基于单元配方约束的无监督学习系统
Unsupervised Learning System with Prescription Constraint for Each Unit

作者: 周 瑾 :湖北第二师范学院数学与数量经济学院; 林 卉 , 童恒庆 :武汉理工大学理学院数学系;

关键词: 无监督学习系统配方条件约束最小二乘确定性线性算法Unsupervised Learning System Prescription Condition Constraint Least Squares Definite Linear Algorithms

摘要:
本文核心内容是提出了一种基于单元配方约束条件(所有权系数非负而其和为1)的无监督学习系统,以及基于约束最小二乘解的确定性算法。系统本身类似于结构方程模型(SEM),属于不定方程组,传统的算法包括偏最小二乘(PLS)与协方差拟合(LISREL)算法都是不确定的迭代算法,存在计算可能不收敛、结果可能不唯一的问题。本文则根据因子分析思想构造逆向影响方程,利用模长约束(潜变量的长度假设为1)作为中间技巧求得过渡解,最后添加合理的配方约束进行潜变量回归,成功构造了系统的确定性线性算法,从而替代了传统的迭代算法。两个数据例子,包括收入和价格扩散指数的汇总问题和军队士气模型,演示了系统在经济和心理领域的分析和分类功能,也是对无监督学习系统应用范围的极好扩充。
>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.

文章引用: 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

参考文献

[1] 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.

[2] D. LeLy, P. Chow. High-performance reconfigurable hardware architecture for restricted Boltzmann machines. IEEE Transactions on Neural Networks, 2010, 21(11): 1780-1792.

[3] W. K. Wong, M. Sun. Deep learning regularized Fisher mappings. IEEE Transactions on Neural Networks, 2011, 22(10): 1668-1675.

[4] 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.

[5] R. Gençay, R. Gibson. Model risk for European-style stock index options. IEEE Transactions on Neural Networks, 2007, 18(1): 193-202.

[6] 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.

[7] 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.

[8] 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.

[9] 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.

[10] C. Wang, H. Tong. Best iterative initial values for PLS in a CSI model. Mathematical and Computer Modelling, 2007, 46(3-4): 439-444.

[11] 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.

[12] 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.

[13] 童恒庆. 数据分析与统计计算软件DASC[M]. 北京: 科学出版社, 2005.

[14] 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.

[15] 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.

[16] C. Li. Review of morale research. Advances in Psychological Science, 2006, 14(2): 193-198.

[17] 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.

[18] T. L. Tien. A new grey prediction model FGM(1, 1). Mathematical and Computer Modelling, 2009, 49(7-8): 1416-1426.

[19] H. Arabshahi. Modeling low field electron mobility in group III nitride materials. Computer Science and Application, 2012, 1(1): 4-8.

[20] T. L. Saaty. Decision making with the analytic hierarchy process. International Journal of Services Sciences, 2008, 1: 83-98.

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