__author__ = ["chrisholder", "TonyBagnall"]
from collections.abc import Callable
from typing import Any, Union
import numpy as np
from sktime.distances._ddtw import _DdtwDistance
from sktime.distances._dtw import _DtwDistance
from sktime.distances._edr import _EdrDistance
from sktime.distances._erp import _ErpDistance
from sktime.distances._euclidean import _EuclideanDistance
from sktime.distances._lcss import _LcssDistance
from sktime.distances._msm import _MsmDistance
from sktime.distances._resolve_metric import (
_resolve_dist_instance,
_resolve_metric_to_factory,
)
from sktime.distances._squared import _SquaredDistance
from sktime.distances._twe import _TweDistance
from sktime.distances._wddtw import _WddtwDistance
from sktime.distances._wdtw import _WdtwDistance
from sktime.distances.base import (
AlignmentPathReturn,
DistanceAlignmentPathCallable,
DistanceCallable,
MetricInfo,
NumbaDistance,
)
[文档]def erp_distance(
x: np.ndarray,
y: np.ndarray,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: Union[np.ndarray, None] = None,
g: float = 0.0,
**kwargs: Any,
) -> float:
"""Compute the Edit distance for real penalty (ERP) distance between two series.
ERP, first proposed in [1]_, attempts align time series
by better considering how indexes are carried forward through the cost matrix.
Usually in the dtw cost matrix, if an alignment can't be found the previous value
is carried forward. Erp instead proposes the idea of gaps or sequences of points
that have no matches. These gaps are then punished based on their distance from 'g'.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
g: float, defaults = 0.
The reference value to penalise gaps.
kwargs: Any
Extra kwargs.
Returns
-------
float
ERP distance between x and y.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 3 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If g is not a float.
If both window and itakura_max_slope are set
Examples
--------
>>> import numpy as np
>>> from sktime.distances import erp_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> erp_distance(x_1d, y_1d)
16.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> erp_distance(x_2d, y_2d)
45.254833995939045
References
----------
.. [1] Lei Chen and Raymond Ng. 2004. On the marriage of Lp-norms and edit distance.
In Proceedings of the Thirtieth international conference on Very large data bases
- Volume 30 (VLDB '04). VLDB Endowment, 792-803.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"g": g,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="erp", **format_kwargs)
[文档]def edr_distance(
x: np.ndarray,
y: np.ndarray,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: Union[np.ndarray, None] = None,
epsilon: float = None,
**kwargs: Any,
) -> float:
"""Compute the Edit distance for real sequences (EDR) between two series.
EDR computes the minimum number of elements (as a percentage) that must be removed
from x and y so that the sum of the distance between the remaining signal elements
lies within the tolerance (epsilon). EDR was originally proposed in [1]_.
The value returned will be between 0 and 1 per time series. The value will
represent as a percentage of elements that must be removed for the time series to
be an exact match.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d array), defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
epsilon : float, defaults = None
Matching threshold to determine if two subsequences are considered close
enough to be considered 'common'. If not specified as per the original paper
epsilon is set to a quarter of the maximum standard deviation.
kwargs: Any
Extra kwargs.
Returns
-------
float
Edr distance between the x and y. The value will be between 0.0 and 1.0
where 0.0 is an exact match between time series (i.e. they are the same) and
1.0 where there are no matching subsequences.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 3 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If both window and itakura_max_slope are set
Examples
--------
>>> import numpy as np
>>> from sktime.distances import edr_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> edr_distance(x_1d, y_1d)
1.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> edr_distance(x_2d, y_2d)
1.0
References
----------
.. [1] Lei Chen, M. Tamer Özsu, and Vincent Oria. 2005. Robust and fast similarity
search for moving object trajectories. In Proceedings of the 2005 ACM SIGMOD
international conference on Management of data (SIGMOD '05). Association for
Computing Machinery, New York, NY, USA, 491-502.
DOI:https://doi.org/10.1145/1066157.1066213
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"epsilon": epsilon,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="edr", **format_kwargs)
[文档]def lcss_distance(
x: np.ndarray,
y: np.ndarray,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: Union[np.ndarray, None] = None,
epsilon: float = 1.0,
**kwargs: Any,
) -> float:
"""Compute the longest common subsequence (LCSS) score between two time series.
LCSS attempts to find the longest common sequence between two time series and
returns a value that is the percentage that longest common sequence assumes.
Originally present in [1]_, LCSS is computed by matching indexes that are
similar up until a defined threshold (epsilon).
The value returned will be between 0.0 and 1.0, where 0.0 means the two time series
are exactly the same and 1.0 means they are complete opposites.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
epsilon : float, defaults = 1.
Matching threshold to determine if two subsequences are considered close
enough to be considered 'common'.
kwargs: Any
Extra kwargs.
Returns
-------
float
Lcss distance between x and y. The value returned will be between 0.0 and 1.0,
where 0.0 means the two time series are exactly the same and 1.0 means they
are complete opposites.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If both window and itakura_max_slope are set
References
----------
.. [1] M. Vlachos, D. Gunopoulos, and G. Kollios. 2002. "Discovering
Similar Multidimensional Trajectories", In Proceedings of the
18th International Conference on Data Engineering (ICDE '02).
IEEE Computer Society, USA, 673.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"epsilon": epsilon,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="lcss", **format_kwargs)
[文档]def wddtw_distance(
x: np.ndarray,
y: np.ndarray,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: Union[np.ndarray, None] = None,
compute_derivative=None,
g: float = 0.0,
**kwargs: Any,
) -> float:
r"""Compute the weighted derivative dynamic time warping (WDDTW) distance.
WDDTW was first proposed in [1]_ as an extension of DDTW. By adding a weight
to the derivative it means the alignment isn't only considering the shape of the
time series, but also the phase.
Formally the derivative is calculated as:
.. math::
D_{x}[q] = \frac{{}(q_{i} - q_{i-1} + ((q_{i+1} - q_{i-1}/2)}{2}
Therefore a weighted derivative can be calculated using D (the derivative) as:
.. math::
d_{w}(x_{i}, y_{j}) = ||w_{|i-j|}(D_{x_{i}} - D_{y_{j}})||
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
compute_derivative: Callable[[np.ndarray], np.ndarray],
defaults = average slope difference
Callable that computes the derivative. If none is provided the average of the
slope between two points used.
g: float, defaults = 0.
