dtwclust (version 6.0.0)

compute_envelope: Time series warping envelopes

Description

This function computes the envelopes for DTW lower bound calculations with a Sakoe-Chiba band for a given univariate time series using the streaming algorithm proposed by Lemire (2009).

Usage

compute_envelope(x, window.size, error.check = TRUE)

Value

A list with two elements (lower and upper envelopes respectively): lower and upper.

Arguments

x

A univariate time series.

window.size

Window size for envelope calculation. See details.

error.check

Logical indicating whether the function should try to detect inconsistencies and give more informative errors messages. Also used internally to avoid repeating checks.

Details

The windowing constraint uses a centered window. The calculations expect a value in window.size that represents the distance between the point considered and one of the edges of the window. Therefore, if, for example, window.size = 10, the warping for an observation \(x_i\) considers the points between \(x_{i-10}\) and \(x_{i+10}\), resulting in 10(2) + 1 = 21 observations falling within the window.

References

Lemire D (2009). ``Faster retrieval with a two-pass dynamic-time-warping lower bound .'' Pattern Recognition, 42(9), pp. 2169 - 2180. ISSN 0031-3203, tools:::Rd_expr_doi("10.1016/j.patcog.2008.11.030"), https://www.sciencedirect.com/science/article/pii/S0031320308004925.

Examples

data(uciCT)

H <- compute_envelope(CharTraj[[1L]], 18L)

matplot(do.call(cbind, H), type = "l", col = 2:3)
lines(CharTraj[[1L]])