ellip.kmeans.torus: K-Means Clustering to K-Spheres Clustering on Torus

Description

ellip.kmeans.torus prepares the parameters for conformity scores which are derived by k-means clustering on torus.

Usage

ellip.kmeans.torus(
  data,
  centers = 10,
  type = c("homogeneous-circular", "heterogeneous-circular", "ellipsoids", "general"),
  init = c("kmeans", "hierarchical"),
  d = NULL,
  additional.condition = TRUE,
  THRESHOLD = 1e-10,
  maxiter = 200,
  verbose = TRUE,
  ...
)

Arguments

data

data n x d matrix of toroidal data on \([0, 2\pi)^d\)

centers

either the number of clusters or a set of initial cluster centers. If a number, a random set of row in x is chosen as the initial centers.

type

character which must be "homogeneous-circular", "heterogeneous-circular", or "general". If "homogeneous-circular", the radii of k-spheres are identical. If "heterogeneous-circular", the radii of k-spheres may be different. If "ellipsoids", cluster with k-ellipsoids without optimized parameters. If, "general", clustering with k-ellipsoids. The parameters to construct the ellipses are optimized with elliptical k-means algorithm, which is modified for toroidal space. See references for the detail. Default is "homogeneous-circular".

init

determine the initial parameter for option "general". Must be "kmeans" or "hierarchical". If "kmeans", the initial parameters are obtained with extrinsic kmeans method. If "hierarchical", the initial parameters are obtained with hierarchical clustering method. Default is "hierarchical".

pairwise distance matrix(dist object) for init = "hierarchical", which used in hierarchical clustering. If init = "hierarchical" and d = NULL, d will be automatically filled with ang.pdist(data).

additional.condition

boolean index. If TRUE, a singular matrix will be altered to the scalar identity.

THRESHOLD

number of threshold for difference between updating and updated parameters. Default is 1e-10.

maxiter

the maximal number of iteration. Default is 200.

verbose

boolean index, which indicates whether display additional details as to what the algorithm is doing or how many loops are done. Default is TRUE.

...

Further arguments for argument init. If init = "kmeans", these are for kmeans. If init = "hierarchical", there are for hclust.

Value

returns a list, containing all values which determines the shape and location of spheres.

References

Jung, S., Park, K., & Kim, B. (2021). Clustering on the torus by conformal prediction. The Annals of Applied Statistics, 15(4), 1583-1603.

Mardia, K. V., Kent, J. T., Zhang, Z., Taylor, C. C., & Hamelryck, T. (2012). Mixtures of concentrated multivariate sine distributions with applications to bioinformatics. Journal of Applied Statistics, 39(11), 2475-2492.

Shin, J., Rinaldo, A., & Wasserman, L. (2019). Predictive clustering. arXiv preprint arXiv:1903.08125.

Examples

Run this code

# NOT RUN {
data <- ILE[1:200, 1:2]

ellip.kmeans.torus(data, centers = 3, type = "general", init = "hierarchical")
# }