TakensEmbedding¶

class gtda.time_series.TakensEmbedding(time_delay=1, dimension=2, stride=1, flatten=True, ensure_last_value=True)[source]¶

Point clouds from collections of time series via independent Takens embeddings.

This transformer takes collections of (possibly multivariate) time series as input, applies the Takens embedding algorithm described in SingleTakensEmbedding to each independently, and returns a corresponding collection of point clouds in Euclidean space (or possibly higher-dimensional structures, see flatten).

Parameters

time_delay (int, optional, default: 1) – Time delay between two consecutive values for constructing one embedded point.
dimension (int, optional, default: 2) – Dimension of the embedding space (per variable, in the multivariate case).
stride (int, optional, default: 1) – Stride duration between two consecutive embedded points.
flatten (bool, optional, default: True) – Only relevant when the input of transform represents a collection of multivariate or tensor-valued time series. If True, ensures that the output is a 3D ndarray or list of 2D arrays. If False, each entry of the input collection leads to an array of dimension one higher than the entry’s dimension. See Examples.
ensure_last_value (bool, optional, default: True) – Whether the value(s) representing the last measurement(s) must be be present in the output as the last coordinate(s) of the last embedding vector(s). If False, the first measurement(s) is (are) present as the 0-th coordinate(s) of the 0-th vector(s) instead.

Examples

>>> import numpy as np
>>> from gtda.time_series import TakensEmbedding

Two univariate time series of duration 4:

>>> X = np.arange(8).reshape(2, 4)
>>> print(X)
[[0 1 2 3]
 [4 5 6 7]]
>>> TE = TakensEmbedding(time_delay=1, dimension=2)
>>> print(TE.fit_transform(X))
[[[0 1]
  [1 2]
  [2 3]]
 [[5 6]
  [6 7]
  [7 8]]]

Two multivariate time series of duration 4, with 2 variables:

>>> x = np.arange(8).reshape(2, 1, 4)
>>> X = np.concatenate([x, -x], axis=1)
>>> print(X)
[[[ 0  1  2  3]
  [ 0 -1 -2 -3]]
 [[ 4  5  6  7]
  [-4 -5 -6 -7]]]

Pass flatten as True (default):

>>> TE = TakensEmbedding(time_delay=1, dimension=2, flatten=True)
>>> print(TE.fit_transform(X))
[[[ 0  1  0 -1]
  [ 1  2 -1 -2]
  [ 2  3 -2 -3]]
 [[ 4  5 -4 -5]
  [ 5  6 -5 -6]
  [ 6  7 -6 -7]]]

Pass flatten as False:

>>> TE = TakensEmbedding(time_delay=1, dimension=2, flatten=False)
>>> print(TE.fit_transform(X))
[[[[ 0  1]
   [ 1  2]
   [ 2  3]]
  [[ 0 -1]
   [-1 -2]
   [-2 -3]]]
 [[[ 4  5]
   [ 5  6]
   [ 6  7]]
  [[-4 -5]
   [-5 -6]
   [-6 -7]]]]