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

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.