二维隐马尔可夫模型的几个等价定义

Formal Definitions Equivalent for Two Dimensional Hidden Markov Models

摘要: 为了对一般二维隐马尔可夫模型建立严格的形式化定义,在参照低阶二维隐马尔可夫模型定义的基础上,通过对高阶模型进行分析,总结了一般二维隐马尔可夫模型的5个形式化定义,并证明了它们之间的等价性.这些等价性结果有助于加深对二维隐马尔可夫模型本质的理解,为进一步研究提供严格的形式化基础.

Abstract: In order to build formal definitions for general Two-dimensional Hidden Markov Models(2-D HMM) and to facilitate their studies in theory and application,this paper summarizes five strict definitions of 2-D HMM with their equivalence proven by high-order cases on low-order ones.These equivalent results are helpful to understand the nature of 2-D HMM and to provide a strict basis of formalization for further research.