| Title: | Methods for Joint Dimension Reduction and Clustering |
|---|---|
| Description: | A class of methods that combine dimension reduction and clustering of continuous, categorical or mixed-type data (Markos, Iodice D'Enza and van de Velden 2019; <DOI:10.18637/jss.v091.i10>). For continuous data, the package contains implementations of factorial K-means (Vichi and Kiers 2001; <DOI:10.1016/S0167-9473(00)00064-5>) and reduced K-means (De Soete and Carroll 1994; <DOI:10.1007/978-3-642-51175-2_24>); both methods that combine principal component analysis with K-means clustering. For categorical data, the package provides MCA K-means (Hwang, Dillon and Takane 2006; <DOI:10.1007/s11336-004-1173-x>), i-FCB (Iodice D'Enza and Palumbo 2013, <DOI:10.1007/s00180-012-0329-x>) and Cluster Correspondence Analysis (van de Velden, Iodice D'Enza and Palumbo 2017; <DOI:10.1007/s11336-016-9514-0>), which combine multiple correspondence analysis with K-means. For mixed-type data, it provides mixed Reduced K-means and mixed Factorial K-means (van de Velden, Iodice D'Enza and Markos 2019; <DOI:10.1002/wics.1456>), which combine PCA for mixed-type data with K-means. |
| Authors: | Angelos Markos [aut, cre], Alfonso Iodice D'Enza [aut], Michel van de Velden [aut] |
| Maintainer: | Angelos Markos <[email protected]> |
| License: | GPL-3 |
| Version: | 1.4.0 |
| Built: | 2025-01-27 02:39:17 UTC |
| Source: | https://github.com/cran/clustrd |
A class of methods that combine dimension reduction and clustering of continuous, categorical or mixed-type data (Markos, Iodice D'Enza and van de Velden 2019; <DOI:10.18637/jss.v091.i10>). For continuous data, the package contains implementations of factorial K-means (Vichi and Kiers 2001; <DOI:10.1016/S0167-9473(00)00064-5>) and reduced K-means (De Soete and Carroll 1994; <DOI:10.1007/978-3-642-51175-2_24>); both methods that combine principal component analysis with K-means clustering. For categorical data, the package provides MCA K-means (Hwang, Dillon and Takane 2006; <DOI:10.1007/s11336-004-1173-x>), i-FCB (Iodice D'Enza and Palumbo 2013, <DOI:10.1007/s00180-012-0329-x>) and Cluster Correspondence Analysis (van de Velden, Iodice D'Enza and Palumbo 2017; <DOI:10.1007/s11336-016-9514-0>), which combine multiple correspondence analysis with K-means. For mixed-type data, it provides mixed Reduced K-means and mixed Factorial K-means (van de Velden, Iodice D'Enza and Markos 2019; <DOI:10.1002/wics.1456>), which combine PCA for mixed-type data with K-means.
| Package: | clustrd |
| Type: | Package |
| Version: | 1.3.6-2 |
| Date: | 2019-10-28 |
| License: | GPL-3 |
Angelos Markos [aut, cre], Alfonso Iodice D' Enza [aut], Michel van de Velden [aut]
Markos, A., Iodice D'Enza, A., & van de Velden, M. (2019). Beyond Tandem Analysis: Joint Dimension Reduction and Clustering in R. Journal of Statistical Software, 91(10), 1–24. doi:10.18637/jss.v091.i10.
The data set refers to a collection of 55 articles on bribery cases from central Russian newspapers 1999-2000 (Mirkin, 2005). The variables reflect the following five-fold structure of bribery situations: two interacting sides - the office and the client, their interaction, the corrupt service rendered, and the environment in which it all occurs. These structural aspects can be characterized by 11 variables that have been manually recovered from the newspaper articles.
data("bribery")data("bribery")
A data frame with 55 observations on 11 categorical variables.