Constant that controls the curvature (slope) of the function; that is, g
controls the level of penalisation for the points with larger phase
difference.
kwargs: Any
Extra kwargs.
Returns
-------
float
Wddtw distance between x and y.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If the compute derivative callable is not no_python compiled.
If the value of g is not a float
If both window and itakura_max_slope are set
Examples
--------
>>> import numpy as np
>>> from sktime.distances import wddtw_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> wddtw_distance(x_1d, y_1d) # doctest: +SKIP
0.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> wddtw_distance(x_2d, y_2d) # doctest: +SKIP
0.0
References
----------
.. [1] Young-Seon Jeong, Myong K. Jeong, Olufemi A. Omitaomu, Weighted dynamic time
warping for time series classification, Pattern Recognition, Volume 44, Issue 9,
2011, Pages 2231-2240, ISSN 0031-3203, https://doi.org/10.1016/j.patcog.2010.09.022.
"""
if compute_derivative is None:
from sktime.distances._ddtw_numba import average_of_slope
compute_derivative = average_of_slope
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"compute_derivative": compute_derivative,
"g": g,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="wddtw", **format_kwargs)
[文档]def wdtw_distance(
x: np.ndarray,
y: np.ndarray,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: np.ndarray = None,
g: float = 0.05,
**kwargs: Any,
) -> float:
"""Compute the weighted dynamic time warping (WDTW) distance between time series.
First proposed in [1]_, WDTW adds a adds a multiplicative weight penalty based on
the warping distance. This means that time series with lower phase difference have
a smaller weight imposed (i.e less penalty imposed) and time series with larger
phase difference have a larger weight imposed (i.e. larger penalty imposed).
Formally this can be described as:
.. math::
d_{w}(x_{i}, y_{j}) = ||w_{|i-j|}(x_{i} - y_{j})||
Where d_w is the distance with a the weight applied to it for points i, j, where
w(|i-j|) is a positive weight between the two points x_i and y_j.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
g: float, defaults = 0.
Constant that controls the curvature (slope) of the function; that is, g
controls the level of penalisation for the points with larger phase
difference.
kwargs: Any
Extra kwargs.
Returns
-------
float
Wdtw distance between the x and y.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If both window and itakura_max_slope are set
Examples
--------
>>> import numpy as np
>>> from sktime.distances import wdtw_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> wdtw_distance(x_1d, y_1d)
27.975712863958133
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> wdtw_distance(x_2d, y_2d)
243.2106560107827
References
----------
.. [1] Young-Seon Jeong, Myong K. Jeong, Olufemi A. Omitaomu, Weighted dynamic time
warping for time series classification, Pattern Recognition, Volume 44, Issue 9,
2011, Pages 2231-2240, ISSN 0031-3203, https://doi.org/10.1016/j.patcog.2010.09.022.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"g": g,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="wdtw", **format_kwargs)
[文档]def ddtw_distance(
x: np.ndarray,
y: np.ndarray,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: np.ndarray = None,
compute_derivative=None,
**kwargs: Any,
) -> float:
r"""Compute the derivative dynamic time warping (DDTW) distance between time series.
DDTW is an adaptation of DTW originally proposed in [1]_. DDTW attempts to
improve on dtw by better account for the 'shape' of the time series.
This is done by considering y axis data points as higher level features of 'shape'.
To do this the first derivative of the sequence is taken, and then using this
derived sequence a dtw computation is done.
The default derivative used is:
.. math::
D_{x}[q] = \frac{{}(q_{i} - q_{i-1} + ((q_{i+1} - q_{i-1}/2)}{2}
Where q is the original time series and d_q is the derived time series.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
compute_derivative: Callable[[np.ndarray], np.ndarray],
defaults = average slope difference
Callable that computes the derivative. If none is provided the average of the
slope between two points used.
kwargs: Any
Extra kwargs.
Returns
-------
float
Ddtw distance between the x and y.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric or compute derivative callable is not no_python compiled.
If the metric type cannot be determined
If the compute derivative callable is not no_python compiled.
If both window and itakura_max_slope are set
Examples
--------
>>> import numpy as np
>>> from sktime.distances import ddtw_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> ddtw_distance(x_1d, y_1d) # doctest: +SKIP
0.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> ddtw_distance(x_2d, y_2d) # doctest: +SKIP
0.0
References
----------
.. [1] Keogh, Eamonn & Pazzani, Michael. (2002). Derivative Dynamic Time Warping.
First SIAM International Conference on Data Mining.
1. 10.1137/1.9781611972719.1.
"""
if compute_derivative is None:
from sktime.distances._ddtw_numba import average_of_slope
compute_derivative = average_of_slope
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"compute_derivative": compute_derivative,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="ddtw", **format_kwargs)
[文档]def dtw_distance(
x: np.ndarray,
y: np.ndarray,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: np.ndarray = None,
**kwargs: Any,
) -> float:
r"""Compute the dynamic time warping (DTW) distance between two time series.
Originally proposed in [1]_, DTW is an elastic
distance measure, i.e., it is a distance computed after realigning (warping)
two time series to best match each other via time axis distortions [2]_.
This function computes time warping distances only for:
* sequences, time index is ignored
* two time series of equal length
* the Euclidean pairwise distance
For unequal length time series, use ``sktime.dists_kernels.DistFromAligner``
with a time warping aligner such as ``sktime.aligners.AlignerDTW``.
To use arbitrary pairwise distances, use ``sktime.aligners.AlignerDTWfromDist``.
Mathematically, for two sequences
:math:'\mathbf{a}=\{a_1,a_2,\ldots,a_m\}' and :math:'\mathbf{b}=\{b_1,b_2,\ldots,
b_n\}', (assumed equal length for simplicity), DTW first calculates
the pairwise distance matrix :math:'M(
\mathbf{a},\mathbf{b})', the :math:'m \times n',
between series :math:'\mathbf{a}' and :math:'\mathbf{b}',
where :math:'M_{i,j} = d(a_i, b_j)', for a chosen distance measure
:math:`d: \mathbb{R}^h \times \mathbb{R}^h \rightarrow \mathbb{R}`.
