| Title: | Soft Clustering Algorithms |
|---|---|
| Description: | It contains soft clustering algorithms, in particular approaches derived from rough set theory: Lingras & West original rough k-means, Peters' refined rough k-means, and PI rough k-means. It also contains classic k-means and a corresponding illustrative demo. |
| Authors: | G. Peters (Ed.) |
| Maintainer: | G. Peters <[email protected]> |
| License: | GPL-2 |
| Version: | 2.1.3 |
| Built: | 2024-12-18 06:27:08 UTC |
| Source: | CRAN |
Creates a lower approximation out of an upper approximation.
createLowerMShipMatrix(upperMShipMatrix)createLowerMShipMatrix(upperMShipMatrix)
upperMShipMatrix |
An upper approximation matrix. |
Returns the corresponding lower approximation.
G. Peters.
Checks for integer.
datatypeInteger(x)datatypeInteger(x)
x |
As a replacement for is.integer(). is.integer() delivers FALSE when the variable is numeric (as superset for integer etc.) |
TRUE if x is integer otherwise FALSE.
G. Peters.
A small two-dimensional dataset with two clusters for demonstration purposes. See examples in the Help/Description of a function, e.g. for HardKMeansDemo().
data(DemoDataC2D2a)data(DemoDataC2D2a)
Rows: objects, columns: features
data(DemoDataC2D2a)data(DemoDataC2D2a)
HardKMeans performs classic (hard) k-means.
HardKMeans(dataMatrix, meansMatrix, nClusters, maxIterations)HardKMeans(dataMatrix, meansMatrix, nClusters, maxIterations)
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. |
$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.
M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.
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>.
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>.
# An illustrative example clustering the sample data set DemoDataC2D2a.txt HardKMeans(DemoDataC2D2a, 2, 2, 100)# An illustrative example clustering the sample data set DemoDataC2D2a.txt HardKMeans(DemoDataC2D2a, 2, 2, 100)
HardKMeansDemo shows how hard k-means performs stepwise. The number of features is set to 2 and the maximum number of iterations is 100.
HardKMeansDemo(dataMatrix, meansMatrix, nClusters)HardKMeansDemo(dataMatrix, meansMatrix, nClusters)
dataMatrix |
Matrix with the objects to be clustered. Dimension: [nObjects x nFeatures]. Default: no default set. |
meansMatrix |
Select means derived from 1 = random (unity interval), 2 = maximum distances, matrix [nClusters x nFeatures=2] = self-defined means. Default: meansMatrix=1 (random). |
nClusters |
Number of clusters: Integer in [2, min(5, nObjects-1)]. 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. |
None.
G. Peters.
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>.
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>.
# Clustering the data set DemoDataC2D2a.txt (nClusters=2, random initial means) HardKMeansDemo(DemoDataC2D2a,1,2) # Clustering the data set DemoDataC2D2a.txt (nClusters=2,3,4; initially set means) HardKMeansDemo(DemoDataC2D2a,initMeansC2D2a,2) HardKMeansDemo(DemoDataC2D2a,initMeansC3D2a,3) HardKMeansDemo(DemoDataC2D2a,initMeansC4D2a,4) # Clustering the data set DemoDataC2D2a.txt (nClusters=5, initially set means) # It leads to an empty cluster: a (rare) case for an abnormal termination of k-means. HardKMeansDemo(DemoDataC2D2a,initMeansC5D2a,5)# Clustering the data set DemoDataC2D2a.txt (nClusters=2, random initial means) HardKMeansDemo(DemoDataC2D2a,1,2) # Clustering the data set DemoDataC2D2a.txt (nClusters=2,3,4; initially set means) HardKMeansDemo(DemoDataC2D2a,initMeansC2D2a,2) HardKMeansDemo(DemoDataC2D2a,initMeansC3D2a,3) HardKMeansDemo(DemoDataC2D2a,initMeansC4D2a,4) # Clustering the data set DemoDataC2D2a.txt (nClusters=5, initially set means) # It leads to an empty cluster: a (rare) case for an abnormal termination of k-means. HardKMeansDemo(DemoDataC2D2a,initMeansC5D2a,5)
initializeMeansMatrix delivers an initial means matrix.
initializeMeansMatrix(dataMatrix, nClusters, meansMatrix)initializeMeansMatrix(dataMatrix, nClusters, meansMatrix)
dataMatrix |
Matrix with the objects as basis for the means matrix. |
nClusters |
Number of clusters. |
meansMatrix |
Select means derived from 1 = random (unity interval), 2 = maximum distances, matrix [nClusters x nFeatures] = self-defined means (will be returned unchanged). Default: 2 = maximum distances. |
Initial means matrix [nClusters x nFeatures].
M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.
