本論文建立一資料探勘之因素分析的流程，對大量的資料進行因素分析，找尋出影響系統的重要因素。因素分析的過程不單必需保持因素的獨立性，還必而確保分析出的因素對系統是具有足夠的影響力，即對因素依其重要的程度排序。
為了保持因素的獨立性，本論文引用模糊集合論的概念來描述因素之間的獨立性並刪除不具獨立性的因素，使因素間具有某種程度以上的獨立性。另外對於量測因素的重要性則是利用類神經網路的方法，採以一監督式學習的類神經網路來學習因素的重要性。並且考慮階層式的因素結構，使得在系統資訊不足的情況下，提供一個明確的指標來提取因素，且還可藉由觀察整合的未知因素的重要性來判斷系統的資訊量是否充足。

運用此因素分析的方法到電信市場的顧客的貢獻度分析及顧客流失率管理，皆可在學習的誤差值很小的情況下，尋得影響較巨的因素。

In this study, we proposed a method of factor analysis for a huge database so that not only the independence among the factors can be considered, but also the levels of their importance can be measured. To keep the independence between factors, a statistical correlation analysis and the concept of fuzzy set theory are employed, and to measure the importance of factors a neural-based model is developed. A fuzzy set ‘factors are almost dependent’ is used to measure the degree of dependence between factors, and then a hierarchical clustering method is adopted to detect the dependent factors with an -level dependence. Hence, the independent factors also satisfy the same level of requirement. Then, a supervised feedforward neural network is developed to learn the weights of importance of independent factors. In addition, with the designed hierarchical structure, the proposed model facilitates the extraction of new factors when the information of system is not complete. The applicability of the proposed model is evaluated by two cases of customers’ contribution analysis and churn analysis of a telecom company with 0.08% and 1% error rate.

[1] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithm, Plenum Press, New York, 1987.
[2] R. K. De, N. R. Pal and S. K. Pal, “Feature analysis: neural network and fuzzy set theoretic approaches,” Pattern Recognition, Vol 30, No 10, pp.1579-1590, 1997.
[3] S. Goldman, Information Theory, New York: Dover Publications Inc.. 1968.
[4] Martin T. Hagan, Howard B. Demuth and Mark Beale, Neural Network Design, PWS IPT, 1996.
[5] R. A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, Englewood Cliffs, N. J.: Prentice-Hall, 1988.
[6] D. A. Linkens and Min-You Chen, “Input selection and partition validation for fuzzy modeling using neural network”, Fuzzy Sets and Systems, Vol 107, pp 299-308, 1999.
[7] William Mendenhall and Terry Sincich, Statistics for Engineering and the Sciences, Prentice-Hall, 1995.
[8] L. Mikenina and H.-J. Zimmermann, “Improved feature selection and classifica-tion by the 2-additives fuzzy measure”, Fuzzy Sets and Systems, Vol 107, pp 197-218, 1999.
[9] Patrenahalli M. Narendra and Keinosuke Fukunaga, “A branch and bound algorithm for feature subset selection”, IEEE Transactions on Computers, Vol c-26 (9), pp917-922, 1977.
[10] N. R. Pal, “Soft computing for feature analysis,” Fuzzy Sets and Systems, Vol 103, pp.201-221, 1998.
[11] N. R. Pal, J.C. Nandi and M.K Kundu, “Self-crossover: a new genetic operator and its application to feature selection,” Int. J. System Sci. , Vol 29(2), pp.207-212, 1998.
[12] R.J. Kuo, S.C. Chi and S.S. Kao, “A decision support system for locating convenience store through fuzzy AHP,” Computers and Industrial Engineering, Vol 37, pp.323-326, 1999.
[13] M. Ramze Rezaee, B. Goedhart, B.P.F. Lelieveldt, and J.H.C. Reiber, “Fuzzy feature selection”, Pattern Recognition, Vol 32, pp 2011-2019, 1999.
[14] Rudy Setiono and Huan Liu, “Neural-network feature selector”, IEEE Transactions on Neural Networks, Vol 8(3), pp 654-661, 1997.
[15] Wojciech Siedlecki and Jack Sklansly, “On automatic feature selection”, Int. J. Pattern Recognition Arti. Intell., Vol 2(2), pp 197-210, 1988
[16] W. Siedlecki and J. Sklansky, “A note on genetic algorithms for large-scale feature selection”, Pattern Recognition Letter, Vol 10, pp 335-347, 1989.
[17] H. F. Wang and L. S. Lin, “Feature selection in a learning process,” IEEE Trans. Syst., Man, Cybern., to be published.
[18] H. F. Wang and L. S. Lin, “ -Complete information in factor space,” IEEE Transactions on Fuzzy Systems, Vol 6, No 4, pp 553-592, 1998.
[19] H. F. Wang and L. S. Lin, “Factor selection for a system development process,” International Journal of Cybernetics and Systems, to be published.
[20] P. Z. Wang and M. Sugeno, “The factor fields and background structure for fuzzy sets,” Fuzzy Math., Vol 2, No2, pp.45-54, 1982.
[21] P. Z. Wang, “A factor space approach to knowledge representation,” Fuzzy Sets and Systems, Vol 36, pp 113-124, 1990.
[22] Christopher Westphal and Teresa Blaxton, Data Mining Solutions – Methods and Tools for Solving Real-World Problems, John Wiley & Sons, Inc., 1998.
[23] L. A. Zadeh, “Fuzzy sets,” Information and Control, New York: Academic Press, Vol 8, pp.338-353, 1965.
[24] H. –J. Zimmermann, Fuzzy Set Theory and Its Application, Kluwer Academic Publishers, 1991.