# GraphGeodesicDistance¶

class gtda.graphs.GraphGeodesicDistance(n_jobs=None, directed=False, unweighted=False, method='auto')[source]

Distance matrices arising from geodesic distances on graphs.

For each (possibly weighted and/or directed) graph in a collection, this transformer calculates the length of the shortest (directed or undirected) path between any two of its vertices, setting it to numpy.inf when two vertices cannot be connected by a path.

The graphs are represented by their adjacency matrices which can be dense arrays, sparse matrices or masked arrays. The following rules apply:

• In dense arrays of Boolean type, entries which are False represent absent edges.

• In dense arrays of integer or float type, zero entries represent edges of length 0. Absent edges must be indicated by numpy.inf.

• In sparse matrices, non-stored values represent absent edges. Explicitly stored zero or False edges represent edges of length 0.

Parameters
• 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.

• directed (bool, optional, default: True) – If True (default), then find the shortest path on a directed graph. If False, then find the shortest path on an undirected graph.

• unweighted (bool, optional, default: False) – If True, then find unweighted distances. That is, rather than finding the path between each point such that the sum of weights is minimized, find the path such that the number of edges is minimized.

• method ('auto' | 'FW' | 'D' | 'BF' | 'J', optional, default: 'auto') – Algorithm to use for shortest paths. See the scipy documentation.

Examples

>>> import numpy as np
>>> from gtda.graphs import TransitionGraph, GraphGeodesicDistance
>>> X = np.arange(4).reshape(1, -1, 1)
>>> X_tg = TransitionGraph(func=None).fit_transform(X)
>>> print(X_tg.toarray())
[[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
[0 0 0 0]]
>>> X_ggd = GraphGeodesicDistance(directed=False).fit_transform(X_tg)
>>> print(X_ggd)
[[0. 1. 2. 3.]
[1. 0. 1. 2.]
[2. 1. 0. 1.]
[3. 2. 1. 0.]]

__init__(n_jobs=None, directed=False, unweighted=False, method='auto')[source]

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

fit(X, y=None)[source]

Do nothing and return the estimator unchanged.

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

Parameters
• X (list of length n_samples, or ndarray of shape (n_samples, n_vertices, n_vertices)) – Input data: a collection of adjacency matrices of graphs. Each adjacency matrix may be a dense or a sparse array.

• y (None) – There is no need for a target in a transformer, yet the pipeline API requires this parameter.

Returns

self

Return type

object

fit_transform(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
• X (list of length n_samples, or ndarray of shape (n_samples, n_vertices, n_vertices)) – Input data: a collection of adjacency matrices of graphs. Each adjacency matrix may be a dense or a sparse array.

• y (None) – There is no need for a target in a transformer, yet the pipeline API requires this parameter.

Returns

Xt – Output collection of dense distance matrices. If the distance matrices all have the same shape, a single 3D ndarray is returned.

Return type

list of length n_samples, or ndarray of shape (n_samples, n_vertices, n_vertices)

fit_transform_plot(X, y=None, sample=0, **plot_params)

Fit to data, then apply transform_plot.

Parameters
• X (ndarray of shape (n_samples, ..)) – Input data.

• y (ndarray of shape (n_samples,) or None) – Target values for supervised problems.

• sample (int) – Sample to be plotted.

• **plot_params – Optional plotting parameters.

Returns

Xt – Transformed one-sample slice from the input.

Return type

ndarray of shape (1, ..)

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

mapping of string to any

static plot(Xt, sample=0, colorscale='blues', plotly_params=None)[source]

Plot a sample from a collection of distance matrices.

Parameters
• Xt (list of length n_samples, or ndarray of shape (n_samples, n_vertices, n_vertices)) – Collection of distance matrices, such as returned by transform.

• sample (int, optional, default: 0) – Index of the sample to be plotted.

• colorscale (str, optional, default: 'blues') – Color scale to be used in the heat map. Can be anything allowed by plotly.graph_objects.Heatmap.

• plotly_params (dict or None, optional, default: None) – Custom parameters to configure the plotly figure. Allowed keys are "trace" and "layout", and the corresponding values should be dictionaries containing keyword arguments as would be fed to the update_traces and update_layout methods of plotly.graph_objects.Figure.

Returns

fig – Plotly figure.

Return type

plotly.graph_objects.Figure object

set_params(**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.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

object

transform(X, y=None)[source]

Compute the lengths of graph shortest paths between any two vertices.

Parameters
• X (list of length n_samples, or ndarray of shape (n_samples, n_vertices, n_vertices)) – Input data: a collection of n_samples adjacency matrices of graphs. Each adjacency matrix may be a dense array, a sparse matrix, or a masked array.

• y (None) – Ignored.

Returns

Xt – Output collection of dense distance matrices. If the distance matrices all have the same shape, a single 3D ndarray is returned.

Return type

list of length n_samples, or ndarray of shape (n_samples, n_vertices, n_vertices)

transform_plot(X, sample=0, **plot_params)

Take a one-sample slice from the input collection and transform it. Before returning the transformed object, plot the transformed sample.

Parameters
• X (ndarray of shape (n_samples, ..)) – Input data.

• sample (int) – Sample to be plotted.

• **plot_params – Optional plotting parameters.

Returns

Xt – Transformed one-sample slice from the input.

Return type

ndarray of shape (1, ..)