【摘要】 复杂海量数据往往表现为多种结构特征的混合体 ,回归类混合模型就是对这种混合体的一个描述 .该文基于统计学的有限混合分布理论和可识别性的相关结果 ,针对回归变量的三种情形 :(1)解释变量固定 ,(2 )解释变量随机 ,(3 )解释变量固定且类别参数指定 ,分别讨论挖掘一般回归类的混合模型的可识别性问题 ,并给出同族回归类混合模型可识别的相应充分条件 .这些条件的一个共同特点是它们都与一类特别的解释变量集合有关 ,而该类集合是由同族的回归函数与回归参数唯一确定的 ,其元素使不同的回归参数对应回归函数的相同值 .特别地 ,当回归函数线性时 ,这类集合就是解释变量空间中的超平面 .更多还原

【Abstract】 Complex and massive data usually appear as a mixture of multiple classes of structures and mixture model of regression classes is a description of such mixture. In this paper, we consider three cases on regression variables: (1) fixed explanatory variables; (2) random explanatory variables; and (3) fixed explanatory variables and specified class parameters. Based on the finite mixture distribution theory from statistics and the related results on identifiability, we discuss the identifiability of mixture models for mining general regression classes in these three cases and give the corresponding sufficient conditions in which mixture models of regression classes with the same regression function are identifiable. All of these conditions are related with a class of sets of explanatory variables. The sets are uniquely determined by the regression function and regression parameters, and their elements make different regression parameters to have the same values of regression function. In particular, when regression functions are linear, these sets become hyperplanes in explanatory variables spaces.更多还原