Vector Representations of Persistence Diagrams
Project description
diagram2vec
Diagram2vec provides the following finite-dimensional vector representations of the persistence diagrams:
- persistence statistics (statistics of quanitites such as persistence, midlife, mult.life)
- Euler characteristic curve
- k-th Betti number curves
- persistence curves (curves of quanitites such as persistence, midlife, multitplicative life)
- entropy curves (curves of entropy of quanitites such as persistence, midlife, multitplicative life)
- Adcock-Carlsson polynomials (https://arxiv.org/abs/1304.0530)
All representations have ε-robust versions, i.e. not taking into account intervals with persistence below a certain threshold function.
Installation
Dependencies
- python (>= 3.6)
- numpy
- scipy
The latest version of the diagram2vec can be installed with pip:
pip install diagram2vec
Example of usage
import diagram2vec # list of lists of ndarrays, representing a collection of persistence diagrams diagrams = [ [np.array([[0.0, np.inf], [0.0, 0.4], [0.0, 0.5]]), np.array([[0.1, 0.6], [0.2, 0.4]])], [np.array([[0.0, np.inf], [0.0, 0.1]]), np.array([[0.4, 0.7]])], ] # compute a list of statistics of a distribution of the persistence p := (d - b) quantity stats = diagram2vec.statistics(diagrams, quantity="persistence", statistics=["min", "mean", "count"]) # compute an Euler characteristic curve (a vector of dimension 10) euler_curve = diagram2vec.euler_curve(diagrams, m=10) # compute a Betti number curve, which is default quantity for the `persistence_curve` # (a vector of dimension 50, intervals with persistence below 0.05 are not used) betti_curve = diagram2dec.persistence_curve(diagrams, m=50, f="linear", b=0.05) # compute a curve of persistence quantity # available quanities: 'betti', 'persistence', 'midlife', 'multlife' persistence_curve = diagram2vec.persistence_curve(diagrams, quantity="persistence", m=50) # compute a curve of midlife entropy # available quanities: 'persistence', 'midlife', 'multlife' entropy_curve = diagram2vec.entropy_curve(diagrams, quantity="midlife", m=20) # compute Adcock-Carlsson polynomials polynomials = diagram2vec.polynomials(diagrams, terms=[["birth", "persistence"], ["dmax", "persistence"]], powers=[[1, 1], [2, 4]])
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