TransitionGraph¶

class gtda.graphs.TransitionGraph(func=<function argsort>, func_params=None, n_jobs=None)[source]¶

Undirected transition graphs from arrays of time-evolving states.

Let A be a two-dimensional array viewed as a time series (along the row axis) of one-dimensional arrays encoding the “state” of a system. The corresponding undirected transition graph (or network) has as vertex set the set of all unique states (rows) in A, and there is an edge between two vertices if and only if one of the corresponding states immediately follows the other in A.

Given a collection of two-dimensional arrays, this transformer performs two tasks:

Optionally, it preprocesses the arrays by applying a function row by row to them. This can be used e.g. as a “compression” step to reduce the size of the state space.

It computes the undirected transition graph of each array as a sparse matrix.

Parameters

func (None or callable, optional, default: numpy.argsort) – If a callable, it is the function to be applied to each row of each array as a preprocessing steps. Allowed callables are functions mapping 1-D arrays to 1-D arrays of constant length, and must be compatible with numpy.apply_along_axis. If None, this function is the identity (no preprocessing). The default is numpy.argsort, which makes the final transition graphs ordinal partition networks 1 2 3.
func_params (None or dict, optional, default: None) – Additional keyword arguments for func.
n_jobs (int or None, optional, default: None) – The number of jobs to use for the computation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors.

effective_func_params\_

A copy of func_params if this was not set to None, otherwise an empty dictionary.

Type: dict

Examples

>>> import numpy as np
>>> from gtda.graphs import TransitionGraph
>>> X = np.array([[[1, 0], [2, 3], [5, 4]],
...               [[5, 4], [5, 4], [5, 4]])
>>> tg = TransitionGraph()
>>> tg = tg.fit(X)
>>> print(tg.transform(X)[0].toarray())
[[0 1]
 [1 0]]
>>> print(tg.transform(X)[1].toarray())
[[1 0]
 [0 0]]