本文的主要目的是延續以資料間距為基礎的非監督式聚類演算法,並提供了一個較佳的分割方式,避免在圓形分佈的切割方式下,將不屬於當前聚類的資料點給切割進來。接著再以適當的猜測方式決定初始聚類中心位置後,除了利用兩兩相鄰資料點間距大小的特徵來決定聚類切割處之外,並針對此切割範圍內的所有資料點,以單維度方向兩兩相鄰資料點的間距為特徵,選定為矩形的半長,做矩形切割。此做法可以節省多餘的切割空間,更利於延展型聚類的分類結果。最後,為了試驗本文所提出的方法,總共模擬了六組不同特性的資料樣本。在模擬過程中,除了將這六組試驗樣本以本文所提的演算法執行分類,並將Fuzzy c-Means演算法、以資料間距為基礎的非監督式聚類演算法的分類結果以圖示列出對照。模擬結果顯示,本文所提出的方法比起Fuzzy c-Means演算法、以資料間距為基礎的非監督式聚類演算法擁有更高的正確性。

The main purpose of this paper is extended based on “An unsupervised clustering approach based on its data distribution” to offer a better way of cutting apart between the cluster and its neighbors. The new method presented in this paper will cut apart clusters by rectangle division. Comparing with round division, rectangle division can save some space and makes the clustered result more correct when dividing tall and slender data sets. The algorithm presented in this paper has been implemented, analysed and tested on six data sets. The results show that the proposed algorithm has much better classified ability than the Fuzzy c-Means algorithm and the algorithm of “An unsupervised clustering approach based on its data distribution”.

[1] J.M. Keller, M.R. Gray and J.A. Givens, “A fuzzy k-nearest neighbors algorithm,” IEEE Transactions on System, Man, and Cybernetics,Vol. SMC-15, pp. 580-585, 1985.
[2] B. Bhattacharya, D. Kaller, “Reference set thinning for the k-nearest neighbor decision rule,” Pattern Recognition, In proc. of the 14th International Conference, Vol. 1, pp. 238-242, 1998.
[3] R.J. Schalkoff, Pattern recognition: statistical, structural and neural approaches, John Wiley & Sons, 1992.
[4] S. Miyamoto, “An overview and new methods in fuzzy clustering,” Knowledge-Based Intelligent Electronic Systems, In proc. of the KES '98 2nd International Conference,Vol. 1, pp. 33-40, 1998.
[5] N.B. Karayiannis, “Generalized fuzzy c-means algorithms, ” Fuzzy Systems, In Proc. of the Fifth IEEE International Conference, Vol. 2, pp. 1036 -1042 , 1996.
[6] D. Hershfinkel, “Accelerated fuzzy c-means clustering algorithm,” In SPIE Proc. , Vol. 2761, pp.41-52,1996.
[7] J. Pei, J. Fan,W. Xie and X. Yang, “ A new effective soft clustering method--sectional set fuzzy c-means (S2FCM) clustering,” Signal Processing, In Proc. of the 3rd International Conference,Vol. 1, pp. 773 -776 , 1996.
[8] J. Liu and W. Xie, “ A genetics-based approach to fuzzy clustering,” Fuzzy Systems, In Proc. of the Fourth IEEE International Conference,Vol. 4, pp. 2233 -2240, 1995.
[9] M.A. Egan, “Locating clusters in noisy data: a genetic fuzzy c-means clustering algorithm, ” Fuzzy Information Processing Society - NAFIPS, Conference of the North American, pp. 178 –182, 1998.
[10] M. Gen and R. Cheng, Genetic algorithms and engineering design, John Wiley & Sons, 1997.
[11] M.A. Egan, M. Krishnamoorthy and K. Rajan, “Comparative study of a genetic fuzzy c-means algorithm and a validity guided fuzzy c-means algorithm for locating clusters in noisy data,” Evolutionary Computation, In Proc. of the IEEE International Conference, pp. 440 -445, 1998
[12] T.P. Hong and C.Y. Lee, “Induction of fuzzy rules and membership functions from training examples,” Fuzzy Sets and Systems, Vol. 84, pp. 33-47, 1996.