OfType of Office
ClLevel of Client
ServType of service: obstruction of justice, favours, cover-up, change of category, extortion of money for rendering free services
OccFrequency of occurrence
InitWho initiated the bribery act
BribBribe Level in $
TypType of corruption
NetCorruption network
ConCondition of corruption
BranBranch at which the corrupt service occurred
PunPunishment
Mirkin, B. (2005). Clustering for data mining: a data recovery approach. Chapman and Hall/CRC.
data(bribery)data(bribery)
This function implements MCA K-means (Hwang, Dillon and Takane, 2006), i-FCB (Iodice D' Enza and Palumbo, 2013) and Cluster Correspondence Analysis (van de Velden, Iodice D' Enza and Palumbo, 2017). The methods combine variants of Correspondence Analysis for dimension reduction with K-means for clustering.
clusmca(data, nclus, ndim, method=c("clusCA","iFCB","MCAk"), alphak = .5, nstart = 100, smartStart = NULL, gamma = TRUE, inboot = FALSE, seed = NULL) ## S3 method for class 'clusmca' print(x, ...) ## S3 method for class 'clusmca' summary(object, ...) ## S3 method for class 'clusmca' fitted(object, mth = c("centers", "classes"), ...)clusmca(data, nclus, ndim, method=c("clusCA","iFCB","MCAk"), alphak = .5, nstart = 100, smartStart = NULL, gamma = TRUE, inboot = FALSE, seed = NULL) ## S3 method for class 'clusmca' print(x, ...) ## S3 method for class 'clusmca' summary(object, ...) ## S3 method for class 'clusmca' fitted(object, mth = c("centers", "classes"), ...)
data |
Dataset with categorical variables |
nclus |
Number of clusters (nclus = 1 returns the MCA solution; see Details) |
ndim |
Dimensionality of the solution |
method |
Specifies the method. Options are MCAk for MCA K-means, iFCB for Iterative Factorial Clustering of Binary variables and clusCA for Cluster Correspondence Analysis (default = |
alphak |
Non-negative scalar to adjust for the relative importance of MCA ( |
nstart |
Number of random starts (default = 100) |
smartStart |
If |
gamma |
Scaling parameter that leads to similar spread in the object and variable scores (default = |
seed |
An integer that is used as argument by |
inboot |
Used internally in the bootstrap functions to perform bootstrapping on the indicator matrix. |
x |
For the |
object |
For the |
mth |
For the |
... |
Not used |
For the K-means part, the algorithm of Hartigan-Wong is used by default.
The hidden print and summary methods print out some key components of an object of class clusmca.
The hidden fitted method returns cluster fitted values. If method is "classes", this is a vector of cluster membership (the cluster component of the "clusmca" object). If method is "centers", this is a matrix where each row is the cluster center for the observation. The rownames of the matrix are the cluster membership values.
When nclus = 1 the function returns the MCA solution with objects in principal and variables in standard coordinates. plot(object) shows the corresponding asymmetric biplot.
obscoord |
Object scores |
attcoord |
Attribute scores |
centroid |
Cluster centroids |
cluster |
Cluster membership |
criterion |
Optimal value of the objective criterion |
size |
The number of objects in each cluster |
nstart |
A copy of |
odata |
A copy of |
Hwang, H., Dillon, W. R., and Takane, Y. (2006). An extension of multiple correspondence analysis for identifying heterogenous subgroups of respondents. Psychometrika, 71, 161-171.
