kmeans.torus {ClusTorus}

K-Means Clustering on Torus

Description

kmeans.torus implements extrinsic k-means clustering on toroidal space.

Usage

kmeans.torus(data, centers = 10, ...)

## S3 method for class 'kmeans.torus'
predict(object, newdata, ...)

Arguments

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.

...

additional parameter

object

kmeans.torus object

newdata

n x d matrix of toroidal data on [0, 2\pi)^d. Dimension d must be the same as data used for kmeans.torus object.

Details

In Euclidean space, we know that the total sum of squares is equal to the summation of the within cluster sum of squares and the between cluster centers sum of squares. However, toroidal space does not satisfy the property; the equality does not hold. Thus, you need to be careful to use the sum of squares.

Extrinsic k-means algorithm uses the ambient space for [0, 2\pi)^d. Each datum is transformed to a vector in 2d-dimensional Euclidean space, whose elements are sine and cosine values of the datum, then a usual k-means algorithm is applied to transformed data.

Value

returns a kmeans object, which contains

extrinsic.results

extrinsic k-means clustering results using ordinary kmeans algorithm.

centers

A matrix of cluster centers.

membership

A vector of integers indicating the cluster to which each point is allocated.

size

The number of points in each cluster.

withinss

Vector of within-cluster sum of squares, one component per cluster.

totss

The total sum of squares, based on angular distance.

betweenss

The between-cluster sum of squares.

References

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

Gao, Y., Wang, S., Deng, M., & Xu, J. (2018). RaptorX-Angle: real-value prediction of protein backbone dihedral angles through a hybrid method of clustering and deep learning. BMC bioinformatics, 19(4), 73-84.

See Also

kmeans, ang.minus, ang.dist

Examples

data <- ILE[1:200, 1:2]

kmeans.torus(data, centers = 2,
             iter.max = 100, nstart = 1)