離線式手寫數字辨識雖已被研究多年，但因為手寫字變異性大，對辨識研究者是極大挑戰；雖然手寫數字辨識已有高辨識率但仍有學習及辨識耗時間等缺點，本研究重點能改善上述缺點，但是仍要有高辨識率。
本研究採用MNIST資料庫做為訓練及測試用資料。特徵抽取，使用統計式特徵(Statistic feature)方法。雖然統計式特徵會有特徵向量維度很高的缺點，但本研究以有效特徵抽取方法，使特徵維度再130低維度就能將十種分類區分開。
為了提升辨識效果，在這研究中加入Fisher’s LDF (Linear discriminant function)特徵轉換，經實驗証實在不分群情況下，以特徵轉換後的特徵(未經學習訓練)做辨識就有92.6%的極高辨識率。本研究係以GLVQ(Generalized Learning Vector Quantization)為基礎，GLVQ為針對LVQ的收歛性與完整性加以改善。本研究除了探討LVQ及GLVQ理論並將其應用於手寫數字辨識，經實驗証明了兩者都有不錯辨識效果，也證實我們的特徵處理方法是有效的。
本研究中提出加了權重(weight)的LVQ及GLVQ成為WLVQ及WGLVQ，新學習法WLVQ及WGLVQ在每次學習過程中除了調整代表分類的參考向量外，同時也調整各分量權重，對權重輕的每次往下調的多點使權重輕的與權重重的權種值區分的更加明顯，經實驗証明WGLVQ或WLVQ都比原先分類器有較好辨識效果。
經過WGLVQ分類器學習訓練後以測試資料辨識(open test)會有97.6%辨識率，若再把每種分類分成16群，則更可將辨識率提高到98.2%，辨識率雖不及Ernst所提出的LIRA分類法有99.3%辨識率，但本研究辨識10000筆資料僅需1~2分鐘，相較於LIRA分類法虛耗時高達30分鐘，本系統應屬具有實用性。

Recognition of off-line handwritten numerals has been the subject of research for many years. Since handwritten numerals widely vary in their shapes, recognizing them has been difficult and challenging. Although a high level of recognition has been achieved, the shortcomings of time-consuming learning and recognition still persist. The present research focuses on overcoming these defects, while maintaining a high recognition level.
The research discussed in the present paper makes use of the MNIST database for learning and testing. For feature extraction, statistic features are used in the present research. Employing statistic features is saddled with the difficulty of a high number of dimensions, yet the present research, by using 130 dimensions, is able to distinguish between ten classifications.
To make character recognition more effective, in the present research transformation by Fisher's LDF (linear discriminant function) is applied to input characters. As experiments have shown, after transformation of non-clustered features (without learning) a level of recognition of 92.6% is achieved. In the present research, the method of WGLVQ, which is based on GLVQ (generalized learning vector quantization), is employed. Better convergence is achieved by GLVQ, and it is able to improve for LVQ. Experiments conducted within the current research have shown that both LVQ and GLVQ, applied to recognizing handwritten numerals, have quite good convergence behavior, also confirming the effectiveness of feature processing presented here.
In the present research, the methods of LVQ and GLVQ are enhanced by weighting, yielding novel methods of WLVQ and WGLVQ. Therein, in every learning step, not only directions classifying reference vectors are adjusted, but also weights of every vector. With every step the weights of less-weighted vectors decrease, resulting in more pronounced distinctions of light and heavy weights. According to experiments, both WLVQ and WGLVQ exhibit more effective character recognition.
With classification by WGLVQ and including learning, in an open test a level of recognition of 97.6% is achieved. With 16 clusters for each class, the recognition level rises to 98.2%. This result trails the level of 99.3% attained by Ernst using classification by LIRA, but while recognizing 10000 samples takes 30 minutes for the LIRA’s classification, the present approach allows recognition of 10000 samples in 1 - 2 minutes. The present research offers a more practical approach.

英文部分：
1.D.-F. Chang, J. Y.-J. Hsu, and C.-S Fuh. Handwritten character recognition using a neural network. 5th OCR & DA, pp. 17-20, Taiwan 1996.
