This function massages the input quaternion time series to apply hierarchical agglomerative clustering on them, with the possibility of separating amplitude and phase variability and of choosing the source of variability through which clusters should be searched.

## Usage

```
hclust(x, metric, linkage_criterion, ...)
# S3 method for default
hclust(
x,
metric = c("euclidean", "maximum", "manhattan", "canberra", "binary", "minkowski"),
linkage_criterion = c("complete", "average", "single", "ward.D2"),
...
)
# S3 method for qts_sample
hclust(
x,
metric = c("l2", "pearson"),
linkage_criterion = c("complete", "average", "single", "ward.D2"),
n_clusters = 1L,
warping_class = c("affine", "dilation", "none", "shift", "srsf"),
centroid_type = "mean",
cluster_on_phase = FALSE,
...
)
```

## Arguments

- x
Either a numeric matrix of data, or an object that can be coerced to such a matrix (such as a numeric vector or a data frame with all numeric columns) or an object of class qts_sample.

- metric
A character string specifying the distance measure to be used. This must be one of

`"euclidean"`

,`"maximum"`

,`"manhattan"`

,`"canberra"`

,`"binary"`

or`"minkowski"`

if`x`

is not a QTS sample. Otherwise, it must be one of`"l2"`

,`"pearson"`

or`"dtw"`

.- linkage_criterion
A string specifying which linkage criterion should be used to compute distances between sets of curves. Choices are

`"complete"`

for complete linkage,`"average"`

for average linkage and`"single"`

for single linkage. See`stats::hclust()`

for more details. Defaults to`"complete"`

.- ...
Further graphical arguments. E.g.,

`cex`

controls the size of the labels (if plotted) in the same way as`text`

.- n_clusters
An integer value specifying the number of clusters. Defaults to

`1L`

.- warping_class
A string specifying the warping class Choices are

`"affine"`

,`"dilation"`

,`"none"`

,`"shift"`

or`"srsf"`

. Defaults to`"affine"`

. The SRSF class is the only class which is boundary-preserving.- centroid_type
A string specifying the type of centroid to compute. Choices are

`"mean"`

,`"median"`

`"medoid"`

,`"lowess"`

or`"poly"`

. Defaults to`"mean"`

. If LOWESS appproximation is chosen, the user can append an integer between 0 and 100 as in`"lowess20"`

. This number will be used as the smoother span. This gives the proportion of points in the plot which influence the smooth at each value. Larger values give more smoothness. The default value is 10%. If polynomial approximation is chosen, the user can append an positive integer as in`"poly3"`

. This number will be used as the degree of the polynomial model. The default value is`4L`

.- cluster_on_phase
A boolean specifying whether clustering should be based on phase variation or amplitude variation. Defaults to

`FALSE`

which implies amplitude variation.

## Value

An object of class `stats::kmeans`

or `stats::hclust`

or
`dbscan_fast`

if the input `x`

is NOT of class `qts_sample`

. Otherwise,
an object of class `qtsclust`

which is effectively a list with four
components:

`qts_aligned`

: An object of class`qts_sample`

storing the sample of aligned QTS;`qts_centers`

: A list of objects of class`qts`

representing the centers of the clusters;`best_clustering`

: An object of class`fdacluster::caps`

storing the results of the best k-mean alignment result among all initialization that were tried.`call_name`

: A string storing the name of the function that was used to produce the clustering structure;`call_args`

: A list containing the exact arguments that were passed to the function`call_name`

that produced this output.

## Examples

```
out <- hclust(vespa64$igp[1:10], n_clusters = 2)
plot(out)
```