Iodice D'Enza, A., and Palumbo, F. (2013). Iterative factor clustering of binary data. Computational Statistics, 28(2), 789-807.
van de Velden M., Iodice D' Enza, A., and Palumbo, F. (2017). Cluster correspondence analysis. Psychometrika, 82(1), 158-185.
data(cmc) # Preprocessing: values of wife's age and number of children were categorized # into three groups based on quartiles cmc$W_AGE = ordered(cut(cmc$W_AGE, c(16,26,39,49), include.lowest = TRUE)) levels(cmc$W_AGE) = c("16-26","27-39","40-49") cmc$NCHILD = ordered(cut(cmc$NCHILD, c(0,1,4,17), right = FALSE)) levels(cmc$NCHILD) = c("0","1-4","5 and above") #Cluster Correspondence Analysis solution with 3 clusters in 2 dimensions #after 10 random starts outclusCA = clusmca(cmc, 3, 2, method = "clusCA", nstart = 10, seed = 1234) outclusCA #Scatterplot (dimensions 1 and 2) plot(outclusCA) #MCA K-means solution with 3 clusters in 2 dimensions after 10 random starts outMCAk = clusmca(cmc, 3, 2, method = "MCAk", nstart = 10, seed = 1234) outMCAk #Scatterplot (dimensions 1 and 2) plot(outMCAk) #nclus = 1 just gives the MCA solution #outMCA = clusmca(cmc, 1, 2) #outMCA #Scatterplot (dimensions 1 and 2) #asymmetric biplot with scaling gamma = TRUE #plot(outMCA)data(cmc) # Preprocessing: values of wife's age and number of children were categorized # into three groups based on quartiles cmc$W_AGE = ordered(cut(cmc$W_AGE, c(16,26,39,49), include.lowest = TRUE)) levels(cmc$W_AGE) = c("16-26","27-39","40-49") cmc$NCHILD = ordered(cut(cmc$NCHILD, c(0,1,4,17), right = FALSE)) levels(cmc$NCHILD) = c("0","1-4","5 and above") #Cluster Correspondence Analysis solution with 3 clusters in 2 dimensions #after 10 random starts outclusCA = clusmca(cmc, 3, 2, method = "clusCA", nstart = 10, seed = 1234) outclusCA #Scatterplot (dimensions 1 and 2) plot(outclusCA) #MCA K-means solution with 3 clusters in 2 dimensions after 10 random starts outMCAk = clusmca(cmc, 3, 2, method = "MCAk", nstart = 10, seed = 1234) outMCAk #Scatterplot (dimensions 1 and 2) plot(outMCAk) #nclus = 1 just gives the MCA solution #outMCA = clusmca(cmc, 1, 2) #outMCA #Scatterplot (dimensions 1 and 2) #asymmetric biplot with scaling gamma = TRUE #plot(outMCA)
This function implements Factorial K-means (Vichi and Kiers, 2001) and Reduced K-means (De Soete and Carroll, 1994), as well as a compromise version of these two methods. The methods combine Principal Component Analysis for dimension reduction with K-means for clustering.
cluspca(data, nclus, ndim, alpha = NULL, method = c("RKM","FKM"), center = TRUE, scale = TRUE, rotation = "none", nstart = 100, smartStart = NULL, seed = NULL) ## S3 method for class 'cluspca' print(x, ...) ## S3 method for class 'cluspca' summary(object, ...) ## S3 method for class 'cluspca' fitted(object, mth = c("centers", "classes"), ...)cluspca(data, nclus, ndim, alpha = NULL, method = c("RKM","FKM"), center = TRUE, scale = TRUE, rotation = "none", nstart = 100, smartStart = NULL, seed = NULL) ## S3 method for class 'cluspca' print(x, ...) ## S3 method for class 'cluspca' summary(object, ...) ## S3 method for class 'cluspca' fitted(object, mth = c("centers", "classes"), ...)
data |
Dataset with metric variables |
nclus |
Number of clusters (nclus = 1 returns the PCA solution |
ndim |
Dimensionality of the solution |
method |
Specifies the method. Options are RKM for reduced K-means and FKM for factorial K-means (default = |
alpha |
Adjusts for the relative importance of RKM and FKM in the objective function; |
center |
A logical value indicating whether the variables should be shifted to be zero centered (default = |
scale |
A logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place (default = |
rotation |
Specifies the method used to rotate the factors. Options are |
nstart |
Number of starts (default = 100) |
smartStart |
If |
seed |
An integer that is used as argument by |
x |
For the |
object |
For the |
mth |
For the |
... |
Not used |
For the K-means part, the algorithm of Hartigan-Wong is used by default.