In this estimator, the squared Euclidean distance is used, i.e.,
:math:`d(x, y):= (x-y)^2`. A warping path
.. math:: P=((i_1, j_1), (i_2, j_2), \ldots, (i_s, j_s))
is an ordered tuple of indices
:math:`i_k \in \{1, \dots, m\}, j_k \in \{1, \dots, n\}`
which define a traversal path of matrix :math:'M'.
This implementation assumes for warping paths that:
* closed paths: :math:`i_1 = j_1 = 1`; :math:`i_s = m, j_s = n`
* monotonous paths: :math:`i_k \le i_{k+1}, j_k \le j_{k+1}` for all :math:`k`
* strictly monotonous paths: :math:`(i_k, j_k) \neq (i_{k+1}, j_{k+1})` for all
:math:`k`
The DTW path between sequences is the path through :math:'M' that minimizes the total
distance,
over all valid paths (satisfying the above assumptions), given the sequences.
Formally:
The distance for a warping path :math:'P' of length :math:'s' is
.. math:: D_P(\mathbf{a},\mathbf{b}) = \sum_{k=1}^s M_{i_k,j_k}.
If :math:'\mathcal{P}' is the set of all possible paths, the DTW path :math:'P^*'
is the path that has the minimum distance amongst those:
.. math:: P^* = \argmin_{P\in \mathcal{P}} D_{P}(\mathbf{a},\mathbf{b}).
The DTW distance between the two sequences :math:'\mathbf{a},\mathbf{b}' is
the minimum warping path distance:
.. math:: d_{dtw}(\mathbf{a}, \mathbf{b}) = \min_{P\in \mathcal{P}} D_{P}(\mathbf{a},\mathbf{b}) =
D_{P^*}(\mathbf{a},\mathbf{b}).
The optimal warping path $P^*$ can be found exactly through dynamic programming.
This can be a time consuming operation, and it is common to put a
restriction on the amount of warping allowed. This is implemented through
the ``bounding_matrix`` structure, that restricts allowable warpings by a mask.
Common bounding strategies include the Sakoe-Chiba band [3]_ and the Itakura
parallelogram [4_]. The Sakoe-Chiba band creates a warping path window that has
the same width along the diagonal of :math:'M'. The Itakura paralleogram allows
for less warping at the start or end of the sequence than in the middle.
If the function is called with multivariate time series, note that
the matrix :math:'M' is computed with the multivariate squared Euclidean distance,
:math:`d(x, y):= (x-y)^2` = \sum_{i=1}^h (x_i - y_i)^2`
This is sometimes called the "dependent" version of DTW, DTW_D, see [5]_.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
kwargs: Any
Extra kwargs.
Returns
-------
float
Dtw distance between x and y.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined
If both window and itakura_max_slope are set
Examples
--------
>>> import numpy as np
>>> from sktime.distances import dtw_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> dtw_distance(x_1d, y_1d)
58.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> dtw_distance(x_2d, y_2d)
512.0
References
----------
.. [1] H. Sakoe, S. Chiba, "Dynamic programming algorithm optimization for
spoken word recognition," IEEE Transactions on Acoustics, Speech and
Signal Processing, vol. 26(1), pp. 43--49, 1978.
.. [2] Ratanamahatana C and Keogh E.: Three myths about dynamic time warping data
mining Proceedings of 5th SIAM International Conference on Data Mining, 2005
.. [3] Sakoe H. and Chiba S.: Dynamic programming algorithm optimization for
spoken word recognition. IEEE Transactions on Acoustics, Speech, and Signal
Processing 26(1):43-49, 1978.
.. [4] Itakura F: Minimum prediction residual principle applied to speech
recognition. IEEE Transactions on Acoustics, Speech, and Signal Processing 23(
1):67-72, 1975.
.. [5] Shokoohi-Yekta M et al.: Generalizing DTW to the multi-dimensional case
requires an adaptive approach. Data Mining and Knowledge Discovery, 31, 1-31 (2017).
""" # noqa: E501
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="dtw", **format_kwargs)
[文档]def msm_distance(
x: np.ndarray,
y: np.ndarray,
c: float = 1.0,
window: float = None,
itakura_max_slope: float = None,
bounding_matrix: np.ndarray = None,
**kwargs: dict,
) -> float:
"""Compute the move-split-merge distance.
This metric uses as building blocks three fundamental operations: Move, Split,
and Merge. A Move operation changes the value of a single element, a Split
operation converts a single element into two consecutive elements, and a Merge
operation merges two consecutive elements into one. Each operation has an
associated cost, and the MSM distance between two time series is defined to be
the cost of the cheapest sequence of operations that transforms the first time
series into the second one.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
c: float, default = 1.0
Cost for split or merge operation.
window: Float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Must be between 0 and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Must be between 0 and 1.
bounding_matrix: np.ndarray (2d array of shape (m1,m2)), defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should
be infinity.
kwargs: any
extra kwargs.
Returns
-------
float
Msm distance between x and y.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined
References
----------
.. [1]A. Stefan, V. Athitsos, and G. Das. The Move-Split-Merge metric
for time series. IEEE Transactions on Knowledge and Data Engineering,
25(6):1425-1438, 2013.
"""
format_kwargs = {
"c": c,
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="msm", **format_kwargs)
[文档]def twe_distance(
x: np.ndarray,
y: np.ndarray,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: np.ndarray = None,
lmbda: float = 1.0,
nu: float = 0.001,
p: int = 2,
**kwargs: Any,
) -> float:
"""Time Warp Edit (TWE) distance between two time series.
The Time Warp Edit (TWE) distance is a distance measure for discrete time series
matching with time 'elasticity'. In comparison to other distance measures, (e.g.
DTW (Dynamic Time Warping) or LCS (Longest Common Subsequence Problem)), TWE is a
metric. Its computational time complexity is O(n^2), but can be drastically reduced
in some specific situation by using a corridor to reduce the search space. Its
memory space complexity can be reduced to O(n). It was first proposed in [1].
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
lmbda: float, defaults = 1.0
A constant penalty that punishes the editing efforts. Must be >= 1.0.
nu: float, defaults = 0.001
A non-negative constant which characterizes the stiffness of the elastic
twe measure. Must be > 0.
p: int, defaults = 2
Order of the p-norm for local cost.
kwargs: Any
Extra kwargs.
