Vol.3 No.4 (July 2013)
Unsupervised Learning System with Prescription Constraint for Each Unit
周 瑾 ：湖北第二师范学院数学与数量经济学院
>An unsupervised learning system with prescription condition (the weight coefficients are nonnegative and their sum is 1) is constructed, and its definite linear algorithms, the constraint least squares solutions, are proposed. This is the kernel content of this paper. The unsupervised learning system composed of some basic units is similar to a structural equation model (SEM), and is a kind of indeterminate equations. The traditional algorithms of SEM including partial least squares (PLS) and linear structure relationship (LISREL) are indefinite iterative algorithms, and may be non- convergent and non-unique. This paper constructed the inverse equations according to the idea of factor analysis, and obtained a middle solution based on modular length constraint (the length of latent variable is temporarily assumed as 1). Then the definite linear algorithm of the model making use of the latent regression with prescription constraints is constructed and to substitute traditional iterative algorithms. Data examples, including the index summarizing model for the Diffusion Indexes of Income and Price, and the model of Army Moral Index, show the analysis abilities and classification functions of the learning systems for economic or psychological problems, and extend the application scope of unsupervised learning systems. A kind of index summarizing modular with a latent variable and unknown weight coefficients are the basic units in the systems.
周 瑾 , 林 卉 , 童恒庆 (2013) 基于单元配方约束的无监督学习系统。 计算机科学与应用， 3， 222-227. doi: 10.12677/CSA.2013.34038
 R. I. Chang, P. Y. Hsiao. Unsupervised query-based learning of neural networks using selective-attention and self-regulation. IEEE Transactions on Neural Networks, 1997, 8(2): 205-217.
 D. LeLy, P. Chow. High-performance reconfigurable hardware architecture for restricted Boltzmann machines. IEEE Transactions on Neural Networks, 2010, 21(11): 1780-1792.
 W. K. Wong, M. Sun. Deep learning regularized Fisher mappings. IEEE Transactions on Neural Networks, 2011, 22(10): 1668-1675.
 K. Labusch, E. Barth and T. Martinetz. Simple method for high- performance digit recognition based on sparse coding. IEEE Transactions on Neural Networks, 2008, 19(11): 1985-1989.
 R. Gençay, R. Gibson. Model risk for European-style stock index options. IEEE Transactions on Neural Networks, 2007, 18(1): 193-202.
 H. J. Ader, I. Bramsen. Computer modeling of social processes, Chapter 7: Representation of a structural equation model as a neural network. London: SAGE Publications, 1998: 126-138.
 H. Tong, L. Xiong and H. Peng. Self-organized path constraint neural network structure and algorithm. 13th International Conference on Neural Information Processing, Hong Kong, 3-6 October 2006, 457-466.
 C. Fornell, M. D. Johnson, E. W. Anderson, J. Cha and B. E. Bryant. The American customer satisfaction index: Nature, purpose, and findings. Journal of Marketing, 1996, 60(4): 7-18.
 S. Hsua, W. Chenb and M. Hsiehc. Robustness testing of PLS, LISREL, EQS and ANN-based SEM for measuring customer satisfaction. Total Quality Management & Business Excellence, 2006, 17(3): 355-372.
 C. Wang, H. Tong. Best iterative initial values for PLS in a CSI model. Mathematical and Computer Modelling, 2007, 46(3-4): 439-444.
 Q. Tong, X. Zou, C. Wang and H. Tong. A definite linear algorithm for structural equation model. Mathematical and Computer Modelling, 2010, 52(5-6): 744-751.
 方开泰, 王东谦, 吴国富. 一类带约束的回归——配方回归[M]. 计算数学, 1982, 4: 57-69.
 童恒庆. 数据分析与统计计算软件DASC[M]. 北京: 科学出版社, 2005.
 H. Tong, T. K. Kumar and Y. Huang. Developing econometrics —Statistical inference for simultaneous equations model; Definite linear algorithm for SEM. Chichester: John Wiley & Sons, 2011.
 M. Artelli, R. Deckro, D. Zalewski, S. Leach and M. Perry. A control theory model of deployed soldiers’ morale. International Journal of Operational Research, 2010, 7(1): 31-53.
 C. Li. Review of morale research. Advances in Psychological Science, 2006, 14(2): 193-198.
 郭树行, 李妍. 基于投影寻踪方法的模糊综合估计与聚类的工程项目风险评估[J]. Computer Science and Application, 2011, 1(2): 63-68.
 T. L. Tien. A new grey prediction model FGM(1, 1). Mathematical and Computer Modelling, 2009, 49(7-8): 1416-1426.
 H. Arabshahi. Modeling low field electron mobility in group III nitride materials. Computer Science and Application, 2012, 1(1): 4-8.
 T. L. Saaty. Decision making with the analytic hierarchy process. International Journal of Services Sciences, 2008, 1: 83-98.