OTW

Implementation of OTW, presented in [LLSH23]

For more details see : - https://ieeexplore.ieee.org/document/10095915 - https://arxiv.org/abs/2306.00620

Authors

Alberto Zancanaro <alberto.zancanaro@uni.lu>

class dtw_loss_functions.otw.otw(m: float = 1, s: int | float = 0.5, beta: float = 1, reduction: str = 'mean')[source]

Bases: Module

Methods

forward(x, y)

Computes the OTW distance between two time series.
forward(x: Tensor, y: Tensor) → Tensor[source]

Computes the OTW distance between two time series.

Parameters:

  • x (torch.Tensor) – First time series, of shape (B, L) where B is the batch size and L is the length of the time series.

  • y (torch.Tensor) – Second time series, of shape (B, L) where B is the batch size and L is the length of the time series.

Returns:

OTW distance between the two time series

Return type:

torch.Tensor

dtw_loss_functions.otw.otw_distance(x: Tensor, y: Tensor, m: float = 1, s: int | float = 0.5, beta: float = 1, reduction: str = 'mean') → Tensor[source]

Implements the OTW distance between two time series, as defined in equation (10) of the paper.

Parameters:

  • x (torch.Tensor) – First time series, of shape (B, L) where B is the batch size and L is the length of the time series.

  • y (torch.Tensor) – Second time series, of shape (B, L) where B is the batch size and L is the length of the time series.

  • m (float) – Waste cost parameter, default is 1.

  • s (int | float) – Window size parameter, it can be an integer or a float between 0 and 1. Default is 0.5. If float, it is interpreted as a fraction of the length of the time series. If integer, it is interpreted as the number of time steps.

  • beta (float) – Hyperparameter for the smooth l1 loss, default is 1.

Returns:

OTW distance between the two time series

Return type:

torch.Tensor

dtw_loss_functions.otw.smooth_l1_loss(x: Tensor, beta: float, reduction='mean') → Tensor[source]

Computes the smooth l1 of the input tensor x, as defined in equation (9) of the paper.

Parameters:

  • x (torch.Tensor) – Input tensor of shape (B). Each element corresponds to the difference between two time series.

  • beta (float) – Hyperparameter for the smooth l1 loss.

  • reduction (str) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. Default: ‘mean’.

Returns:

Smooth l1 loss of the input tensor. If reduction is ‘none’, the output has the same shape as x. If reduction is ‘mean’ or ‘sum’, the output is a scalar.

Return type:

torch.Tensor

dtw_loss_functions.otw.window_cumsum(x: Tensor, s: int) → Tensor[source]

Computes the cumulative sum of the input tensor x as defined in equation (7) of the paper.

Given a time series A represented as an array of values [a1, a2, ..., aL], the window cumsum is computed as : window_cumsum(A) = cumsum(A) - cumsum(A[0:L-s]) (i.e. the cumsum of all the array minus the cumsum of the array excluding the last s elements)

Parameters:

  • x (torch.Tensor) – Input tensor of shape (B, L).

  • s (int) – Window size.

Returns:

Cumulative sum over the sliding window, of shape (B).

Return type:

torch.Tensor