企業為了提升競爭力及滿足顧客需求，產品不但多元化，並更加縮短產品生命週期。在時間與成本壓力下，新產品開發過程往往在未取得有效數量樣本數前即進行量產。樣本數不足的問題普遍存在實務上，如何從有少數樣本中挖掘有意義資訊是小樣本學習的重要議題。目前小樣本學習方法已有學者發展出:資料的轉換、擴充虛擬樣本以增加資料量、以及建構新屬性等方法。其中小樣本學習虛擬樣本產生方法以整體趨勢擴展技術(mega diffusion techniques；MTD)較為成熟，然而整體趨勢擴展技術存在實務使用上的限制，其假設資料屬性間必須是獨立，但是大多實務上資料屬性之間存在一定程度的相關性，因此，本研究結合基因表示規劃法(gene expression programming；GEP)與整體趨勢擴展技術，建構具非線性關聯性虛擬樣本，並用以解決整體趨勢擴展技術不適用於相關性資料的問題，提升實務資料預測準確度。本研究以台灣某面板廠新產品小樣本資料做為實驗案例，實驗結果顯示本研究方法確實較原樣本預測誤差有顯著改善，與整體擴展技術相比較有更佳的預測效果。

In order to enhance competitiveness and meet customer needs, enterprises make various products and shorten product life cycles. Under the pressure of time and cost, new product development process often start mass production before acquiring valid number of samples. The problem of inadequate number of samples exists in practice. Hence, how to mine meaningful information from limited quantity of data is an important issue of small data learning. Nowadays, the small data learning methods include data transformed, attributes construction and expansion of virtual samples to increase the Quantity of data. Mega diffusion techniques (MTD) is a mature method of generating virtual samples in small data learning, but MTD has some restrictions on using in practice, which assumes that attributes of the data must be independent. However, most of the data exist some correlation between attributes in practice. Therefore, the study combines gene expression programming (GEP) and MTD to construct nonlinearly related virtual samples, which solves the problem of MTD’s inability to apply to related information, and improve the accuracy of forecasting. The study take the small samples of TFT-LCD production as experiment case in the research. The experimental result shows that the method indeed has significant improvement in contrast to the prediction error of the original data, and better prediction than MTD.

葉怡成，民國92年3月，神經網路模式應用與實作，儒林圖書公司.
Amrit, T., 2000. The knowledge management toolki : practical techniques for building a knowledge management system, Prentice Hall, N.J.
Chi, M.T.H., Glaser, R., and Farr, M. J., 1988. The nature of expertise, London : Lawrence Erlbuam Associates.
Chen, S. T., Chang, I. F., Shie, C. T., and Yu, P. S., 2006. Flood stage forecasting model using support vector machines. Journal of Taiwan Water Conservancy, 54(2), 50-61.
Drucker, H., Burges, C. J. C., Kaufman, L., Smola, A., and Vapnik, V.,1997. Support vector regression machines. Advances in Neural Information Processing Systems, 9, 155-161.
Ferreira, C., 2001. Gene expression programming : A new adaptive algorithm for solving problems . Complex Systems , 13 (2) ,87-129.
Ferreira, C., 2002. Genetic representation and neutrality in gene expression programming . Advances in Complex Systems , 5(4), 389-408.
Goldberg, D. E.,1989, Genetic algorithms in search, optimization, and machine learning, Addison-Wesley.
Goldberg, D. E., and Miller, B. L.,1995. Genetic algorithms, tournament selection ,and the effects of noise. Complex Systems, 9 (3) , 193-212.
Huang, C. F., 1997. Principle of information diffusion. Fuzzy Sets and Systems, 91, 69-90.
Huang, C.F., and Moraga, C., 2004. A diffusion-neural-network for learning from small samples. International Journal of Approximate Reasoning, 35, 137-161.
Jang, J. S. R., 1993. ANFIS: adaptive-network-based fuzzy inference systems. IEEE Transactions on Systems, Man and Cybernetics, 23, 665-685.
Koza, J. R., 1992. Genetic Programming. Cambridge, MA: MIT Press.
Kubat, M., Holte , B. C., and Matwin , S.,1998, Machine learning for the detection of oil spills in satellite radar images. Machine Learning, 30, 195-215.
Li, D. C., Chen, L. S., and Lin, Y. S., 2003. Using functional virtual population as assistance to learn scheduling knowledge in dynamic manufacturing environments. International Journal of Production Research, 41, 4011-4024.
Li, D. C., Hsu, H. C., Tsai, T.I., Lu, T. J., and Hu, S. C., 2007b. A new method to help diagnose cancers for small sample size. Expert Systems with Applications, 33, 420-424.
Li, D. C., Tsai, T. I., and Shi, s., 2009. A prediction of the dielectric constant of multi-layer ceramic capacitors using the mega-trend-diffusion technique in powder pilot runs : case study. International Journal of Production Research, 19, 51-69.
Li, D. C., Wu, C. S., and Chang, 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. S., Tsai, T. I., and Chang, F.M., 2006. Using mega-fuzzification and data trend estimation in small data set learning for early FMS scheduling knowledge. Computers and Operations Research, 33 (6), 1857–1869.
Li, D. C., Wu, C. S., Tsai, T. I., and Lin, Y.S., 2007a. Using mega-trend-diffusion and artificial samples in small data set learning for early flexible manufacturing system scheduling knowledge. Computers and Operations Research, 34 (4), 966–982.
Li, D. C., Chen, C. C., Chang, C.J., and Chen, W. C., 2011. Employing Box-and-Whisker plots for learning more knowledge in TFT-LCD pilot runs. International Journal of Production Research.( In Press)
Johnson, E.J., 1988. Expertise and decision under uncertainty : performance and process. In: Chi, M.T.H., Glaser, R., Farr, M.J.(Eds.), The Nature of Expertise. Lawrence Erlbaum, Hillsdale, NJ, 209–228.
MacCormack, A., Verganti, R. and Iansiti, M., 2001. Developing products on internet time: The anatomy of a flexible development process, Management Science 47(1), 133–150.
Mitra, P., Murthy, C. A., and Pal, S. K.,2002. Unsupervised feature selection using feature similarity. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(3), 301–312.
Nonaka, I. and Hirotake, T., 1995. The Knowledge – Creating Company, Oxford University Press, New York.
Niyogi, P., Girosi, F., and Tomaso, P., 1998. Incorporating prior information in machine learning by creating virtual examples. Proceeding of the IEEE, 275-298.
Polanyi, M., 1966. The tacit dimension. London: Routledge & Kegan Paul.
Rumelhart, D. E., Hinton, G. E., and Willians, R. J., 1986. Learning representations by back-propagating errors. Nature, 323, 533-536.
Vapnik, V. N., 1995. The Nature of Statistical Learning Theory, Springer-Verlag, New York.
Whitley, D.,1989. The Genitor Algorithm and Selection Pressure :Why Rank−Based Allocation of Reproductive Trials is Best, Proceeding of the Third International Conference on Genetic Algorithms, 116−121, Morgan Kaufmann Publishers, San Mateo, California.