Alternating Recursive Method for Q-matrix Learning
Alternating Recursive Method for Q-matrix Learning
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发表时间：
2014
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通讯作者：
Yuan Sun;Shiwei Ye;Shunya Inoue;Yi Sun
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作者：
Yuan Sun;Shiwei Ye;Shunya Inoue;Yi Sun
影响认知诊断模型（CDM）的关键问题是如何指定属性和 Q 矩阵。在本文中，我们首先尝试使用布尔矩阵分解（BMF）方法来表达CDM中的联合模型。由于 BMF 是一个 NPhard 问题 [2]，我们提出了一种递归方法，在每一步中更新属性矩阵（其秩等于 1）。由于布尔代数是不可逆的，因此需要时间来递归计算和更新矩阵，特别是当属性数量很大时。为了加快计算速度，我们使用了 Heaviside 阶跃函数，它允许我们将递归计算过程分解为普通非负矩阵，并通过将它们映射回布尔矩阵来获得结果。提出了两种不同的算法：确定性启发式算法和随机算法。实际测试的仿真结果表明，该方法可以很好地从项目响应数据中学习原始Q矩阵。
The key issue affecting Cognitive Diagnostic Models (CDMs) is how to specify attributes and the Q-matrix. In this paper, we first attempt to use the Boolean Matrix Factorization (BMF) method to express conjunctive models in CDMs. Because BMF is an NPhard problem [2], we propose a recursive method that updates the attribute matrix (its rank equals to one) in each step. As Boolean algebra is irreversible, it requires time to recursively compute and update the matrix, especially when the number of attributes is large. To speed up computations, we use a Heaviside step function, which allows us to decompose the recursive computing process into normal non-negative matrices and get the results by mapping them back into a Boolean matrix. Two different algorithms are presented: a deterministic heuristic algorithm and a stochastic algorithm. Simulation results from an actual test show that the proposed method can learn the original Q-matrix well from item response data.