Topological Data Analysis (TDA) employs concepts from algebraic topology to mine structural characteristics of data.  In particular, TDA involves computing topological invariants of the data over an associated filtration. Topological invariants, such as homology, have been employed for a growing set of bioinformatic and network applications where statistical measures are insufficient in detecting topological characteristics of the data. This paper introduces a new topological measure called Incremental Critical Cells (iCC) that detects homology class changes of a topological filtration of discrete data.  The iCC algorithm is scalable and can identify homology classes beyond that of current TDA tools. This capability is demonstrated through analysis and experimental results.

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Incremental Critical Cells for Homology Characterization

  • Nicholas O. Malott,
  • Anurag Yadav,
  • Philip A. Wilsey

摘要

Topological Data Analysis (TDA) employs concepts from algebraic topology to mine structural characteristics of data.  In particular, TDA involves computing topological invariants of the data over an associated filtration. Topological invariants, such as homology, have been employed for a growing set of bioinformatic and network applications where statistical measures are insufficient in detecting topological characteristics of the data. This paper introduces a new topological measure called Incremental Critical Cells (iCC) that detects homology class changes of a topological filtration of discrete data.  The iCC algorithm is scalable and can identify homology classes beyond that of current TDA tools. This capability is demonstrated through analysis and experimental results.