# ConsecutiveRescaling¶

class gtda.point_clouds.ConsecutiveRescaling(metric='euclidean', metric_params=None, factor=0.0, n_jobs=None)[source]

Rescaling of distances between consecutive pairs of points by a fixed factor.

The computation during transform depends on the nature of the array X. If each entry in X along axis 0 represents a distance matrix $$D$$, then the corresponding entry in the transformed array is the distance matrix $$D'_{i,i+1} = \alpha D_{i,i+1}$$ where $$\alpha$$ is a positive factor. If the entries in X represent point clouds, their distance matrices are first computed, and then rescaled according to the same formula.

Parameters
• metric (string or callable, optional, default: 'euclidean') – If set to 'precomputed', each entry in X along axis 0 is interpreted to be a distance matrix. Otherwise, entries are interpreted as feature arrays, and metric determines a rule with which to calculate distances between pairs of instances (i.e. rows) in these arrays. If metric is a string, it must be one of the options allowed by scipy.spatial.distance.pdist for its metric parameter, or a metric listed in sklearn.pairwise.PAIRWISE_DISTANCE_FUNCTIONS, including “euclidean”, “manhattan” or “cosine”. If metric is a callable function, it is called on each pair of instances and the resulting value recorded. The callable should take two arrays from the entry in X as input, and return a value indicating the distance between them.

• metric_params (dict or None, optional, default: None) – Additional keyword arguments for the metric function.

• factor (float, optional, default: 0.) – Factor by which to multiply the distance between consecutive points.

• 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_metric_params_

Dictionary containing all information present in metric_params. If metric_params is None, it is set to the empty dictionary.

Type

dict

Examples

>>> import numpy as np
>>> from gtda.point_clouds import ConsecutiveRescaling
>>> X = np.array([[[0, 0], [1, 2], [5, 6]]])
>>> cr = ConsecutiveRescaling()
>>> X_rescaled = cr.fit_transform(X)
>>> print(X_rescaled.shape)
(1, 3, 3)

__init__(metric='euclidean', metric_params=None, factor=0.0, n_jobs=None)[source]

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

fit(X, y=None)[source]

Calculate effective_metric_params_. 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_points, n_points) or (n_samples, n_points, n_dimensions)) – Input data. If metric == 'precomputed', the input should be an ndarray whose each entry along axis 0 is a distance matrix of shape (n_points, n_points). Otherwise, each such entry will be interpreted as an array of n_points row vectors in n_dimensions-dimensional space.

• 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_points, n_points) or (n_samples, n_points, n_dimensions)) – Input data. If metric == 'precomputed', the input should be an ndarray whose each entry along axis 0 is a distance matrix of shape (n_points, n_points). Otherwise, each such entry will be interpreted as an array of n_points row vectors in n_dimensions-dimensional space.

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

Returns

Xt – Array containing (as entries along axis 0) the distance matrices after consecutive rescaling.

Return type

ndarray of shape (n_samples, n_points, n_points)

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 (ndarray of shape (n_samples, n_points, n_points)) – 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]

For each entry in the input data array X, find the metric structure after consecutive rescaling and encode it as a distance matrix.

Parameters
• X (ndarray of shape (n_samples, n_points, n_points) or (n_samples, n_points, n_dimensions)) – Input data. If metric == 'precomputed', the input should be an ndarray whose each entry along axis 0 is a distance matrix of shape (n_points, n_points). Otherwise, each such entry will be interpreted as an array of n_points row vectors in n_dimensions-dimensional space.

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

Returns

Xt – Array containing (as entries along axis 0) the distance matrices after consecutive rescaling.

Return type

ndarray of shape (n_samples, n_points, n_points)

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, ..)