# giotto.graphs.TransitionGraph¶

class giotto.graphs.TransitionGraph(func=<function argsort>, func_params=None, n_jobs=None)

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:

1. 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.

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

Parameters
funcNone 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_paramsNone or dict, optional, default: None

n_jobsint 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.

Attributes
effective_func_params_dict

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

Notes

In general, the shapes of the sparse matrices output by transform will be different across samples, and the same row or column index will refer to different states in different samples.

References

1

M. Small, “Complex networks from time series: Capturing dynamics”, 2013 IEEE International Symposium on Circuits and Systems (IS-CAS2013), 2013; doi: 10.1109/iscas.2013.6572389.

2

M. McCullough, M. Small, T. Stemler, and H. Ho-Ching Iu, “Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems”; Chaos: An Interdisciplinary Journal of Nonlinear Science 25 (5), p. 053101, 2015; doi: 10.1063/1.4919075.

3

A. Myers, E. Munch, and F. A. Khasawneh, “Persistent homology of complex networks for dynamic state detection”; Phys. Rev. E 100, 022314, 2019; doi: 10.1103/PhysRevE.100.022314.

Examples

>>> import numpy as np
>>> from giotto.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]]


Methods

 fit(self, X[, y]) Do nothing and return the estimator unchanged. fit_transform(self, X[, y]) Fit to data, then transform it. get_params(self[, deep]) Get parameters for this estimator. set_params(self, \*\*params) Set the parameters of this estimator. transform(self, X[, y]) Create transition graphs from the input data and return their adjacency matrices.
__init__(self, func=<function argsort at 0x10f7b81e0>, func_params=None, n_jobs=None)

Initialize self. See help(type(self)) for accurate signature.

fit(self, X, y=None)

Do nothing and return the estimator unchanged.

This method is there to implement the usual scikit-learn API and hence work in pipelines.

Parameters
Xndarray, shape (n_samples, n_time_steps, n_features)

Input data.

yNone

There is no need for a target in a transformer, yet the pipeline API requires this parameter.

Returns
selfobject
fit_transform(self, X, y=None, **fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters
Xnumpy array of shape [n_samples, n_features]

Training set.

ynumpy array of shape [n_samples]

Target values.

Returns
X_newnumpy array of shape [n_samples, n_features_new]

Transformed array.

get_params(self, deep=True)

Get parameters for this estimator.

Parameters
deepboolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns
paramsmapping of string to any

Parameter names mapped to their values.

set_params(self, **params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns
self
transform(self, X, y=None)

Create transition graphs from the input data and return their adjacency matrices. The graphs are simple, undirected and unweighted, and the adjacency matrices are sparse matrices of type bool.

Parameters
Xndarray, shape (n_samples, n_time_steps, n_features)

Input data.

yNone

There is no need for a target in a transformer, yet the pipeline API requires this parameter.

Returns
Xtarray of sparse boolean matrices, shape (n_samples,)

The collection of n_samples transition graphs. Each transition graph is encoded by a sparse matrix of boolean type.