Returns
-------
float
Dtw distance between x and y.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined
If both window and itakura_max_slope are set
Examples
--------
>>> import numpy as np
>>> from sktime.distances import twe_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> twe_distance(x_1d, y_1d)
28.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> twe_distance(x_2d, y_2d)
78.37353236814714
References
----------
.. [1] Marteau, P.; F. (2009). "Time Warp Edit Distance with Stiffness Adjustment
for Time Series Matching". IEEE Transactions on Pattern Analysis and Machine
Intelligence. 31 (2): 306-318.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"lmbda": lmbda,
"nu": nu,
"p": p,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance(x, y, metric="twe", **format_kwargs)
[文档]def squared_distance(x: np.ndarray, y: np.ndarray, **kwargs: Any) -> float:
r"""Compute the squared distance between two time series.
The squared distance between two time series is defined as:
.. math::
sd(x, y) = \sum_{i=1}^{n} (x_i - y_i)^2
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
kwargs: Any
Extra kwargs. For squared there are none however, this is kept for
consistency.
Returns
-------
float
Squared distance between x and y.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined.
Examples
--------
>>> import numpy as np
>>> from sktime.distances import squared_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> squared_distance(x_1d, y_1d)
64.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> squared_distance(x_2d, y_2d)
512.0
"""
return distance(x, y, metric="squared", **kwargs)
[文档]def euclidean_distance(x: np.ndarray, y: np.ndarray, **kwargs: Any) -> float:
r"""Compute the Euclidean distance between two time series.
Euclidean distance is supported for 1d, 2d and 3d arrays.
The Euclidean distance between two time series of length m is the square root of
the squared distance and is defined as:
.. math::
ed(x, y) = \sqrt{\sum_{i=1}^{n} (x_i - y_i)^2}
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
kwargs: Any
Extra kwargs. For euclidean there are none however, this is kept for
consistency.
Returns
-------
float
Euclidean distance between x and y.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined.
Examples
--------
>>> import numpy as np
>>> from sktime.distances import euclidean_distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> euclidean_distance(x_1d, y_1d)
8.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> euclidean_distance(x_2d, y_2d)
22.627416997969522
"""
return distance(x, y, metric="euclidean", **kwargs)
def dtw_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: np.ndarray = None,
**kwargs: Any,
) -> AlignmentPathReturn:
r"""Compute the dynamic time warping (DTW) alignment path.
Originally proposed in [1]_ DTW computes the distance between two time series by
considering their alignments during the calculation. This is done by measuring
the pointwise distance (normally using Euclidean) between all elements of the two
time series and then using dynamic programming to find the warping path
that minimises the total pointwise distance between realigned series.
Mathematically dtw can be defined as:
.. math::
dtw(x, y) = \sqrt{\sum_{(i, j) \in \pi} \|x_{i} - y_{j}\|^2}
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
kwargs: Any
Extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the dtw alignment path.
float
Dtw distance between x and y.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined
If both window and itakura_max_slope are set
References
----------
.. [1] H. Sakoe, S. Chiba, "Dynamic programming algorithm optimization for
spoken word recognition," IEEE Transactions on Acoustics, Speech and
Signal Processing, vol. 26(1), pp. 43--49, 1978.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="dtw", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def wdtw_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: np.ndarray = None,
g: float = 0.05,
**kwargs: Any,
) -> AlignmentPathReturn:
"""Compute the weighted dynamic time warping (wdtw) alignment path.
First proposed in [1]_, WDTW adds a adds a multiplicative weight penalty based on
the warping distance. This means that time series with lower phase difference have
a smaller weight imposed (i.e less penalty imposed) and time series with larger
phase difference have a larger weight imposed (i.e. larger penalty imposed).
Formally this can be described as:
.. math::
d_{w}(x_{i}, y_{j}) = ||w_{|i-j|}(x_{i} - y_{j})||
Where d_w is the distance with a the weight applied to it for points i, j, where
w(|i-j|) is a positive weight between the two points x_i and y_j.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
g: float, defaults = 0.
Constant that controls the curvature (slope) of the function; that is, g
controls the level of penalisation for the points with larger phase
difference.
kwargs: Any
Extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the wdtw alignment path.
float
Wdtw distance between x and y.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If both window and itakura_max_slope are set
References
----------
.. [1] Young-Seon Jeong, Myong K. Jeong, Olufemi A. Omitaomu, Weighted dynamic time
warping for time series classification, Pattern Recognition, Volume 44, Issue 9,
2011, Pages 2231-2240, ISSN 0031-3203, https://doi.org/10.1016/j.patcog.2010.09.022.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"g": g,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="wdtw", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def ddtw_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: np.ndarray = None,
compute_derivative=None,
**kwargs: Any,
) -> AlignmentPathReturn:
r"""Compute the derivative dynamic time warping (DDTW) alignment path.
DDTW is an adaptation of DTW originally proposed in [1]_. DDTW attempts to
improve on dtw by better account for the 'shape' of the time series.
This is done by considering y axis data points as higher level features of 'shape'.
To do this the first derivative of the sequence is taken, and then using this
derived sequence a dtw computation is done.
The default derivative used is:
.. math::
D_{x}[q] = \frac{{}(q_{i} - q_{i-1} + ((q_{i+1} - q_{i-1}/2)}{2}
Where q is the original time series and d_q is the derived time series.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
compute_derivative: Callable[[np.ndarray], np.ndarray],
defaults = average slope difference
Callable that computes the derivative. If none is provided the average of the
slope between two points used.
kwargs: Any
Extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the ddtw alignment path.
float
Ddtw distance between x and y.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric or compute derivative callable is not no_python compiled.
If the metric type cannot be determined
If the compute derivative callable is not no_python compiled.
If both window and itakura_max_slope are set
References
----------
.. [1] Keogh, Eamonn & Pazzani, Michael. (2002). Derivative Dynamic Time Warping.
First SIAM International Conference on Data Mining.
1. 10.1137/1.9781611972719.1.
"""
if compute_derivative is None:
from sktime.distances._ddtw_numba import average_of_slope
compute_derivative = average_of_slope
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"compute_derivative": compute_derivative,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="ddtw", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def wddtw_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: Union[np.ndarray, None] = None,
compute_derivative=None,
g: float = 0.0,
**kwargs: Any,
) -> AlignmentPathReturn:
r"""Compute the weighted derivative dynamic time warping (WDDTW) alignment path.
