dtwclust (version 5.5.12)

SBD: Shape-based distance

Description

Distance based on coefficient-normalized cross-correlation as proposed by Paparrizos and Gravano (2015) for the k-Shape clustering algorithm.

Usage

SBD(x, y, znorm = FALSE, error.check = TRUE, return.shifted = TRUE)
sbd(x, y, znorm = FALSE, error.check = TRUE, return.shifted = TRUE)

Value

For return.shifted = FALSE, the numeric distance value, otherwise a list with:

• dist: The shape-based distance between x and y.

• yshift: A shifted version of y so that it optimally matches x (based on NCCc()).

Arguments

x, y

Univariate time series.

znorm

Logical. Should each series be z-normalized before calculating the distance?

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.

return.shifted

Logical. Should the shifted version of y be returned? See details.

Proxy version

The version registered with dist is custom (loop = FALSE in pr_DB). The custom function handles multi-threaded parallelization directly (with RcppParallel). It uses all available threads by default (see RcppParallel::defaultNumThreads()), but this can be changed by the user with RcppParallel::setThreadOptions().

An exception to the above is when it is called within a foreach parallel loop made by dtwclust. If the parallel workers do not have the number of threads explicitly specified, this function will default to 1 thread per worker. See the parallelization vignette for more information (browseVignettes("dtwclust")).

It also includes symmetric optimizations to calculate only half a distance matrix when appropriate---only one list of series should be provided in x. If you want to avoid this optimization, call dist by giving the same list of series in both x and y.

In some situations, e.g. for relatively small distance matrices, the overhead introduced by the logic that computes only half the distance matrix can be bigger than just calculating the whole matrix.

Details

This distance works best if the series are z-normalized. If not, at least they should have appropriate amplitudes, since the values of the signals do affect the outcome.

If x and y do not have the same length, it would be best if the longer sequence is provided in y, because it will be shifted to match x. After matching, the series may have to be truncated or extended and padded with zeros if needed.

The output values lie between 0 and 2, with 0 indicating perfect similarity.

References

Paparrizos J and Gravano L (2015). ``k-Shape: Efficient and Accurate Clustering of Time Series.'' In Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, series SIGMOD '15, pp. 1855-1870. ISBN 978-1-4503-2758-9, tools:::Rd_expr_doi("10.1145/2723372.2737793").

See Also

NCCc(), shape_extraction()

Examples

# load data
data(uciCT)

# distance between series of different lengths
sbd <- SBD(CharTraj[[1]], CharTraj[[100]], znorm = TRUE)$dist

# cross-distance matrix for series subset (notice the two-list input)
sbD <- proxy::dist(CharTraj[1:10], CharTraj[1:10], method = "SBD", znorm = TRUE)