ConsistentRescaling¶

class gtda.point_clouds.ConsistentRescaling(metric='euclidean', metric_params=None, neighbor_rank=1, n_jobs=None)[source]¶

Rescaling of distances between pairs of points by the geometric mean of the distances to the respective \(k\)-th nearest neighbours.

Based on ideas in 1. 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 \(D'_{i,j} = D_{i,j}/\sqrt{D_{i,k_i}D_{j,k_j}}\), where \(k_i\) is the index of the \(k\)-th largest value in row \(i\) (and similarly for \(j\)). 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.
neighbor_rank (int, optional, default: 1) – Rank of the neighbors used to modify the metric structure according to the “consistent rescaling” procedure.
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 ConsistentRescaling
>>> X = np.array([[[0, 0], [1, 2], [5, 6]]])
>>> cr = ConsistentRescaling()
>>> X_rescaled = cr.fit_transform(X)
>>> print(X_rescaled.shape)
(1, 3, 3)