WDDTW was first proposed in [1]_ as an extension of DDTW. By adding a weight
to the derivative it means the alignment isn't only considering the shape of the
time series, but also the phase.
Formally the derivative is calculated as:
.. math::
D_{x}[q] = \frac{{}(q_{i} - q_{i-1} + ((q_{i+1} - q_{i-1}/2)}{2}
Therefore a weighted derivative can be calculated using D (the derivative) as:
.. math::
d_{w}(x_{i}, y_{j}) = ||w_{|i-j|}(D_{x_{i}} - D_{y_{j}})||
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
compute_derivative: Callable[[np.ndarray], np.ndarray],
defaults = average slope difference
Callable that computes the derivative. If none is provided the average of the
slope between two points used.
g: float, defaults = 0.
Constant that controls the curvature (slope) of the function; that is, g
controls the level of penalisation for the points with larger phase
difference.
kwargs: Any
Extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the wddtw alignment path.
float
Wddtw distance between x and y.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If the compute derivative callable is not no_python compiled.
If the value of g is not a float
If both window and itakura_max_slope are set
References
----------
.. [1] Young-Seon Jeong, Myong K. Jeong, Olufemi A. Omitaomu, Weighted dynamic time
warping for time series classification, Pattern Recognition, Volume 44, Issue 9,
2011, Pages 2231-2240, ISSN 0031-3203, https://doi.org/10.1016/j.patcog.2010.09.022.
"""
if compute_derivative is None:
from sktime.distances._ddtw_numba import average_of_slope
compute_derivative = average_of_slope
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"compute_derivative": compute_derivative,
"g": g,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="wddtw", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def edr_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: Union[np.ndarray, None] = None,
epsilon: float = None,
**kwargs: Any,
) -> AlignmentPathReturn:
"""Compute the Edit distance for real sequences (EDR) alignment path.
EDR computes the minimum number of elements (as a percentage) that must be removed
from x and y so that the sum of the distance between the remaining signal elements
lies within the tolerance (epsilon). EDR was originally proposed in [1]_.
The value returned will be between 0 and 1 per time series. The value will
represent as a percentage of elements that must be removed for the time series to
be an exact match.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d array), defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
epsilon : float, defaults = None
Matching threshold to determine if two subsequences are considered close
enough to be considered 'common'. If not specified as per the original paper
epsilon is set to a quarter of the maximum standard deviation.
kwargs: Any
Extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the edr alignment path.
float
Edr distance between x and y.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 3 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If both window and itakura_max_slope are set
References
----------
.. [1] Lei Chen, M. Tamer Özsu, and Vincent Oria. 2005. Robust and fast similarity
search for moving object trajectories. In Proceedings of the 2005 ACM SIGMOD
international conference on Management of data (SIGMOD '05). Association for
Computing Machinery, New York, NY, USA, 491-502.
DOI:https://doi.org/10.1145/1066157.1066213
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"epsilon": epsilon,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="edr", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def erp_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: Union[np.ndarray, None] = None,
g: float = 0.0,
**kwargs: Any,
) -> AlignmentPathReturn:
"""Compute the Edit distance for real penalty (ERP) alignment path.
ERP, first proposed in [1]_, attempts align time series
by better considering how indexes are carried forward through the cost matrix.
Usually in the dtw cost matrix, if an alignment can't be found the previous value
is carried forward. Erp instead proposes the idea of gaps or sequences of points
that have no matches. These gaps are then punished based on their distance from 'g'.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
g: float, defaults = 0.
The reference value to penalise gaps.
kwargs: Any
Extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the erp alignment path.
float
Erp distance between x and y.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 3 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If g is not a float.
If both window and itakura_max_slope are set
References
----------
.. [1] Lei Chen and Raymond Ng. 2004. On the marriage of Lp-norms and edit distance.
In Proceedings of the Thirtieth international conference on Very large data bases
- Volume 30 (VLDB '04). VLDB Endowment, 792-803.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"g": g,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="erp", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def lcss_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
window: Union[float, None] = None,
itakura_max_slope: Union[float, None] = None,
bounding_matrix: Union[np.ndarray, None] = None,
epsilon: float = 1.0,
**kwargs: Any,
) -> AlignmentPathReturn:
"""Compute the longest common subsequence (LCSS) alignment path.
LCSS attempts to find the longest common sequence between two time series and
returns a value that is the percentage that longest common sequence assumes.
Originally present in [1]_, LCSS is computed by matching indexes that are
similar up until a defined threshold (epsilon).
The value returned will be between 0.0 and 1.0, where 0.0 means the two time series
are exactly the same and 1.0 means they are complete opposites.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
epsilon : float, defaults = 1.
Matching threshold to determine if two subsequences are considered close
enough to be considered 'common'.
kwargs: Any
Extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the lcss alignment path.
float
Lcss distance between x and y. The value returned will be between 0.0 and 1.0,
where 0.0 means the two time series are exactly the same and 1.0 means they
are complete opposites.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If the metric type cannot be determined
If both window and itakura_max_slope are set
References
----------
.. [1] M. Vlachos, D. Gunopoulos, and G. Kollios. 2002. "Discovering
Similar Multidimensional Trajectories", In Proceedings of the
18th International Conference on Data Engineering (ICDE '02).
IEEE Computer Society, USA, 673.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"epsilon": epsilon,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="lcss", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def msm_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
c: float = 1.0,
window: float = None,
itakura_max_slope: float = None,
bounding_matrix: np.ndarray = None,
**kwargs: dict,
) -> AlignmentPathReturn:
"""Compute the move-split-merge alignment path.
This metric uses as building blocks three fundamental operations: Move, Split,
and Merge. A Move operation changes the value of a single element, a Split
operation converts a single element into two consecutive elements, and a Merge
operation merges two consecutive elements into one. Each operation has an
associated cost, and the MSM distance between two time series is defined to be
the cost of the cheapest sequence of operations that transforms the first time
series into the second one.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
c: float, default = 1.0
Cost for split or merge operation.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Must be between 0 and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Must be between 0 and 1.
bounding_matrix: np.ndarray (2d array of shape (m1,m2)), defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should
be infinity.
kwargs: any
extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the msm alignment path.
float
Msm distance between x and y.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined
References
----------
.. [1]A. Stefan, V. Athitsos, and G. Das. The Move-Split-Merge metric
for time series. IEEE Transactions on Knowledge and Data Engineering,
25(6):1425-1438, 2013.
