Time series

A time series is a (temporally) ordered sequence of real values. A univariate time series has a single dimension, whereas a multivariate time series has multiple dimensions. In Wildboar, time series are represented by Numpy-arrays. A single univariate time series is represented as an array of shape (1, n_timestep) (or (n_timestep, )). Wildboar represents a multivariate time series as an array of shape (1, n_dims, n_timestep) (or (n_dims, n_timestep) depending on context). A dataset of time series is an array of n_samples, i.e., for univariate time series an array of shape (n_samples, n_timestep) (or (n_samples, 1, n_timestep)) and a multivarete time series is represented as an array of shape (n_samples, n_dims, n_timestep).

Most algorithms in wildboar assumes that the time series are of equal length and without missing values. However, some datasets contain both missing values and/or have time series or dimensions of unequal length. Wildboar represents the End-of-Sequence identifier as EOS and value is missing by nupy.nan. The EoS value is a valid IEEE754 NaN value, and will be treated as True by numpy.isnan, whereas is_end_of_series will treat numpy.nan as False.

Note

By having EoS treated as NaN, we can ignore it and just treat them as missing values.

import numpy as np
from wildboar.utils.variable_len import EOS

t1 = np.array([1, 2, 3, 1, 1, 1], dtype=float)
t2 = np.array([1, 2, 3, 1, EOS, EOS], dtype=float)
t3 = np.array([1, np.nan, 3, 3, 3, 3], dtype=float)
x = np.vstack([t1, t2, t3])  # dataset of (3, 6)
x

array([[ 1.,  2.,  3.,  1.,  1.,  1.],
       [ 1.,  2.,  3.,  1., nan, nan],
       [ 1., nan,  3.,  3.,  3.,  3.]])

In the example, we construct a dataset comprising 3 samples, each containing 6 timesteps, where:

• x[0] contains no missing values and has a sequence length equal to n_timestep.

• x[1] also contains no missing values but has a sequence length of 4.

• x[2] includes one missing value at the second index position.

Variable length time series

Warning

Support for variable length time series is not stable and the API will change