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...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 algo-rithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outper-forms 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.展开更多
Let E be non-negative integer set Z+ or integer set Z. Q=（q<sub> </sub>: i, j∈E） is called a birth-and-death matrix if Q satisfies the following （ⅰ）—（ⅲ）: （ⅰ） q<sub> </sub>=0, |i-j|...Let E be non-negative integer set Z+ or integer set Z. Q=（q<sub> </sub>: i, j∈E） is called a birth-and-death matrix if Q satisfies the following （ⅰ）—（ⅲ）: （ⅰ） q<sub> </sub>=0, |i-j|】1, 0【q<sub> </sub>【+∞, |i-j|=1, （1） （ⅱ） sum from j≠i q<sub> </sub>≤q<sub>i</sub>≡-q<sub>ü</sub>≤+∞, （2） （ⅲ） if E=Z<sub>+</sub>, q<sub>i</sub>【+∞ and i≠0 or E=Z and q<sub>i</sub>【+∞ then q<sub>ü-1</sub>+q<sub>ü+1</sub> =q<sub>i</sub> （3） Let Q be a birth-and-death matrix. We call Q a birth-and-death matrix with展开更多
基金Supported by the National Natural Science Foundation of China (30860084,60673014,60263005)the Backbone Young Teachers Foundation of Fujian Normal University(2008100244)the Department of Education Foundation of Fujian Province (ZA09047)~~
文摘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 algo-rithm and the Tatsuoka algorithm upon the running time. Empirical evidence shows that the algorithm outper-forms 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.
基金the National Natural Science Foundation of China.
文摘Let E be non-negative integer set Z+ or integer set Z. Q=（q<sub> </sub>: i, j∈E） is called a birth-and-death matrix if Q satisfies the following （ⅰ）—（ⅲ）: （ⅰ） q<sub> </sub>=0, |i-j|】1, 0【q<sub> </sub>【+∞, |i-j|=1, （1） （ⅱ） sum from j≠i q<sub> </sub>≤q<sub>i</sub>≡-q<sub>ü</sub>≤+∞, （2） （ⅲ） if E=Z<sub>+</sub>, q<sub>i</sub>【+∞ and i≠0 or E=Z and q<sub>i</sub>【+∞ then q<sub>ü-1</sub>+q<sub>ü+1</sub> =q<sub>i</sub> （3） Let Q be a birth-and-death matrix. We call Q a birth-and-death matrix with
