Distances¶

Lockstep Distances¶

tssearch.distances.lockstep_distances.braycurtis_distance(x, y, weight=None)[source]¶

Computes the Braycurtis distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Braycurtis distance value.
Return type:	float

tssearch.distances.lockstep_distances.canberra_distance(x, y, weight=None)[source]¶

Computes the Canberra distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Canberra distance value.
Return type:	float

tssearch.distances.lockstep_distances.chebyshev_distance(x, y, weight=None)[source]¶

Computes the Chebyshev distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Chebyshev distance value.
Return type:	float

tssearch.distances.lockstep_distances.correlation_distance(x, y, weight=None)[source]¶

Computes the correlation distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Correlation distance value.
Return type:	float

tssearch.distances.lockstep_distances.cosine_distance(x, y, weight=None)[source]¶

Computes the cosine distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Cosine distance value.
Return type:	float

tssearch.distances.lockstep_distances.euclidean_distance(x, y, weight=None)[source]¶

Computes the Euclidean distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Euclidean distance value.
Return type:	float

tssearch.distances.lockstep_distances.hamming_distance(x, y, weight=None)[source]¶

Computes the Hamming distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Hamming distance value.
Return type:	float

tssearch.distances.lockstep_distances.mahalanobis_distance(x, y, weight=None)[source]¶

Computes the Mahalanobis distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Mahalanobis distance value.
Return type:	float

tssearch.distances.lockstep_distances.manhattan_distance(x, y, weight=None)[source]¶

Computes the Manhattan distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Manhattan distance value.
Return type:	float

tssearch.distances.lockstep_distances.minkowski_distance(x, y, weight=None, p=3)[source]¶

Computes the Minkowski distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values. p (int) – Lp norm distance degree.
Returns:	Minkowski distance value.
Return type:	float

tssearch.distances.lockstep_distances.pearson_correlation(x, y, beta=None)[source]¶

Computes the Pearson correlation between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. beta (float) – Beta coefficient.
Returns:	Pearson correlation value.
Return type:	float

tssearch.distances.lockstep_distances.short_time_series_distance(x, y, tx=None, ty=None)[source]¶

Computes the short time series distance (STS) between two time series.

Reference: Möller-Levet, C. S., Klawonn, F., Cho, K., and Wolkenhauer, O. (2003).

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. tx (nd-array) – Sampling index of time series x. ty (nd-array) – Sampling index of time series y.
Returns:	Short time series distance value.
Return type:	float

tssearch.distances.lockstep_distances.sqeuclidean_distance(x, y, weight=None)[source]¶

Computes the squared Euclidean distance between two time series.

If the time series do not have the same length, an interpolation is performed.

Parameters:	x (nd-array) – Time series x. y (nd-array) – Time series y. weight (nd-array (Default: None)) – query weight values.
Returns:	Squared Euclidean distance value.
Return type:	float

Elastic Distances¶

tssearch.distances.elastic_distances.dlp(x, y, p=2)[source]¶

Computes Lp norm distance between two time series.

Parameters:	x (nd-array) – Time series x (query). y (nd-array) – Time series y. p (int) – Lp norm distance degree for local cost computation.
Returns:
Return type:	The Lp distance.

tssearch.distances.elastic_distances.dtw(x, y, weight=None, **kwargs)[source]¶

Computes Dynamic Time Warping (DTW) of two time series.

Parameters:

x (nd-array) – Time series x (query).
y (nd-array) – Time series y.
dist (function) – The distance used as a local cost measure. None defaults to the squared euclidean distance.
**kwargs –
below (See) –
do_sign_norm (bool) -- (*) – If True the signals will be normalized before computing the DTW, (default: False)
do_dist_norm (bool) -- (*) – If True the DTW distance will be normalized by dividing the summation of the path dimension. (default: True)
window (String) -- (*) – Selects the global window constrains. Available options are None and sakoe-chiba. (default: None)
factor (Float) -- (*) – Selects the global constrain factor. (default: min(xl, yl) * .50)

Returns:

d (float) – The DTW distance.
ac (nd-array) – The accumulated cost matrix.
path (nd-array) – The optimal warping path between the two sequences.

tssearch.distances.elastic_distances.lcss(x, y, eps=1, **kwargs)[source]¶

Computes the Longest Common Subsequence (LCSS) distance between two numeric time series.

Parameters:

x (nd-array) – Time series x (query).
y (nd-array) – Time series y.
eps (float) – Amplitude matching threshold.
**kwargs –
below (See) –
window (String) -- (*) – Selects the global window constrains. Available options are None and sakoe-chiba. (default: None)

Returns:

d (float) – The LCSS distance.
ac (nd-array) – The similarity matrix.
path (nd-array) – The optimal path between the two sequences.

tssearch.distances.elastic_distances.twed(x, y, tx, ty, nu=0.001, lmbda=1.0, p=2, report='distance')[source]¶

Computes Time Warp Edit Distance (TWED) of two time series.

Reference :: 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. arXiv:cs/0703033 http://people.irisa.fr/Pierre-Francois.Marteau/

Parameters:

x (nd-array) – Time series x (query).
y (nd-array) – Time series y.
tx (nd-array) – Time stamp time series x.
ty (nd-array) – Time stamp time series y.
nu (int) –

Stiffness parameter (nu >= 0)

nu = 0, TWED distance measure on amplitude. nu > 0, TWED distance measure on amplitude x time.
lmbda (int) – Penalty for deletion operation (lmbda >= 0).
p (int) – Lp norm distance degree for local cost computation.
report (str) – distance, cost matrix, path.

Returns:

d (float) – The TWED distance.
ac (nd-array) – The accumulated cost matrix.
path (nd-array) – The optimal warping path between the two sequences.

Time Distances¶

tssearch.distances.time_distances.tam(x, y)[source]¶

Calculates the Time Alignment Measurement (TAM) based on an optimal warping path between two time series.

Reference: Folgado et. al, Time Alignment Measurement for Time Series, 2016.

Parameters:

x (nd-array) – Time series x.
y (nd-array) – Time series y.

Returns:

In case report=instants the number of indexes in advance, delay and phase
will be returned.
For report=ratios, the ratio of advance, delay and phase.
will be returned. In case report=distance, only the TAM will be returned.