与数据挖掘相关的整数矩阵的左右可逆性研究  

Research on Left-Right Invertibility for Integer Matrix Related with Data Mining

作　　者：陆成刚[1] 

机构地区：[1]浙江工业大学理学院,杭州310023

出　　处：《计算机科学》2016年第5期247-251,268,共6页Computer Science

基　　金：浙江省重点科技专项重大工业项目(2013C01045)资助

摘　　要：考虑了数据挖掘中基于整数矩阵的离散数据观测模型,并提出了观测矩阵的整数分解问题。该问题实质上是求解经典的线性丢番图系统,只是要求基矩阵是被分解矩阵的一个部分。提出了一个新的求解方法——左右逆法,并研究了与此相关的一类满秩非方整数矩阵的整数左右可逆性问题,提出了一些左右可逆的充分条件以及求整数左右逆的方法。该方法可以求出某些最小二乘法无法求出的整数逆,并与最小二乘法结合构成了一个整数分解的完整解决方案。We considered the discrete data observation model based on integer matrix like boolean observation matrix,or non-negative observation matrix in history.We proposed the problem on the integer decomposition for any integer observation matrix.The problem is equivalent to solving one classical Diophantine linear system in nature,but the only condition is that the base matrix is originated from the decomposed matrix part.Then we provided a new method based on left-right inverse to find the integer inverse of the base matrix.Because the base matrix choice is an option designing in engineering,it is convenient to consider the base matrixes only of possessing integer inverse.Additionally,it is known that any non-full rank matrix can be decomposed into the product of two full rank matrixes.So we explored some sufficient conditions on the existence of integer left-right inverse only for full-rank rectangular matrix,and also designed the integer inverse algorithm in computation.Our proposed integer inverse constructor can find integer inverse under some conditions while the constructor based on the least squares method fails.Lastly our method merged with the least squares method will become a complete solution to integer decomposition of integer observation matrix.

关 键 词：整数矩阵 整数左右可逆性 MOORE-PENROSE逆 最小二乘法 

分 类 号：O151.21[理学—数学]