The hidden print and summary methods print out some key components of an object of class cluspca.
The hidden fitted method returns cluster fitted values. If method is "classes", this is a vector of cluster membership (the cluster component of the "cluspca" object). If method is "centers", this is a matrix where each row is the cluster center for the observation. The rownames of the matrix are the cluster membership values.
When nclus = 1 the function returns the PCA solution and plot(object) shows the corresponding biplot.
obscoord |
Object scores |
attcoord |
Variable scores |
centroid |
Cluster centroids |
cluster |
Cluster membership |
criterion |
Optimal value of the objective function |
size |
The number of objects in each cluster |
scale |
A copy of |
center |
A copy of |
nstart |
A copy of |
odata |
A copy of |
De Soete, G., and Carroll, J. D. (1994). K-means clustering in a low-dimensional Euclidean space. In Diday E. et al. (Eds.), New Approaches in Classification and Data Analysis, Heidelberg: Springer, 212-219.
Vichi, M., and Kiers, H.A.L. (2001). Factorial K-means analysis for two-way data. Computational Statistics and Data Analysis, 37, 49-64.
#Reduced K-means with 3 clusters in 2 dimensions after 10 random starts data(macro) outRKM = cluspca(macro, 3, 2, method = "RKM", rotation = "varimax", scale = FALSE, nstart = 10) summary(outRKM) #Scatterplot (dimensions 1 and 2) and cluster description plot plot(outRKM, cludesc = TRUE) #Factorial K-means with 3 clusters in 2 dimensions #with a Reduced K-means starting solution data(macro) outFKM = cluspca(macro, 3, 2, method = "FKM", rotation = "varimax", scale = FALSE, smartStart = outRKM$cluster) outFKM #Scatterplot (dimensions 1 and 2) and cluster description plot plot(outFKM, cludesc = TRUE) #To get the Tandem approach (PCA(SVD) + K-means) outTandem = cluspca(macro, 3, 2, alpha = 1, seed = 1234) plot(outTandem) #nclus = 1 just gives the PCA solution #outPCA = cluspca(macro, 1, 2) #outPCA #Scatterplot (dimensions 1 and 2) #plot(outPCA)#Reduced K-means with 3 clusters in 2 dimensions after 10 random starts data(macro) outRKM = cluspca(macro, 3, 2, method = "RKM", rotation = "varimax", scale = FALSE, nstart = 10) summary(outRKM) #Scatterplot (dimensions 1 and 2) and cluster description plot plot(outRKM, cludesc = TRUE) #Factorial K-means with 3 clusters in 2 dimensions #with a Reduced K-means starting solution data(macro) outFKM = cluspca(macro, 3, 2, method = "FKM", rotation = "varimax", scale = FALSE, smartStart = outRKM$cluster) outFKM #Scatterplot (dimensions 1 and 2) and cluster description plot plot(outFKM, cludesc = TRUE) #To get the Tandem approach (PCA(SVD) + K-means) outTandem = cluspca(macro, 3, 2, alpha = 1, seed = 1234) plot(outTandem) #nclus = 1 just gives the PCA solution #outPCA = cluspca(macro, 1, 2) #outPCA #Scatterplot (dimensions 1 and 2) #plot(outPCA)
This function implements clustering and dimension reduction for mixed-type variables, i.e., categorical and metric (see, Yamamoto & Hwang, 2014; van de Velden, Iodice D'Enza, & Markos 2019; Vichi, Vicari, & Kiers, 2019). This framework includes Mixed Reduced K-means and Mixed Factorial K-means, as well as a compromise of these two methods. The methods combine Principal Component Analysis of mixed-data for dimension reduction with K-means for clustering.
