简化Q矩阵的渐增式扩张生成算法

简化Q矩阵（Qr阵）是规则空间模型与属性层次方法的重要概念。基于属性层次结构，提出有效／无效项目的定义，研究属性层次结构的可达矩阵与有效项目之间的关系，给出有效／无效项目的判定定理。基于逐步向前回归的思想提出了求解Qr阵的渐增式扩张算法，给出相关理论依据。在考虑有效项目数的基础上，与Tatsuoka方法进行了实验比较，对属性个数为10的情况采用线性回归方法为两种方法建立了数学模型。

INCREMENTAL AUGMENT ALGORITHM BASED ON REDUCED Q-MATRIX

Reduced Q-matrix (Qr matrix) plays an important role in the rule space model (RSM) and the attribute hierarchy method (AHM). Based on the attribute hierarchy, a valid/invalid item is defined. The judgment method of the valid/invalid item is developed on the relation between reachability matrix and valid items. And valid items are explained from the perspective of graph theory. An incremental augment algorithm for constructing Qr matrix is proposed based on the idea of incremental forward regression, and its validity is theoretically considered. Results of empirical tests are given in order to compare the performance of the incremental augment algorithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outperforms the Tatsuoka algorithm, and the analysis of the two algorithms also show linear growth with respect to the number of valid items. Mathematical models with 10 attributes are built for the two algorithms by the linear regression analysis.