区间型符号数据的因子分析及其应用

Factor Analysis for Interval-valued Symbolic Data and Its Application

符号数据分析是一种新兴的数据挖掘技术,区间数是最常用的一种符号数据。基于误差分析理论,研究针对区间数据的因子分析方法。将区间数看作一个由中点和半径构成的有序偶,并将半径视为区间数的极限误差。对中点样本阵进行因子分析,得到因子得分的中点值。然后将半径样本阵按照误差传递公式,得到因子得分的极限误差。由因子得分的中点值和极限误差最终得到因子得分的区间值。最后以股票的市场综合表现评价问题为案例,进行了应用研究。

Symbolic data analysis is a new data mining technology and interval number is a most important type of symbolic data. Based on error analysis theory, a factor analysis method for interval-valued symbolic data is proposed. An interval number can be seen as an ordered pair composed of its center and radius, where the radius can be considered as its limit error. A factor analysis is first being done on the center sample data matrix, by which the center factor scores are obtained. In the following, on the basis of the error transferring formula, the limit error of the factor scores is gained by the radius sample data matrix. As a result, the interval factor scores are achieved through the center and limit error of the factor scores. Finally, by virtue of problem of evaluation on several stocks＇ integrated behavior in the market, the application study is made.