導因於全球競爭壓力的增加，使得產品的生命週期越來越短，尤其是在電子產業。因此如果可以加速新產品研發至量產期間的的時間，企業就能夠增加其市場佔有率。然而為了縮短此一時程，工程師常必須依據有限的資料在面對不確定的情況下進行決策，雖然機器學習演算法可協助推導知識，但由於各學習演算法均有其基本之樣本數需求量，此即決定其所能獲取之資訊量，且當樣本數過少時，其學習結果亦可能不考靠。Li等人於2007年在其文章中提出一個名為整體趨勢擴散技術的方法，並將此方法應用在積層陶瓷電容產業的一個案例中。此方法係透過對屬性值域進行延伸並隨機產生許多虛擬值以達填補資料間隙之目的而產生虛擬樣本以協助類神經網路的學習。由於此方法並無討論到輸入屬性與輸出屬性間的相關性，因此本研究使用M5'模式樹僅將屬性間的重要相關性由訓練樣本轉移至產生之虛擬樣本，並同時使用M5'模式樹做為模式建構的方法，實驗除了相同的案例外，亦使用兩筆UCI上所取得之公開資料進行測試比較，結果顯示使用本方法之效果除較原本方法之效果佳外，亦可產出更多的製程知識以供工程師進行參數調校時做為參考。

Product life cycles are becoming shorter, especially in the electrics industry. The issue of time to market has thus become a core competency for firms to increase market share. To shorten the process from product design to mass production, engineers must often make decisions under uncertain conditions with limited information. Although machine learning algorithms can help finding useful information, the smallest training sample size required to establish robust models is important to know, as with insufficient data size the models produced may be unreliable. Li et al. (2009) employed a procedure, called mega-trend-diffusion, to predict the dielectric constant of multi-layer ceramic capacitors in powder pilot runs. The procedure creates more training samples by diffusing the value space of attributes for neural networks to improve predictive capability. In this study, the M5’ model tree is employed to deliver key relations from small data to virtual samples to improve the predictions, and then also applied as the modeling tool to generate classification rules for decision makers. The results of experiments with the case in Li et al. (2009) and two public data sets reveal that the modified method is better than the original approach.

Amirakian, B. and Nishimura, H. (1994), What size network is good for generalization of a specific task of interest? Neural Networks, 7, 321-329.

Anthony, M., Biggs, N. (1997). Computational Learning Theory. Cambridge University Press.

Breiman, L., Friedman, J.H., Olshen, R.A., and Stone, C.J. (1984). Classification and Regression Trees, Belmont, CA：Wadsworth International Group.

Dobra, A. and Gehrke. J.E., (2002). SECRET： A Scalable Linear Regression Tree Algorithm, Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 481-487.

Drucker, H., Burges, C. J. C., Kaufman, L., Smola, A., and Vapnik, V. (1997). Support vector regression machines, in: M. Mozer, M. Jordan, and T. Petsche (Eds.), Advances in Neural Information Processing Systems, vol 9. Cambridge, MA: MIT Press, 1997, pp. 155-161.

Han, J.,& Kamber, M. (2001). Data Mining：Concepts and Techniques. San Francisco：Morgan Kaufmann.

Huang, C. J., Wang, H. F. (2009). Prediction of the Period of Psychotic Episode in Individual Schizophrenics by Simulation-Data Construction Approach.

Huang, C. F., Moraga, C. (2004). A diffusion-neural-network for learning from small samples. International Journal of Approximate Reasoning, 35, 137-161.

Huang, C.F. (1997). Principle of information. Fuzzy Sets and Systems. 91,69-90.

Jang, J.S.R. (1993). ANFIS： adaptive-network-based fuzzy inference systems. IEEE Transactions on Systems, Man and Cybernetics. 23, 665-685.

Karalic, A. (1992). Employing linear regression in regression tree leaves, Proceeding of the 10th European Conference on Artificial Intelligence, 440-441.
Lanouette, R., Thibault, J. and Valade, J. L. (1999), Process modeling with neural networks using small experimental datasets. Computers & Chemical Engineering, 23, 1167-1176.

Li, D. C., Chen, L. S., Lin, Y. S. (2003b). Using functional virtual population as assistance to learn scheduling knowledge in dynamic manufacturing environments. International Journal of Production Research 41(17), 4011-4024.

Li, D. C., Hsu, H. C., Tsai, T. I., Lu, T. J., Hu, S. C. (2007). A new method to help diagnose cancers for small sample size. Expert Systems with Applications, 33 420-424.

Li, D. C., Lin, Y. S. (2006). Using virtual sample generation to build up management knowledge in the early manufacturing stages. European Journal of Operational Research, 175 413-434.

Li, D. C., Liu, C. W. (2009). A Neural Network weight determination model designed uniquely for small data set learning. Expert Systems with Applications 36 9853-9858.

Li, D. C., Wu, C., Chen, F. M. (2005). Using Data-fuzzification Technology in Small Data Set Learning to Improve FMS Scheduling Accuracy. International Journal of Advanced Manufacturing Technology 27, 321-328.

Li, D. C., Wu, C., Tsia, T. I., and Chang, F. M. (2006b). Using Mega-Fuzzification and Data Trend Estimation in Small Data Set Learning for Early FMS Scheduling Knowledge. Computers & Operations Research 33, 1857-1869.

Li, D. C., Wu, S. S., Tsai, T. I., Lina, Y. S. (2007).Using mega-trend-diffusion and artifical samples in small data set learning for early flexible manufacturing system scheduling knowledge, Computers and Operations Research, 34, 966-982.

Li, D.C., Yeh, C.W. (2008). A non-parametric learning algorithm for small manufacturing data sets. Expert Systems with Applications, 34, 391-398.

Loh, W.Y. (2002). Regression trees with unbiased variable selection and interaction detection. Statistica Sinica, 12, 361-386.

Niyogi,P., Girosi, F., Tomaso, P. (1998). Incorporating prior information in machine learning by creating virtual examples. Proceeding of the IEEE 275-298.

Onisko, A., Druzdzel, M.J., Wasyluk, H. (2001). Learning Bayesian network parameters from small data sets: Application of Noisy-OR gates. International Journal of Approximate Reasoning 27, 165–182.

Quinlan, J. R. (1992). Learning with continuous classes. Proceedings of the Australian Joint Conference on Artificial Intelligence, 343-348.

Rhodes, C. J. and Keefe, E. M. J. (2006), Social network topology: a Bayesian approach. Journal of the Operational Research Society advance online publication, 13 December 2006 (DOI 10.1057/palgrave.jors.2602352).

Wang, Z. N., Dimassimo, C., Tham, M. T. and Morris, A. J. (1994), A procedure for determining the topology of multilayer feedforward neural networks. Neural Networks, 7, 291-300.

Wang, X. H., Chen, R. Z., Gui, Z. L. and Li, L. T. (2003), The grain size effect on dielectric properties of BaTiO3 based ceramics. Materials Science and Engineering, 99, 199-202.

Wang, Y., and Witten, I.H. (1997). Inducing model trees for continuous classes, Proceedings of poster papers of the 9th European Conference on Machine Learning.
Wolpert, D. (1992), Stacked generalization. Neural Networks, 5, 241-259.

Yoon, D. H. and Lee, B. I. (2004), Processing of barium titanate tapes with different binders for MLCC applications- Part I: Optimization using design of experiments. Journal of the European Ceramic Society, 24, 739-752.