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# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
# Author(s): Martin Royer, Yuichi Ike, Masatoshi Takenouchi
#
# Copyright (C) 2020 Inria, Copyright (C) 2020 Fujitsu Laboratories Ltd.
# Modification(s):
# - YYYY/MM Author: Description of the modification
import numpy as np
class TimeDelayEmbedding:
"""Point cloud transformation class. Embeds time-series data in the R^d according to
`Takens' Embedding Theorem <https://en.wikipedia.org/wiki/Takens%27s_theorem>`_ and obtains the
coordinates of each point.
Parameters
----------
dim : int, optional (default=3)
`d` of R^d to be embedded.
delay : int, optional (default=1)
Time-Delay embedding.
skip : int, optional (default=1)
How often to skip embedded points.
Example
-------
Given delay=3 and skip=2, a point cloud which is obtained by embedding
a scalar time-series into R^3 is as follows::
time-series = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
point cloud = [[1, 4, 7],
[3, 6, 9]]
Given delay=1 and skip=1, a point cloud which is obtained by embedding
a 2D vector time-series data into R^4 is as follows::
time-series = [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]]
point cloud = [[0, 1, 2, 3],
[2, 3, 4, 5],
[4, 5, 6, 7],
[6, 7, 8, 9]]
"""
def __init__(self, dim=3, delay=1, skip=1):
self._dim = dim
self._delay = delay
self._skip = skip
def __call__(self, ts):
"""Transform method for single time-series data.
Parameters
----------
ts : Iterable[float] or Iterable[Iterable[float]]
A single time-series data, with scalar or vector values.
Returns
-------
point cloud : n x dim numpy arrays
Makes point cloud from a single time-series data.
"""
return self._transform(np.array(ts))
def fit(self, ts, y=None):
return self
def _transform(self, ts):
"""Guts of transform method."""
if ts.ndim == 1:
repeat = self._dim
else:
assert self._dim % ts.shape[1] == 0
repeat = self._dim // ts.shape[1]
end = len(ts) - self._delay * (repeat - 1)
short = np.arange(0, end, self._skip)
vertical = np.arange(0, repeat * self._delay, self._delay)
return ts[np.add.outer(short, vertical)].reshape(len(short), -1)
def transform(self, ts):
"""Transform method for multiple time-series data.
Parameters
----------
ts : Iterable[Iterable[float]] or Iterable[Iterable[Iterable[float]]]
Multiple time-series data, with scalar or vector values.
Returns
-------
point clouds : list of n x dim numpy arrays
Makes point cloud from each time-series data.
"""
return [self._transform(np.array(s)) for s in ts]
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