R: Fast global alignment kernels

GAK {dtwclust} | R Documentation

## Fast global alignment kernels

### Description

Distance based on (triangular) global alignment kernels.

### Usage

    GAK(
      x,
      y,
      ...,
      sigma = NULL,
      window.size = NULL,
      normalize = TRUE,
      error.check = TRUE
    )

    gak(
      x,
      y,
      ...,
      sigma = NULL,
      window.size = NULL,
      normalize = TRUE,
      error.check = TRUE
    )

### Arguments

`x, y` | Time series. A multivariate series should have time spanning the rows and variables spanning the columns.
`...` | Currently ignored.
`sigma` | Parameter for the Gaussian kernel's width. See details for the interpretation of `NULL`.
`window.size` | Parameterization of the constraining band (T in Cuturi (2011)). See details.
`normalize` | Normalize the result by considering diagonal terms.
`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

This function uses the Triangular Global Alignment Kernel (TGAK) described in Cuturi (2011). It supports series of different length and multivariate series, so long as the ratio of the series' lengths doesn't differ by more than 2 (or less than 0.5).

The `window.size` parameter is similar to the one used in DTW, so `NULL` signifies no constraint, and its value should be greater than 1 if used with series of different length.

The Gaussian kernel is parameterized by `sigma`. Providing `NULL` means that the value will be estimated by using the strategy mentioned in Cuturi (2011) with a constant of 1. This estimation is subject to randomness, so consider estimating the value once and re-using it (the estimate is returned as an attribute of the result). See the examples.

For more information, refer to the package vignette and the referenced article.

### Value

The logarithm of the GAK if `normalize = FALSE`, otherwise 1 minus the normalized GAK. The value of `sigma` is assigned as an attribute of the result.

### 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`.

### Note

The estimation of `sigma` does not depend on `window.size`.

If `normalize` is set to `FALSE`, the returned value is not a distance, rather a similarity. The `proxy::dist()` version is thus always normalized. Use `proxy::simil()` with `method` set to "uGAK" if you want the unnormalized similarities.

A constrained unnormalized calculation (i.e. with `window.size > 0` and `normalize = FALSE`) will return negative infinity if `abs(NROW(x)` `-` `NROW(y))` `>` `window.size`. Since the function won't perform calculations in that case, it might be faster, but if this behavior is not desired, consider reinterpolating the time series (see `reinterpolate()`) or increasing the window size.

### References

Cuturi, M. (2011). Fast global alignment kernels. In Proceedings of the 28th international conference on machine learning (ICML-11) (pp. 929-936).

### Examples

    ## Not run:
    data(uciCT)

    set.seed(832)
    GAKd <- proxy::dist(zscore(CharTraj), method = "gak",
                        pairwise = TRUE, window.size = 18L)

    # Obtained estimate of sigma
    sigma <- attr(GAKd, "sigma")

    # Use value for clustering
    tsclust(CharTraj, k = 20L,
            distance = "gak", centroid = "shape",
            trace = TRUE,
            args = tsclust_args(dist = list(sigma = sigma,
                                            window.size = 18L)))

    ## End(Not run)

    # Unnormalized similarities
    proxy::simil(CharTraj[1L:5L], method = "ugak")

[Package dtwclust version 5.5.7 Index]