2.G. M. T. Man, J. C. H. Poon. A new similarity measurement method for fuzzy-attribute graph matching and its application to handwritten character recognition. Fuzzy Logic Technology and Applications, Ed. By R. J. Marks, IEEE, Inc, New York City, 1994.
3.H.-C. Huang and S.-G. Miaou. A simplified neocognitron for recognition of handwritten Arabic numerals. 5th OCR & DA, pp 132-139, Taiwan, 1996.
4.J. Cho, M. Ahmadi, and M. Shridhar. A hierarchical neural network architecture for handwritten numeral recognition. Pattern Recognition, 30(2):289-294, 1997..
5.A Sato and K Yamada, “Generalized Learning Vector Quantization,” Advances in Neural Information Processing 8, MIT Press, Cambridge, MA, USA, pp, 423-429, 1996.
6.Ernst Kussul,Tatyana Baidyk,Improve Method of Handwritten Digit Recognition 2000
7.Pao-Chung Chang, San-Wei Sun and Sin-Horng Chen, “Mandarin Tone Recognition by Multi-Layer Perceptron, “IEEE ICASSP-90, pp. 517-520, 1990.
8.Pao-Chung Chang, Keh-Hwa Shyu and Gan-How Chang, ‘A Hand-Written Chinese Character Recognition System,’ CVGIP-97,1997.
9.T. Kohonen, “LVQ_PAK Version 3.1-The Learning Vector Quantization Program Package, “LVQ Programming Team of the Helsinki University of Technology, 1995.
10.A. Sato and K. Yamada, “A Criterion for Training Reference Vectors and Improved Vector Quantization,” Proc. Of the International Conference on Neural Networks. Pp.161-166, 1994.
11.Pao-Chung Chang and Biing_Hwang Juang, “Discriminative Training of Dynamic Programming Based Speech Recognizers,” IEEE Tr. On Speech and Audio Processing, pp. 135-143, April, 1993.
12.R.O. Duda and P.E. Pattern Classification and Scene Analysis, John Wiley & Sons, Inc., 1973.
13.Pao-Chung Chang, Keh-Hwa Shyu, Ming-Chwen Yang and Gan-How Chang, ‘Hand-Written Digit Recognition with Minimum Error Formulation,’ CVGIP-96, pp. 191-197, 1996.
14.Le Cun, Y. Bottou, L., Bengio, Y. Haffner, P., “Gradient-based Learning Applied to Document Recognition”, Proceeding of the IEEE V.86, N 11, November 1998, pp. 2278-2344.
15.Y. Le Cun, B. Boser, J.S. Denker, D. Henderson “Handwritten Digital Recognition with a Back-Propagation Network”, AT&T Bell Laboratories, Holmdel, N.J. 07733.
16.Sung-Won Yoon & Seong Taek Chung “Handwritten Numeral Recognition Using Eigenimage Method and Feature-Based Method.
17.Suzete E.N. Corriea, “On the performance of Wavelets for Handwritten Numeralg Recognition.”
18.Kussul, E.,Baidyk, T.Kasatina, L., Lukovich, V “Rosenblatt Perceptrons for Handwritten Digit Recognition”. Proceedings of International Joint Conference on Neural Networks IJCNN. 2001, V.2, 2001, pp. 1516-1520.
19.Hsin-Chia Fu, Hung-Yuan Chang, Yeong Yuh Xu, and H-T Pao, “User Adaptive Handwriting Recognition by Self-Growing Probabilistic Decision-Based Neural Networks”, IEEE Transactions on Neural Networks, Vol. 11, No.6,pp.1373-1384,November 2000.
20.J.-M. Chen and W.-H. Tsai. Recognition of multi-font and multi-size printed Chinese characters using attributed graph representations and code matching. 5th OCR & DA. pp.113-121, Taiwan. 1996.
21.Z. Chi, J. Wu, and H. Yan. Handwritten numeral recognition using Self-Organizing Maps Maps and fuzzy rules. Pattern Recognition, 28(1):59-66, 1995.
