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 vertex i and vertex j≠i if and only if the state corresponding to vertex j immediately follows the one corresponding to vertex i, somewhere 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 transition graph of each array as a sparse matrix of zeros and ones.

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 step. Allowed callables are functions mapping 1D arrays to 1D 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]]])
>>> X_tg = TransitionGraph().fit_transform(X)
>>> print(X_tg[0].toarray())
[[0 1]
 [1 0]]
>>> print(X_tg[1].toarray())
[[0]]