Everything about Persistence barcode
Technique in topological data analysis
In topological data analysis, a persistence barcode, sometimes shortened to barcode, is an algebraic invariant associated with a filtered chain complex or a persistence module that characterizes the stability of topological features throughout a growing family of spaces. Formally, a persistence barcode consists of a multiset of intervals in the extended real line, where the length of each interval corresponds to the lifetime of a topological feature in a filtration, usually built on a point cloud, a graph, a function, or, more generally, a simplicial complex or a chain complex. Generally, longer intervals in a barcode correspond to more robust features, whereas shorter intervals are more likely to be noise in the data. A persistence barcode is a complete invariant that captures all the topological information in a filtration. In algebraic topology, the persistence barcodes were first introduced by Sergey Barannikov in 1994 as the "canonical forms" invariants consisting of a multiset of line segments with ends on two parallel lines, and later, in geometry processing, by Gunnar Carlsson et al. in 2004. Wikipedia →
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- Read the overview: Persistence barcodeA 5-minute orientation
- Read the landmark paper: An entropy-based persistence barcodeCited 88 times
- Go sideways: Topological data analysisA closely related topic
- Go sideways: Persistent homologyA closely related topic
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🏆 Landmark papers (most cited)
An entropy-based persistence barcode
Distribution of distances between DNA barcode labels in nanochannels close to the persistence length
Vectorization of persistence barcode with applications in pattern classification of porous structures
The space of barcode bases for persistence modules
Using Persistence Barcode to Show the Impact of Data Complexity on the Neural Network Architecture
Conley–Morse Persistence Barcode: A Homological Signature of Combinatorial Bifurcations
Correction to: The space of barcode bases for persistence modules
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