迭代奇异值分解的学生成绩恢复方法

Iterative singular value decomposition method for recovery of student scores

为了有效地对学生成绩数据进行恢复,提出一种迭代奇异值分解的学生成绩恢复方法。该方法采用矩阵表示学生成绩,利用该矩阵具有低秩的特性,在给定缺失元素的初始值后,利用奇异值分解得到缺失元素的近似值,而该近似值比初始值更加接近真实值。再将求到的近似值代替初始值,经过多次迭代,最终可求到成绩表中缺失元素的真实值。该方法的优点是在缺失元素恢复过程中,利用了所有已知元素信息,并将所有已知元素平等地对待。模拟实验和真实实验结果表明该方法能够快速、精确地恢复出学生的真实成绩。

To recover the missing student scores,an iterative singular value decomposition（SVD）method is presented in this paper. The student scores are depicted by a matrix with low rank. Given initial values of missing data,the approximate values which are nearer the real values than the initial values can be obtained by SVD method. After several iterations,the real values can be recovered. The innovations of the method are that all the known elements are utilized in process ofmissing data recover and all the known elements are treated uniformly. Therefore,the method can precisely recover the missing data. The experimen-tal results with both simulate and real data show that the presented method has the ability to recover the students’scores rapidly and accurately.