Incremental Augment Algorithm Based on Reduced Q-Matrix
Shuqun Yang, Shuliang Ding, Ding Qiu-lin · Transaction of Nanjing University of Aeronautics and Astronautics · 2010
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.