# Rough k-Means Shell RoughKMeans_SHELL performs rough k-means algorithms with options for normalization and a 2D-plot of the results. ```r 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 ## Returns 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. ## Examples ```r # 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) ``` ## References Lloyd, S.P. (1982) Least squares quantization in PCM. **IEEE Transactions on Information Theory** 28 , 128--137. . Lingras, P. and West, C. (2004) Interval Set Clustering of web users with rough k-means. **Journal of Intelligent Information Systems** 23 , 5--16. . Peters, G. (2006) Some refinements of rough k-means clustering. **Pattern Recognition** 39 , 1481--1491. . Lingras, P. and Peters, G. (2011) Rough Clustering. **WIREs Data Mining and Knowledge Discovery** 1 , 64--72. . 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. . 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. . Peters, G. (2014) Rough clustering utilizing the principle of indifference. **Information Sciences** 277 , 358--374. . Peters, G. (2015) Is there any need for rough clustering? **Pattern Recognition Letters** 53 , 31--37. . ## Author(s) M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.

RoughKMeans_SHELL function