"""
format_kwargs = {
"c": c,
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="msm", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def twe_alignment_path(
x: np.ndarray,
y: np.ndarray,
return_cost_matrix: bool = False,
window: float = None,
itakura_max_slope: float = None,
bounding_matrix: np.ndarray = None,
lmbda: float = 1.0,
nu: float = 0.001,
p: int = 2,
**kwargs: Any,
) -> AlignmentPathReturn:
"""Time Warp Edit (TWE) distance between two time series.
The Time Warp Edit (TWE) distance is a distance measure for discrete time series
matching with time 'elasticity'. In comparison to other distance measures, (e.g.
DTW (Dynamic Time Warping) or LCS (Longest Common Subsequence Problem)), TWE is a
metric. Its computational time complexity is O(n^2), but can be drastically reduced
in some specific situation by using a corridor to reduce the search space. Its
memory space complexity can be reduced to O(n). It was first proposed in [1].
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
window: float, defaults = None
Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba
lower bounding). Value must be between 0. and 1.
itakura_max_slope: float, defaults = None
Gradient of the slope for itakura parallelogram (if using Itakura
Parallelogram lower bounding). Value must be between 0. and 1.
bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),
defaults = None
Custom bounding matrix to use. If defined then other lower_bounding params
are ignored. The matrix should be structure so that indexes considered in
bound should be the value 0. and indexes outside the bounding matrix should be
infinity.
lmbda: float, defaults = 1.0
A constant penalty that punishes the editing efforts. Must be >= 1.0.
nu: float, defaults = 0.001
A non-negative constant which characterizes the stiffness of the elastic
twe measure. Must be > 0.
p: int, defaults = 2
Order of the p-norm for local cost.
kwargs: Any
Extra kwargs.
Returns
-------
list[tuple]
List of tuples containing the twe alignment path.
float
Twe distance between x and y. The value returned will be between 0.0 and 1.0,
where 0.0 means the two time series are exactly the same and 1.0 means they
are complete opposites.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
Raises
------
ValueError
If the sakoe_chiba_window_radius is not a float.
If the itakura_max_slope is not a float.
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined
If both window and itakura_max_slope are set
References
----------
.. [1] Marteau, P.; F. (2009). "Time Warp Edit Distance with Stiffness Adjustment
for Time Series Matching". IEEE Transactions on Pattern Analysis and Machine
Intelligence. 31 (2): 306-318.
"""
format_kwargs = {
"window": window,
"itakura_max_slope": itakura_max_slope,
"bounding_matrix": bounding_matrix,
"lmbda": lmbda,
"nu": nu,
"p": p,
}
format_kwargs = {**format_kwargs, **kwargs}
return distance_alignment_path(
x, y, metric="twe", return_cost_matrix=return_cost_matrix, **format_kwargs
)
def distance(
x: np.ndarray,
y: np.ndarray,
metric: Union[
str,
Callable[
[np.ndarray, np.ndarray, dict], Callable[[np.ndarray, np.ndarray], float]
],
Callable[[np.ndarray, np.ndarray], float],
NumbaDistance,
],
**kwargs: Any,
) -> float:
"""Compute the distance between two time series.
First the distance metric is 'resolved'. This means the metric that is passed
is resolved to a callable. The callable is then called with x and y and the
value is then returned.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
metric: str or Callable
The distance metric to use.
If a string is given, the value must be one of the following strings:
'euclidean', 'squared', 'dtw', 'ddtw', 'wdtw', 'wddtw', 'lcss', 'edr', 'erp',
'msm'
If callable then it has to be a distance factory or numba distance callable.
If you want to pass custom kwargs to the distance at runtime, use a distance
factory as it constructs the distance using the kwargs before distance
computation.
A distance callable takes the form (must be no_python compiled):
Callable[[np.ndarray, np.ndarray], float]
A distance factory takes the form (must return a no_python callable):
Callable[[np.ndarray, np.ndarray, bool, dict], Callable[[np.ndarray,
np.ndarray], float]].
kwargs: Any
Arguments for metric. Refer to each metrics documentation for a list of
possible arguments.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined.
Examples
--------
>>> import numpy as np
>>> from sktime.distances import distance
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> distance(x_1d, y_1d, metric='dtw')
58.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> distance(x_2d, y_2d, metric='dtw')
512.0
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> distance(x_2d, y_2d, metric='dtw', window=0.5)
512.0
Returns
-------
float
Distance between the x and y.
"""
from sktime.distances._numba_utils import to_numba_timeseries
_x = to_numba_timeseries(x)
_y = to_numba_timeseries(y)
_metric_callable = _resolve_metric_to_factory(
metric, _x, _y, _METRIC_INFOS, **kwargs
)
return _metric_callable(_x, _y)
def distance_factory(
x: np.ndarray = None,
y: np.ndarray = None,
metric: Union[
str,
Callable[
[np.ndarray, np.ndarray, dict], Callable[[np.ndarray, np.ndarray], float]
],
Callable[[np.ndarray, np.ndarray], float],
NumbaDistance,
] = "euclidean",
**kwargs: Any,
) -> DistanceCallable:
"""Create a no_python distance callable.
Parameters
----------
x: np.ndarray (1d or 2d array), defaults = None
First time series.
y: np.ndarray (1d or 2d array), defaults = None
Second time series.
metric: str or Callable, defaults = 'euclidean'
The distance metric to use.
If a string is given, the value must be one of the following strings:
'euclidean', 'squared', 'dtw', 'ddtw', 'wdtw', 'wddtw', 'lcss', 'edr', 'erp'
If callable then it has to be a distance factory or numba distance callable.
If you want to pass custom kwargs to the distance at runtime, use a distance
factory as it constructs the distance using the kwargs before distance
computation.
