具適應性體積學習之完整與不完整資料之分群與辨認

Clustering and Classification of Complete and Incomplete Data with Adaptive Volume

楊　梓(Tze Yang)

指導教授 ： 姚立德

國立臺北科技大學/電資學院/電機工程系所/碩士(2007年)

https://doi.org/10.6841/NTUT.2007.00008

摘要

在模糊分群的領域中，G-K演算法(Gustafson-Kessel Algorithm)假定了一個固定的體積給所有的橢圓判定區域(Ellipsoid Decision Region)。由於資料的分佈範圍或形式不同，為了提高模糊分群的可靠性應對判定區域的體積做適當調整。
本論文提出對判定區域體積做適應學習之模糊分群演算法，透過梯度下降法(Gradient Descent Method)對G-K演算法之目標函數進行推導，使用適應性學習(Adaptive Learning)的方法直接對橢圓形判定區域的體積做遞迴式更新，使判定區域能更精確的被學習，以降低不同的資料分佈形態可能造成的誤差；另外，在資料開採的領域中，模糊分群的演算易受雜訊干擾而發生偏移，本文結合雜訊群聚(Noise Cluster)的概念至演算步驟中，來確保模糊分群演算時的強健性，並與其它的演算法進行分群與辨認的探討。
在部分生物資訊或工程檢測的資料分群領域中，為解決由測試信號微弱而使得部分空間維度數值遺失所造成的不完整資料(Incomplete Data)，在過去已有許多不同的預測或處理策略被提出。而本文透過對原型資料之特徵訊號的分析，再結合前面提出的方法來對這種類型的問題進行處理，同時與不同的不完整資料預測策略比較以驗證本論文提出的方法。

關鍵字

G-K演算法 ； 適應性學習 ； 模糊分群 ； 雜訊群聚 ； 不完整資料

並列摘要

In fuzzy clustering field, Gustafson-Kessel Algorithm assumes a fixed volume for each ellipsoid decision regions. For the dissimilarity of data distributing range and shape, it should tune the volume of decision regions suitably to raisie the dependability of fuzzy clustering.
This thesis is proposed a fuzzy clustering algorithm with adaptive learning of ellipsoid decision regions through the derivation of G-K objective functional by Gradient Descent Method. Utilizing an adaptive learning approach to update the volume of decision regions recursively let the decision regions can be learned more precisely, and then diminishes the errors resulted by dissimilarity of distribution; Besides, in data mining field, the fuzzy clustering computation is easily affected by the interfered noise. This thesis combines the concept of Noise Cluster to the proposed algorithm to ensure the robust of computing, and then do some discussions of clustering and classification with some other algorithms.
In some data clustering fields of bioinformatics or engineering examining, for solving the incomplete data resulted from missing values of some space dimension, many predicting and handling strategies have already been proposed in the past. In this thesis, it deals with these kinds of problems through analyzing feature signals of prototype data and combining the proposed algorithm. Simultaneously, comparing with other predicting strategies of incomplete data confirms the method proposed in this thesis.

並列關鍵字

G-K Algorithm ； Adaptive Learning ； Fuzzy Clustering ； Noise Cluster ； Incomplete Data

參考文獻

1. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, New York: Plenum, 1981.

2. D. E. Gustafson and W. C. Kessel, “Fuzzy Clustering With a Fuzzy Covariance Matrix,” Proc. IEEE Conf. Decision Contr., San Diego, CA, 1979, pp.761-766.

3. J. K. Dixon, “Pattern Recognition with partly missing data,” IEEE Trans. on System, Man and Cybernetics, vol. SMC-9, Oct. 1979, pp.517-521.

4. H. Timm C. Doring, and R. Kruse, “Different approaches to fuzzy clustering of incomplete datasets,” International Journal of Approximate, pp.239-249, 2004.

5. J. Kittler, “Classification of incomplete pattern vector using modified discriminant function,” IEEE Trans. Comput., vol. C-27, pp.367-375, Apr. 1978.