Persistence modules on commutative ladders of finite type
EG Escolar, Y Hiraoka - Discrete & Computational Geometry, 2016 - Springer
We study persistence modules defined on commutative ladders. This class of persistence
modules frequently appears in topological data analysis, and the theory and algorithm …
modules frequently appears in topological data analysis, and the theory and algorithm …
Algorithmic construction of acyclic partial matchings for multidimensional persistence
M Allili, T Kaczynski, C Landi, F Masoni - Discrete Geometry for Computer …, 2017 - Springer
Given a simplicial complex and a vector-valued function on its vertices, we present an
algorithmic construction of an acyclic partial matching on the cells of the complex. This …
algorithmic construction of an acyclic partial matching on the cells of the complex. This …
[HTML][HTML] Staircase algebras and graded nilpotent pairs
M Boos - Journal of Pure and Applied Algebra, 2017 - Elsevier
We consider a class of finite-dimensional algebras, the so-called “Staircase algebras”
parametrized by Young diagrams. We develop a complete classification of representation …
parametrized by Young diagrams. We develop a complete classification of representation …
A method deciding topological relationship for self-organizing maps by persistent homology analysis
R Futagami, T Shibuya - 2016 55th Annual Conference of the …, 2016 - ieeexplore.ieee.org
Self-organizing maps (SOM) are an effective method to quantize data space into several
subspaces so-called centroids based on the probability distribution over input data space …
subspaces so-called centroids based on the probability distribution over input data space …
[PDF][PDF] Morse Reductions for Quiver Complexes and Persistent Homology on the Finite-Type Commutative Ladder Quivers
エスカラ,エマソンガウ - 2016 - catalog.lib.kyushu-u.ac.jp
Persistent homology is a tool in topological data analysis for studying the robust topological
features of data. The persistence diagram provides a compact way to summarize the …
features of data. The persistence diagram provides a compact way to summarize the …
位相的データ解析とパーシステントホモロジー
平岡裕章 - 数学, 2016 - jstage.jst.go.jp
位相的データ解析とパーシステントホモロジー 平 岡 裕 章 Page 1 361 位相的データ解析とパーシ
ステントホモロジー 平岡裕章 1 序 実験やシミュレーションにより得られる高次元のデータに対して,クラスター …
ステントホモロジー 平岡裕章 1 序 実験やシミュレーションにより得られる高次元のデータに対して,クラスター …