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Sparse-TDA: Sparse Realization of Topological Data Analysis for Multi-Way Classification [article]

Wei Guo, Krithika Manohar, Steven L. Brunton, Ashis G. Banerjee
2017 arXiv   pre-print
TDA, thus, yields key shape descriptors in the form of persistent topological features that can be used for any supervised or unsupervised learning task, including multi-way classification.  ...  Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples.  ...  Another critical tool facilitating multi-way classification is the feature-driven sparse sampling of high-dimensional data.  ... 
arXiv:1701.03212v4 fatcat:gfczyee5a5fonj3gl23g3qp32y

2018 Index IEEE Transactions on Knowledge and Data Engineering Vol. 30

2019 IEEE Transactions on Knowledge and Data Engineering  
., þ, TKDE Oct. 2018 1943-1956 Sparse-TDA: Sparse Realization of Topological Data Analysis for Multi- Way Classification.  ...  TKDE Feb. 2018 400-406 Image classification Sparse-TDA: Sparse Realization of Topological Data Analysis for Multi-Way Classification.  ... 
doi:10.1109/tkde.2018.2882359 fatcat:asiids266jagrkx5eac6higrlq

Learning Representations of Persistence Barcodes

Christoph D. Hofer, Roland Kwitt, Marc Niethammer
2019 Journal of machine learning research  
In particular, we focus on persistent homology, the prevalent tool used in topological data analysis.  ...  We consider the problem of supervised learning with summary representations of topological features in data.  ...  We also thank Robert Elsässer and Gregor Bankhamer for providing the subgraphs for the experiments in Section 6.6, funded by the Austrian Science Fund (FWF project P 27613).  ... 
dblp:journals/jmlr/HoferKN19 fatcat:p7tnxqglqrdmjlhlq5adygelku

Persistence Curves: A canonical framework for summarizing persistence diagrams [article]

Yu-Min Chung, Austin Lawson
2021 arXiv   pre-print
Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data.  ...  For that reason, transforming these diagrams in a way that is compatible with machine learning is an important topic currently researched in TDA.  ...  Introduction Topological data analysis (TDA) is a rising field in mathematics, statistics, and computer science. The fundamental concept of TDA is to understand the shape of data.  ... 
arXiv:1904.07768v4 fatcat:owge2gb2f5b4jcp2dcsyh4rfgu