# BettiCurve¶

class gtda.diagrams.BettiCurve(n_bins=100, n_jobs=None)[source]

Betti curves of persistence diagrams.

Given a persistence diagram consisting of birth-death-dimension triples [b, d, q], subdiagrams corresponding to distinct homology dimensions are considered separately, and their respective Betti curves are obtained by evenly sampling the filtration parameter.

Important note:

• Input collections of persistence diagrams for this transformer must satisfy certain requirements, see e.g. fit.

Parameters
• n_bins (int, optional, default: 100) – The number of filtration parameter values, per available homology dimension, to sample during fit.

• 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.

homology_dimensions_

Homology dimensions seen in fit, sorted in ascending order.

Type

tuple

samplings_

For each number in homology_dimensions_, a discrete sampling of filtration parameters, calculated during fit according to the minimum birth and maximum death values observed across all samples.

Type

dict

Notes

The samplings in samplings_ are in general different between different homology dimensions. This means that the j-th entry of a Betti curve in homology dimension q typically arises from a different parameter values to the j-th entry of a curve in dimension q’.

__init__(n_bins=100, n_jobs=None)[source]

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

fit(X, y=None)[source]

Store all observed homology dimensions in homology_dimensions_ and, for each dimension separately, store evenly sample filtration parameter values in samplings_. Then, return the estimator.

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

Parameters
• X (ndarray of shape (n_samples, n_features, 3)) – Input data. Array of persistence diagrams, each a collection of triples [b, d, q] representing persistent topological features through their birth (b), death (d) and homology dimension (q). It is important that, for each possible homology dimension, the number of triples for which q equals that homology dimension is constants across the entries of X.

• 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 (ndarray of shape (n_samples, n_features, 3)) – Input data. Array of persistence diagrams, each a collection of triples [b, d, q] representing persistent topological features through their birth (b), death (d) and homology dimension (q). It is important that, for each possible homology dimension, the number of triples for which q equals that homology dimension is constants across the entries of X.

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

Returns

Xt – Betti curves: one curve (represented as a one-dimensional array of integer values) per sample and per homology dimension seen in fit. Index i along axis 1 corresponds to the i-th homology dimension in homology_dimensions_.

Return type

ndarray of shape (n_samples, n_homology_dimensions, n_bins)

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

plot(Xt, sample=0, homology_dimensions=None, plotly_params=None)[source]

Plot a sample from a collection of Betti curves arranged as in the output of transform. Include homology in multiple dimensions.

Parameters
• Xt (ndarray of shape (n_samples, n_homology_dimensions, n_bins)) – Collection of Betti curves, such as returned by transform.

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

• homology_dimensions (list, tuple or None, optional, default: None) – Which homology dimensions to include in the plot. None means plotting all dimensions present in homology_dimensions_.

• plotly_params (dict or None, optional, default: None) – Custom parameters to configure the plotly figure. Allowed keys are "traces" 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 Betti curves of diagrams in X.

Parameters
• X (ndarray of shape (n_samples, n_features, 3)) – Input data. Array of persistence diagrams, each a collection of triples [b, d, q] representing persistent topological features through their birth (b), death (d) and homology dimension (q). It is important that, for each possible homology dimension, the number of triples for which q equals that homology dimension is constants across the entries of X.

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

Returns

Xt – Betti curves: one curve (represented as a one-dimensional array of integer values) per sample and per homology dimension seen in fit. Index i along axis 1 corresponds to the i-th homology dimension in homology_dimensions_.

Return type

ndarray of shape (n_samples, n_homology_dimensions, n_bins)

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, ..)