the decision tree and fuzzy clustering. The fuzzy decision tree proposed the classification method by using fuzzy clustering method, and then construct out the decision tree to predict for data. However, in the distance function, the impact of the target space was proportional inversely. This situation could make problems in some dataset. Besides, the output model of each leaf node represented by a constant restricts the representation capability about the data distribution in the node. We propose a more reasonable definition of the distance function by considering both input and target differences with weighting factor. We also extend the output model of each leaf node to a local linear model and estimate the model parameters with a recursive SVD-based least squares estimator. Experimental results have shown that our improved version produces higher recognition rates and smaller mean square errors for classification and regression problems, respectively.

第一章 簡介 1
1.1 模糊C-均值演算法 2
1.2 決策樹 6
1.3 向量量化法 9
第二章 C-模糊決策樹的方法介紹 13
2.1 使用模糊分群法達到分類的效果 14
2.2 C-模糊決策樹分裂停止條件 17
2.3 C-模糊決策樹之建立 20
第三章 我們的方法 23
3.1 改良式模糊C-均值法 24
3.2 局部線性輸出函數 28
3.3 改良式模糊決策樹之建立 34
第四章 應用於向量量化法 39
4.1 樹狀編碼簿法 39
4.2 我們的方法 45
第五章 實驗結果 54
第六章 總結 69
參考文獻 71

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