22.T.Kawatani,”Handwritten Numeral Recognition with the Improve LDA Method”,IEEE June 1996
23.Automatic recognition of handprinted characters-the state of art.Proceedingings of the IEEE ,68(4):469-487,1980
24.A.K. Chhabra, Z. An D.Balick, G. Cerf, K. Loris, P. Sheppard, R. Smith, and B. Wittner. High-order statistically derived combinations of geometric features for handprinted character recognition. Proc. Second Int’l Conf. Doc. Anal. And Recogn. (ICDAR ’93). Pp. 397-401, 1993.
25. C. Y. Suen, C. Nadal, R. Legault, T.A. Mai, and L. Lam. Computer recognition of unconstrained handwritten numerals. Proceedings of IEEE, 80(7):1161-1180, 1992.
26.J. Cao, M. Ahmadi, and M. Shridhar. Recognition of handwritten numerals with multiple feature and multistage classifier, Pattern Recognition, 28(2):153-160, 1995.
27.J.-F Wang and G.-E Wang A new approach for recognition of unconstrained handwritten numerals. Second National Workshop on Optical Character Recognition, Taipei, Taiwan, 1992.
28.M. Shridhar and A. Badreldin. Recognition of isolated and simply connected handwritten numberals. Pattern Recognition, 19(1):1-12, 1996
29.N. W. Strathy and C. Y. Suen. A new system for reading handwritten zip codes. Proc. Third Int’l Conf. Doc. Anal. And Recogn. (ICDAR’95), pp. 74-77, August 1995.
30.S.-B. Cho. Neural-network classifiers for recognizing totally unconstrained handwritten numerals. IEEE Transactions on Neural Networks, 8(1):43-53. January 1997.
31.T. Kohonen. The Self-Organizing Map. Proceedings of the IEEE, 78(9):1464-1480, September 1990.
32.Brazilian Bank Check Handwritten Legal Amount Recognition
Cinthla Obladen De Almendra Freitas, Abdenaim EL Yacoubi, Robert Sabourin
33.O.D.Trier,A.K.Jains and T.Taxt.Feature extraction methods for character-recognition-a-survey.Pattern-Recognition,29(4):641-662,1996
中文部分
[34]郭癸蘭 ,2002，手寫身分證字號辨識系統 ,高雄第一科技大學,碩士論文
[35]呂昶昇 ,2001，手寫成績登錄系統，大同大學,碩士論文
[36]吳偉賢 ,1999，筆劃特徵用於離線中文字的辨認國立中央大學,博士論文
[37]鄭萬旗 ,1999，類神經網路於手寫數字辨識之應用，淡江大學,碩士論文
[38]林育慈，1997，離線手寫印刷體英數字之辨識，國立台灣師範大學，碩士論文
[39]徐克華，1997，特徵轉換用於光學中文文字識別，國立中央大學，博士論文
[40]張保忠，徐克華，以GLVQ進行之手寫數字識別實驗，中華電信研究所研究季刊，2002
[41]陳慶彥，1997，傳真手寫數字自動辨識系統，私立元智大學，碩士論文
[42]陳慶逸，1997，以類神經網路為基礎的文數字辨識技術之研究，私立淡江大學，碩士論文
[43]葉柏園，1996，向量量化器與類神經網路設計及其在圖樣辨識之應用，私立中原大學，碩士論文
[44]阮星明，1991，類神經網路在線上手寫英數字辨識應用之研究，國立交通大學，碩士論文
[45]藍天寶，1993，以二分類神經網路與模糊邏輯之手寫文字辨識系統，私立中原大學，碩士論文
[46]戴敏倫，1989，快速學習類神經網路手寫英數字與中文字辨認系統，私立中原大學，碩士論文
[47]王爵兒，1989，以神經網路作手寫英數字辨認，國立交通大學，碩士論文
[48] 葉怡成，類神經網路模式 應用與實作，儒林圖書公司，2000
[49] 繆紹綱，1999，數位影像處理，全華科技圖書股份有限公司
[50] 蘇木春、張孝德，機器學習、類神經網路、模糊系統以及基因演算法則，全華科技圖書股份有限公司,1997.
[51] 張真誠 黃國峰 陳同孝電子影像技術 松崗圖書公司,2000