Papers › Matrix Method for Persistence Modules on Commutative Ladders of Finite Type
Matrix Method for Persistence Modules on Commutative Ladders of Finite Type
Hideto Asashiba, Emerson G. Escolar, Yasuaki Hiraoka, Hiroshi Takeuchi
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The theory of persistence modules on the commutative ladders CLₙ(τ) provides 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 module M on CLₙ(τ) as a morphism between zigzag modules, which can be expressed in a block matrix form. For the representation finite case (n≤4), 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 of M, and thus its persistence diagram, is obtained.
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