Abstract: A novel data classification algorithm based on matrix projection is presented.When matrix projection is not unique, data classification can not be classified perfectly by the the existing matrix projection algorithm.To solve the problem, a pre-classification algorithm of measured data is introduced and a new algorithm is developed to divide unmeasured data into determinable and indeterminable data, using matrix projection algorithm.For the new algorithm, only two projections of two incidence matrices are required to solve the problem and all data can be classified perfectly.The results of mathematical deduction and a mass reconciliation example show that the presented algorithm accurately classifies all data.

摘要： 提出了一种数据分类的两步矩阵投影算法.指出Crowe提出的矩阵投影算法在数据分类中存在由于投影矩阵不惟一，导致已测可校正数据分类不彻底的缺点.采用已测数据预分类的方法，对其进行了修正.在此基础上，将矩阵投影算法引入到了未测数据分类中，提出了基于矩阵投影算法的未测数据分类算法.新算法只需求解两个投影矩阵就可以实现所有数据分类.从而避免了常规方法在未测数据分类时，求解未测数据关联矩阵绝对线性无关列的计算，提高了计算效率.数学推导和算例验证了新算法的有效性.