Two-dimensional dataset with two initial cluster means for the dataset DemoDataC2D2a. See examples in the Help/Description of a function, e.g. for HardKMeansDemo().
data(initMeansC2D2a)data(initMeansC2D2a)
Rows: objects, columns: features
data(initMeansC2D2a)data(initMeansC2D2a)
Two-dimensional dataset with three initial cluster means for the dataset DemoDataC2D2a. See examples in the Help/Description of a function, e.g. for HardKMeansDemo().
data(initMeansC3D2a)data(initMeansC3D2a)
Rows: objects, columns: features
data(initMeansC3D2a)data(initMeansC3D2a)
Two-dimensional dataset with four initial cluster means for the dataset DemoDataC2D2a. See examples in the Help/Description of a function, e.g. for HardKMeansDemo().
data(initMeansC4D2a)data(initMeansC4D2a)
Rows: objects, columns: features
data(initMeansC4D2a)data(initMeansC4D2a)
Two-dimensional dataset with five initial cluster means for the dataset DemoDataC2D2a. See examples in the Help/Description of a function, e.g. for HardKMeansDemo().
data(initMeansC5D2a)data(initMeansC5D2a)
Rows: objects, columns: features
data(initMeansC5D2a)data(initMeansC5D2a)
normalizeMatrix delivers a normalized matrix.
normalizeMatrix(dataMatrix, normMethod, bycol)normalizeMatrix(dataMatrix, normMethod, bycol)
dataMatrix |
Matrix with the objects to be normalized. |
normMethod |
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). |
bycol |
TRUE = columns are normalized, i.e., each column is considered separately (e.g., in case of the unity interval and a column colA: max(colA)=1 and min(colA)=0). For bycol = FALSE rows are normalized. Default: bycol = TRUE (columns are normalized). |
Normalized matrix.
M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.
plotRoughKMeans plots the rough clustering results in 2D. Note: Plotting is limited to a maximum of 5 clusters.
plotRoughKMeans(dataMatrix, upperMShipMatrix, meansMatrix, plotDimensions, colouredPlot)plotRoughKMeans(dataMatrix, upperMShipMatrix, meansMatrix, plotDimensions, colouredPlot)
dataMatrix |
Matrix with the objects to be plotted. |
upperMShipMatrix |
Corresponding matrix with upper approximations. |
meansMatrix |
Corresponding means matrix. |
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. |
2D-plot of clustering results. The boundary objects are represented by stars (*).
G. Peters.
RoughKMeans_LW performs Lingras & West's k-means clustering algorithm. The commonly accepted relative threshold is applied.
RoughKMeans_LW(dataMatrix, meansMatrix, nClusters, maxIterations, threshold, weightLower)RoughKMeans_LW(dataMatrix, meansMatrix, nClusters, maxIterations, threshold, weightLower)
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. |
weightLower |
Weight of the lower approximation in rough k-means algorithms (0.0 <= weightLower <= 1.0). Default: weightLower = 0.7. |
$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.
M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.
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>.
# An illustrative example clustering the sample data set DemoDataC2D2a.txt RoughKMeans_LW(DemoDataC2D2a, 2, 2, 100, 1.5, 0.7)# An illustrative example clustering the sample data set DemoDataC2D2a.txt RoughKMeans_LW(DemoDataC2D2a, 2, 2, 100, 1.5, 0.7)
RoughKMeans_PE performs Peters' k-means clustering algorithm.
RoughKMeans_PE(dataMatrix, meansMatrix, nClusters, maxIterations, threshold, weightLower)RoughKMeans_PE(dataMatrix, meansMatrix, nClusters, maxIterations, threshold, weightLower)
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. |
weightLower |
Weight of the lower approximation in rough k-means algorithms (0.0 <= weightLower <= 1.0). Default: weightLower = 0.7. |
$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.
M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.
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>.
# An illustrative example clustering the sample data set DemoDataC2D2a.txt RoughKMeans_PE(DemoDataC2D2a, 2, 2, 100, 1.5, 0.7)# An illustrative example clustering the sample data set DemoDataC2D2a.txt RoughKMeans_PE(DemoDataC2D2a, 2, 2, 100, 1.5, 0.7)
PI Rough k-MeansRoughKMeans_PI performs pi k-means clustering algorithm in its standard case. Therefore, weights are not required.
RoughKMeans_PI(dataMatrix, meansMatrix, nClusters, maxIterations, threshold)RoughKMeans_PI(dataMatrix, meansMatrix, nClusters, maxIterations, threshold)
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. |
$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.
M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.
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>.
# An illustrative example clustering the sample data set DemoDataC2D2a.txt RoughKMeans_PI(DemoDataC2D2a, 2, 2, 100, 1.5)# An illustrative example clustering the sample data set DemoDataC2D2a.txt RoughKMeans_PI(DemoDataC2D2a, 2, 2, 100, 1.5)
RoughKMeans_SHELL performs rough k-means algorithms with options for normalization and a 2D-plot of the results.
RoughKMeans_SHELL(clusterAlgorithm, dataMatrix, meansMatrix, nClusters, normalizationMethod, maxIterations, plotDimensions, colouredPlot, threshold, weightLower)RoughKMeans_SHELL(clusterAlgorithm, dataMatrix, meansMatrix, nClusters, normalizationMethod, maxIterations, plotDimensions, colouredPlot, threshold, weightLower)
clusterAlgorithm |
Select 0 = classic k-means, 1 = Lingras & West's rough k-means, 2 = Peters' rough k-means, 3 = |
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 |
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.
M. Goetz, G. Peters, Y. Richter, D. Sacker, T. Wochinger.
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>.
# 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)# 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)