RoughKMeans_SHELL {SoftClustering}

Rough k-Means Shell

Description

RoughKMeans_SHELL performs rough k-means algorithms with options for normalization and a 2D-plot of the results.

Usage

RoughKMeans_SHELL(clusterAlgorithm, dataMatrix, meansMatrix, nClusters, 
                  normalizationMethod, maxIterations, plotDimensions, 
                  colouredPlot, threshold, weightLower)

Arguments

clusterAlgorithm

Select 0 = classic k-means, 1 = Lingras & West's rough k-means, 2 = Peters' rough k-means, 3 = \pi rough k-means. Default: clusterAlgorithm = 3 (\pi rough k-means).

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. Note: Plotting is limited to a maximum of 5 clusters.

normalizationMethod

1 = unity interval, 2 = normal distribution (sample variance), 3 = normal distribution (population variance). Any other value returns the matrix unchanged. Default: meansMatrix = 1 (unity interval).

maxIterations

Maximum number of iterations. Default: maxIterations=100.

plotDimensions

An integer vector of the length 2. Defines the to be plotted feature dimensions, i.e., max(plotDimensions = c(1:2)) <= nFeatures. Default: plotDimensions = c(1:2).

colouredPlot

Select TRUE = colouredPlot plot, FALSE = black/white plot.

threshold

Relative threshold in rough k-means algorithms (threshold >= 1.0). Default: threshold = 1.5. Note: It can be ignored for classic k-means.

weightLower

Weight of the lower approximation in rough k-means algorithms (0.0 <= weightLower <= 1.0). Default: weightLower = 0.7. Note: It can be ignored for classic k-means and \pi rough k-means

Value

2D-plot of clustering results. The boundary objects are represented by stars (*).

$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

Lloyd, S.P. (1982) Least squares quantization in PCM. IEEE Transactions on Information Theory 28, 128–137. <doi:10.1016/j.ijar.2012.10.003>.

Lingras, P. and West, C. (2004) Interval Set Clustering of web users with rough k-means. Journal of Intelligent Information Systems 23, 5–16. <doi:10.1023/b:jiis.0000029668.88665.1a>.

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

Lingras, P. and Peters, G. (2011) Rough Clustering. WIREs Data Mining and Knowledge Discovery 1, 64–72. <doi:10.1002/widm.16>.

Lingras, P. and Peters, G. (2012) Applying rough set concepts to clustering. In: Peters, G.; Lingras, P.; Slezak, D. and Yao, Y. Y. (Eds.) Rough Sets: Selected Methods and Applications in Management and Engineering, Springer, 23–37. <doi:10.1007/978-1-4471-2760-4_2>.

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_SHELL(3, DemoDataC2D2a, 2, 2, 1, 100, c(1:2), TRUE, 1.5, 0.7)