A distance callable takes the form (must be no_python compiled):
Callable[[np.ndarray, np.ndarray], float]
A distance factory takes the form (must return a no_python callable):
Callable[[np.ndarray, np.ndarray, bool, dict], Callable[[np.ndarray,
np.ndarray], float]].
kwargs: Any
Arguments for metric. Refer to each metrics documentation for a list of
possible arguments.
Returns
-------
Callable[[np.ndarray, np.ndarray], float]]
No_python compiled distance callable.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined.
"""
from sktime.distances._numba_utils import _numba_to_timeseries, to_numba_timeseries
from sktime.utils.numba.njit import njit
if x is None:
x = np.zeros((1, 10))
if y is None:
y = np.zeros((1, 10))
_x = to_numba_timeseries(x)
_y = to_numba_timeseries(y)
callable = _resolve_metric_to_factory(metric, _x, _y, _METRIC_INFOS, **kwargs)
@njit(cache=True)
def dist_callable(x: np.ndarray, y: np.ndarray):
_x = _numba_to_timeseries(x)
_y = _numba_to_timeseries(y)
return callable(_x, _y)
return dist_callable
[文档]def pairwise_distance(
x: np.ndarray,
y: np.ndarray = None,
metric: Union[
str,
Callable[
[np.ndarray, np.ndarray, dict], Callable[[np.ndarray, np.ndarray], float]
],
Callable[[np.ndarray, np.ndarray], float],
NumbaDistance,
] = "euclidean",
**kwargs: Any,
) -> np.ndarray:
"""Compute the pairwise distance matrix between two time series.
First the distance metric is 'resolved'. This means the metric that is passed
is resolved to a callable. The callable is then called with x and y and the
value is then returned. Then for each combination of x and y, the distance between
the values are computed resulting in a 2d pairwise matrix.
Parameters
----------
x: np.ndarray (1d, 2d or 3d array)
First time series.
y: np.ndarray (1d, 2d or 3d array), defaults = None
Second time series. If not specified then y is set to the value of x.
metric: str or Callable, defaults = 'euclidean'
The distance metric to use.
If a string is given, the value must be one of the following strings:
'euclidean', 'squared', 'dtw', 'ddtw', 'wdtw', 'wddtw',
'lcss', 'edr', 'erp', 'msm'
If callable then it has to be a distance factory or numba distance callable.
If you want to pass custom kwargs to the distance at runtime, use a distance
factory as it constructs the distance using the kwargs before distance
computation.
A distance callable takes the form (must be no_python compiled):
Callable[[np.ndarray, np.ndarray], float]
A distance factory takes the form (must return a no_python callable):
Callable[[np.ndarray, np.ndarray, bool, dict], Callable[[np.ndarray,
np.ndarray], float]].
kwargs: Any
Extra arguments for metric. Refer to each metric documentation for a list of
possible arguments.
Returns
-------
np.ndarray (2d of size mxn where m is len(x) and n is len(y)).
Pairwise distance matrix between the two time series.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 3 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined.
Examples
--------
>>> import numpy as np
>>> from sktime.distances import pairwise_distance # doctest: +SKIP
>>> x_1d = np.array([1, 2, 3, 4]) # 1d array
>>> y_1d = np.array([5, 6, 7, 8]) # 1d array
>>> pairwise_distance(x_1d, y_1d, metric='dtw') # doctest: +SKIP
array([[16., 25., 36., 49.],
[ 9., 16., 25., 36.],
[ 4., 9., 16., 25.],
[ 1., 4., 9., 16.]])
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> pairwise_distance(x_2d, y_2d, metric='dtw') # doctest: +SKIP
array([[256., 576.],
[ 58., 256.]])
>>> x_3d = np.array([[[1], [2], [3], [4]], [[5], [6], [7], [8]]]) # 3d array
>>> y_3d = np.array([[[9], [10], [11], [12]], [[13], [14], [15], [16]]]) # 3d array
>>> pairwise_distance(x_3d, y_3d, metric='dtw') # doctest: +SKIP
array([[256., 576.],
[ 64., 256.]])
>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]]) # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]]) # 2d array
>>> pairwise_distance(x_2d, y_2d, metric='dtw', window=0.5) # doctest: +SKIP
array([[256., 576.],
[ 58., 256.]])
"""
from sktime.distances._numba_utils import (
_compute_pairwise_distance,
_make_3d_series,
)
_x = _make_3d_series(x)
if y is None:
y = x
_y = _make_3d_series(y)
symmetric = np.array_equal(_x, _y)
_metric_callable = _resolve_metric_to_factory(
metric, _x[0], _y[0], _METRIC_INFOS, **kwargs
)
return _compute_pairwise_distance(_x, _y, symmetric, _metric_callable)
def distance_alignment_path(
x: np.ndarray,
y: np.ndarray,
metric: Union[
str,
Callable[
[np.ndarray, np.ndarray, dict], Callable[[np.ndarray, np.ndarray], float]
],
Callable[[np.ndarray, np.ndarray], float],
NumbaDistance,
],
return_cost_matrix: bool = False,
**kwargs: Any,
) -> AlignmentPathReturn:
"""Compute the alignment path and distance between two time series.
First the distance metric is 'resolved'. This means the metric that is passed
is resolved to a callable. The callable is then called with x and y and the
value is then returned.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
metric: str or Callable
The distance metric to use.
If a string is given, the value must be one of the following strings:
'euclidean', 'squared', 'dtw', 'ddtw', 'wdtw', 'wddtw', 'lcss', 'edr', 'erp',
'msm'
If callable then it has to be a distance factory or numba distance callable.
If you want to pass custom kwargs to the distance at runtime, use a distance
factory as it constructs the distance using the kwargs before distance
computation.
A distance callable takes the form (must be no_python compiled):
Callable[[np.ndarray, np.ndarray], float]
A distance factory takes the form (must return a no_python callable):
Callable[[np.ndarray, np.ndarray, bool, dict], Callable[[np.ndarray,
np.ndarray], float]].
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
kwargs: Any
Arguments for metric. Refer to each metrics documentation for a list of
possible arguments.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined.
Returns
-------
list[tuple]
List of tuples containing the alignment path for the distance.
float
Distance between the x and y.
np.ndarray (of shape (len(x), len(y)).
Optional return only given if return_cost_matrix = True.
Cost matrix used to compute the distance.
