Matrix Method for Persistence Modules on Commutative Ladders of Finite Type
Matrix Method for Persistence Modules on Commutative Ladders of Finite Type
复制标题
有限型交换梯上持久模的矩阵法
DOI：
10.1007/s13160-018-0331-y
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发表时间：
2018
影响因子：
0.9
通讯作者：
Hiroshi
中科院分区：
文献类型：
--
作者：
Asashiba;Hideto; Escolar;Emerson G.; Hiraoka;Yasuaki; and Takeuchi;Hiroshi
交换梯上的持久性模块理论提供了持久同源性的扩展。然而，仍然缺乏计算广义持久性图的有效算法。在这项工作中，我们将持久性模块视为 zigzag 模块之间的态射，可以用块矩阵形式表示。对于表示有限情况 ()，我们提供了一种算法，该算法使用某些允许的行和列运算来计算块矩阵的范式。以这种形式，获得了 M 的不可分解分解，从而获得了其持久性图。
The theory of persistence modules on the commutative laddersprovides an extension of persistent homology. However, an efficient algorithm to compute the generalized persistence diagrams is still lacking. In this work, we view a persistence moduleMonas a morphism between zigzag modules, which can be expressed in a block matrix form. For the representation finite case (), we provide an algorithm that uses certain permissible row and column operations to compute a normal form of the block matrix. In this form an indecomposable decomposition ofM, and thus its persistence diagram, is obtained.