RoughKMeans_PI: 'PI' Rough k-Means

In SoftClustering: Soft Clustering Algorithms

PI Rough k-Means

Description

RoughKMeans_PI performs pi k-means clustering algorithm in its standard case. Therefore, weights are not required.

Usage

RoughKMeans_PI(dataMatrix, meansMatrix, nClusters, maxIterations, threshold)

Arguments

dataMatrix	Matrix with the objects to be clustered. Dimension: [nObjects x nFeatures].
meansMatrix	Select means derived from 1 = random (unity interval), 2 = maximum distances, matrix [nClusters x nFeatures] = self-defined means. Default: 2 = maximum distances.
nClusters	Number of clusters: Integer in [2, nObjects). Note, nCluster must be set even when meansMatrix is a matrix. For transparency, nClusters will not be overridden by the number of clusters derived from meansMatrix. Default: nClusters=2.
maxIterations	Maximum number of iterations. Default: maxIterations=100.
threshold	Relative threshold in rough k-means algorithms (threshold >= 1.0). Default: threshold = 1.5.

Value

$upperApprox: Obtained upper approximations [nObjects x nClusters]. Note: Apply function createLowerMShipMatrix() to obtain lower approximations; and for the boundary: boundary = upperApprox - lowerApprox.

$clusterMeans: Obtained means [nClusters x nFeatures].

$nIterations: Number of iterations.

Author(s)

M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.

References

Peters, G. (2006) Some refinements of rough k-means clustering. Pattern Recognition 39, 1481–1491. <doi:10.1016/j.patcog.2006.02.002>.

Peters, G.; Crespo, F.; Lingras, P. and Weber, R. (2013) Soft clustering – fuzzy and rough approaches and their extensions and derivatives. International Journal of Approximate Reasoning 54, 307–322. <doi:10.1016/j.ijar.2012.10.003>.

Peters, G. (2014) Rough clustering utilizing the principle of indifference. Information Sciences 277, 358–374. <doi:10.1016/j.ins.2014.02.073>.

Peters, G. (2015) Is there any need for rough clustering? Pattern Recognition Letters 53, 31–37. <doi:10.1016/j.patrec.2014.11.003>.

Examples

# An illustrative example clustering the sample data set DemoDataC2D2a.txt
RoughKMeans_PI(DemoDataC2D2a, 2, 2, 100, 1.5)

SoftClustering documentation built on Aug. 18, 2023, 9:08 a.m.