[13] H. Ishibuchi, T. Nakashima and T. Morisawa, “Voting in fuzzy rule-based systems for pattern classification problems,” Fuzzy Sets and Systems, Vol 103, pp. 223-238, 1999.
[14] H. Suh, J.H. Kim and C.H. Rhee, “Convex-set-based fuzzy clustering,” Fuzzy Systems, IEEE Transactions, Vol. 73, pp. 271-285, 1999 .
[15] N. Zahid, O. Abouelala, M. Limouri and A. Essaid, “Unsupervised fuzzy clustering,” Pattern Recognition Letters, Vol. 20, pp. 123-129, 1999.
[16] H.K. Kwan and Y. Cai, “A fuzzy neural network and its application to pattern recognition,” Fuzzy Systems, IEEE Transactions, Vol. 23, pp. 185-193, 1994.
[17] N.R. Pal, G.K. Mandal and E.V. Kumar, “Comments on “A fuzzy neural network and its application to pattern recognition”,” Fuzzy Systems, IEEE Transactions, Vol. 74, pp. 479-480, 1999.
[18] 孫宗瀛,楊英魁, Fuzzy控制:理論、實作與應用, 全華科技圖書, 1995.
[19] 謝維信, 工程模糊數學方法, 儒林圖書, 1992.
[20] 蘇木春,張孝德, 機器學習, 全華科技圖書, 1999.
[21] G.F. Luger and W.A. Stubblefield, Artificial Intelligence, Addison Wesley, 1998.
[22] A.M. Bensaid, L.O. Hall, J.C. Bezdek, L.P. Clarke, M.L. Silbiger, J.A. Arrington and R.F. Murtagh, “Validity-guided (re)clustering with applications to image segmentation,” Fuzzy Systems, IEEE Transactions, Vol. 42, pp. 112 –123, 1996.
[23] H.C. Lu, T.H. Hung and M.F. Yeh, “Approximated clustering via modified grey relational analysis,” The Journal of Grey Systems, Vol. 2, pp. 87-104, 1998.
[24] A. Flores-Sintas, J.M. Cadenas and F. Martin, “ Partition validity and defuzzication,” Fuzzy Sets and Systems, Vol. 112, pp. 433-447, 2000.
[25] Mika Sato-Ilic, “On fuzzy clustering based regression models,” Fuzzy Information,Vol. 1, pp. 216-221, 2004.
[26] Anguita, D. Ridella, S. Rivieccio and F. Zunino R, “Unsupervised clustering and the capacity of support vector machines, ” Neural Networks, IEEE International Conference, Vol. 3, pp. 25-29, 2004.
[27] Byeungwoo Jeon and Landgrebe D.A,“Partially supervised classification using weighted unsupervised clustering, ” Geoscience and Remote Sensing, IEEE Transactions, Vol. 37 ,pp. 1073-1079, 1999.
[28] Yan Zhan, Fang Yuan and Xi-Zhao Wang, “Verification of supervised clustering validity and its applications, ” Machine Learning and Cybernetics, Vol. 4, pp. 1833-1836, 2002.
[29] 林彥廷, 以資料分佈為基礎的非監督式聚類分割法, 台科大碩士論文, 2000.
[30] Rosenberger. C and Chehdi. K, “Unsupervised clustering method with optimal estimation of the number of clusters: application to image segmentation, ” Pattern Recognition, Vol. 1, pp. 656-659, 2000.
[31] Jung-Hyuck Jo, Ingram M.A and Jayant N., “Deterministic angle clustering in rectangular buildings based on ray-tracing, ” Communications, IEEE Transaction, Vol. 53, pp. 1047-1052, 2005.