Filtering

class gtda.diagrams.Filtering(homology_dimensions=None, epsilon=0.01)

Filtering of persistence diagrams.

Filtering a diagram means discarding all points [b, d, q] representing topological features whose lifetime d - b is less than or equal to a cutoff value. Technically, discarded points are replaced by points on the diagonal (i.e. whose birth and death values coincide), which carry no information.

Parameters

• homology_dimensions (list, tuple, or None, optional, default: None) – When set to None, subdiagrams corresponding to all homology dimensions seen in fit will be filtered. Otherwise, it contains the homology dimensions (as non-negative integers) at which filtering should occur.

• epsilon (float, optional, default: 0.01) – The cutoff value controlling the amount of filtering.

homology_dimensions\_

If homology_dimensions is set to None, then this is the list of homology dimensions seen in fit, sorted in ascending order. Otherwise, it is a similarly sorted version of homology_dimensions.

Type

list

See also

PairwiseDistance, ForgetDimension, Scaler, Amplitude

__init__(homology_dimensions=None, epsilon=0.01)

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

fit(X, y=None)

Store relevant homology dimensions in homology_dimensions_. 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).

• 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).

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

Returns

Xt – Filtered persistence diagrams. Only the subdiagrams corresponding to dimensions in homology_dimensions_ are filtered. Discarded points are replaced by points on the diagonal.

Return type

ndarray of shape (n_samples, n_features, 3)

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)

Plot a sample from a collection of persistence diagrams, with homology in multiple dimensions.

Parameters

• Xt (ndarray of shape (n_samples, n_points, 3)) – Collection of persistence diagrams, 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 is equivalent to passing homology_dimensions_.

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)

Filter all relevant persistence subdiagrams.

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).

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

Returns

Xt – Filtered persistence diagrams. Only the subdiagrams corresponding to dimensions in homology_dimensions_ are filtered. Discarded points are replaced by points on the diagonal.

Return type

ndarray of shape (n_samples, n_features, 3)

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 (dict) – Optional plotting parameters.

Returns

Xt – Transformed one-sample slice from the input.

Return type

ndarray of shape (1, ..)