Abstract: The matter of margin is one of the kernel problems when facing the complicated datum.By now，there are two algorithms which can be considered as relatively successful algorithms.They are the maximum margin of Support Vector Machine algorithm and Tangent Vector Quantization algorithm.They both have the merits and defects.The homology theory is introduced into this paper for resolving disadvantages of latest methods，this paper presents a homology boudary division learning algorithm using the idea of the homology and this algorithm is justified through the experiment.

Key words: homology algebra, homology boundary learning algorithm, boundary learning algorithm

摘要： 面对复杂的数据，边缘问题是其核心问题之一。目前比较成功的算法有SVM最大边缘算法和TVQ算法，这些算法各有优缺点。论文针对目前方法中存在的一些不足，引进同调理论，用同调代数的思想构建了一种同调代数的边缘学习算法，并通过实验和实例进行验证。

关键词: 同调代数, 同调边缘学习算法, 边缘学习算法