"""
from sktime.distances._numba_utils import to_numba_timeseries
_x = to_numba_timeseries(x)
_y = to_numba_timeseries(y)
_dist_instance = _resolve_dist_instance(metric, _x, _y, _METRIC_INFOS, **kwargs)
return _dist_instance.distance_alignment_path(
_x, _y, return_cost_matrix=return_cost_matrix, **kwargs
)
def distance_alignment_path_factory(
x: np.ndarray,
y: np.ndarray,
metric: Union[
str,
Callable[
[np.ndarray, np.ndarray, dict], Callable[[np.ndarray, np.ndarray], float]
],
Callable[[np.ndarray, np.ndarray], float],
NumbaDistance,
],
return_cost_matrix: bool = False,
**kwargs: Any,
) -> DistanceAlignmentPathCallable:
"""Produce a distance alignment path factory numba callable.
First the distance metric is 'resolved'. This means the metric that is passed
is resolved to callable. The callable is then called with x and y and the
value is then returned.
Parameters
----------
x: np.ndarray (1d or 2d array)
First time series.
y: np.ndarray (1d or 2d array)
Second time series.
metric: str or Callable
The distance metric to use.
If a string is given, the value must be one of the following strings:
'euclidean', 'squared', 'dtw', 'ddtw', 'wdtw', 'wddtw', 'lcss', 'edr', 'erp',
'msm'
If callable then it has to be a distance factory or numba distance callable.
If you want to pass custom kwargs to the distance at runtime, use a distance
factory as it constructs the distance using the kwargs before distance
computation.
A distance callable takes the form (must be no_python compiled):
Callable[[np.ndarray, np.ndarray], float]
A distance factory takes the form (must return a no_python callable):
Callable[[np.ndarray, np.ndarray, bool, dict], Callable[[np.ndarray,
np.ndarray], float]].
return_cost_matrix: bool, defaults = False
Boolean that when true will also return the cost matrix.
kwargs: Any
Arguments for metric. Refer to each metrics documentation for a list of
possible arguments.
Raises
------
ValueError
If the value of x or y provided is not a numpy array.
If the value of x or y has more than 2 dimensions.
If a metric string provided, and is not a defined valid string.
If a metric object (instance of class) is provided and doesn't inherit from
NumbaDistance.
If a resolved metric is not no_python compiled.
If the metric type cannot be determined.
Returns
-------
Callable[[np.ndarray, np.ndarray], Union[np.ndarray, np.ndarray]]
Callable for the distance path.
"""
from sktime.distances._numba_utils import _numba_to_timeseries, to_numba_timeseries
from sktime.utils.numba.njit import njit
if x is None:
x = np.zeros((1, 10))
if y is None:
y = np.zeros((1, 10))
_x = to_numba_timeseries(x)
_y = to_numba_timeseries(y)
dist_instance = _resolve_dist_instance(metric, _x, _y, _METRIC_INFOS, **kwargs)
callable = dist_instance.distance_alignment_path_factory(
_x, _y, return_cost_matrix, **kwargs
)
@njit(cache=True)
def dist_callable(x: np.ndarray, y: np.ndarray):
_x = _numba_to_timeseries(x)
_y = _numba_to_timeseries(y)
return callable(_x, _y)
return dist_callable
_METRIC_INFOS = [
MetricInfo(
canonical_name="euclidean",
aka={"euclidean", "ed", "euclid", "pythagorean"},
dist_func=euclidean_distance,
dist_instance=_EuclideanDistance(),
),
MetricInfo(
canonical_name="erp",
aka={"erp", "edit distance with real penalty"},
dist_func=erp_distance,
dist_instance=_ErpDistance(),
dist_alignment_path_func=erp_alignment_path,
),
MetricInfo(
canonical_name="edr",
aka={"edr", "edit distance for real sequences"},
dist_func=edr_distance,
dist_instance=_EdrDistance(),
dist_alignment_path_func=edr_alignment_path,
),
MetricInfo(
canonical_name="lcss",
aka={"lcss", "longest common subsequence"},
dist_func=lcss_distance,
dist_instance=_LcssDistance(),
dist_alignment_path_func=lcss_alignment_path,
),
MetricInfo(
canonical_name="squared",
aka={"squared"},
dist_func=squared_distance,
dist_instance=_SquaredDistance(),
),
MetricInfo(
canonical_name="dtw",
aka={"dtw", "dynamic time warping"},
dist_func=dtw_distance,
dist_instance=_DtwDistance(),
dist_alignment_path_func=dtw_alignment_path,
),
MetricInfo(
canonical_name="ddtw",
aka={"ddtw", "derivative dynamic time warping"},
dist_func=ddtw_distance,
dist_instance=_DdtwDistance(),
dist_alignment_path_func=ddtw_alignment_path,
),
MetricInfo(
canonical_name="wdtw",
aka={"wdtw", "weighted dynamic time warping"},
dist_func=wdtw_distance,
dist_instance=_WdtwDistance(),
dist_alignment_path_func=wdtw_alignment_path,
),
MetricInfo(
canonical_name="wddtw",
aka={"wddtw", "weighted derivative dynamic time warping"},
dist_func=wddtw_distance,
dist_instance=_WddtwDistance(),
dist_alignment_path_func=wddtw_alignment_path,
),
MetricInfo(
canonical_name="msm",
aka={"msm", "move-split-merge"},
dist_func=msm_distance,
dist_instance=_MsmDistance(),
dist_alignment_path_func=msm_alignment_path,
),
MetricInfo(
canonical_name="twe",
aka={"twe", "time warped edit"},
dist_func=twe_distance,
dist_instance=_TweDistance(),
dist_alignment_path_func=twe_alignment_path,
),
]
_METRICS = {info.canonical_name: info for info in _METRIC_INFOS}
_METRIC_ALIAS = {alias: info for info in _METRIC_INFOS for alias in info.aka}
_METRIC_CALLABLES = {info.canonical_name: info.dist_func for info in _METRIC_INFOS}
_METRICS_NAMES = list(_METRICS.keys())
ALL_DISTANCES = (
ddtw_distance,
dtw_distance,
edr_distance,
erp_distance,
euclidean_distance,
lcss_distance,
msm_distance,
squared_distance,
wddtw_distance,
wdtw_distance,
twe_distance,
)