cluspcamix(data, nclus, ndim, method=c("mixedRKM", "mixedFKM"), center = TRUE, scale = TRUE, alpha=NULL, rotation="none", nstart = 100, smartStart=NULL, seed=NULL, inboot = FALSE) ## S3 method for class 'cluspcamix' print(x, ...) ## S3 method for class 'cluspcamix' summary(object, ...) ## S3 method for class 'cluspcamix' fitted(object, mth = c("centers", "classes"), ...)cluspcamix(data, nclus, ndim, method=c("mixedRKM", "mixedFKM"), center = TRUE, scale = TRUE, alpha=NULL, rotation="none", nstart = 100, smartStart=NULL, seed=NULL, inboot = FALSE) ## S3 method for class 'cluspcamix' print(x, ...) ## S3 method for class 'cluspcamix' summary(object, ...) ## S3 method for class 'cluspcamix' fitted(object, mth = c("centers", "classes"), ...)
data |
Dataset with categorical and metric variables |
nclus |
Number of clusters (nclus = 1 returns the PCAMIX solution) |
ndim |
Dimensionality of the solution |
method |
Specifies the method. Options are mixedRKM for mixed reduced K-means and mixedFKM for mixed factorial K-means (default = |
center |
A logical value indicating whether the variables should be shifted to be zero centered (default = |
scale |
A logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place (default = |
alpha |
Adjusts for the relative importance of Mixed RKM and Mixed FKM in the objective function; |
rotation |
Specifies the method used to rotate the factors. Options are |
nstart |
Number of random starts (default = 100) |
smartStart |
If |
seed |
An integer that is used as argument by |
inboot |
Used internally in the bootstrap functions to perform bootstrapping on the indicator matrix. |
x |
For the |
object |
For the |
mth |
For the |
... |
Not used |
For the K-means part, the algorithm of Hartigan-Wong is used by default.
The hidden print and summary methods print out some key components of an object of class cluspcamix.
The hidden fitted method returns cluster fitted values. If method is "classes", this is a vector of cluster membership (the cluster component of the "cluspcamix" object). If method is "centers", this is a matrix where each row is the cluster center for the observation. The rownames of the matrix are the cluster membership values.
When nclus = 1 the function returns the solution of PCAMIX and plot(object) shows the corresponding biplot.
obscoord |
Object scores |
attcoord |
Variable scores |
centroid |
Cluster centroids |
cluster |
Cluster membership |
criterion |
Optimal value of the objective criterion |
size |
The number of objects in each cluster |
scale |
A copy of |
center |
A copy of |
nstart |
A copy of |
odata |
A copy of |
van de Velden, M., Iodice D'Enza, A., & Markos, A. (2019). Distance-based clustering of mixed data. Wiley Interdisciplinary Reviews: Computational Statistics, e1456.
Vichi, M., Vicari, D., & Kiers, H.A.L. (2019). Clustering and dimension reduction for mixed variables. Behaviormetrika. doi:10.1007/s41237-018-0068-6.
Yamamoto, M., & Hwang, H. (2014). A general formulation of cluster analysis with dimension reduction and subspace separation. Behaviormetrika, 41, 115-129.
data(diamond) #Mixed Reduced K-means solution with 3 clusters in 2 dimensions #after 10 random starts outmixedRKM = cluspcamix(diamond, 3, 2, method = "mixedRKM", nstart = 10, seed = 1234) outmixedRKM #A graph with the categories and a biplot of the continuous variables (dimensions 1 and 2) plot(outmixedRKM) #Tandem analysis: PCAMIX or FAMD followed by K-means solution #with 3 clusters in 2 dimensions after 10 random starts outTandem = cluspcamix(diamond, 3, 2, alpha = 1, nstart = 10, seed = 1234) outTandem #Scatterplot (dimensions 1 and 2) plot(outTandem) #nclus = 1 just gives the PCAMIX or FAMD solution #outPCAMIX = cluspcamix(diamond, 1, 2) #outPCAMIX #Biplot (dimensions 1 and 2) #plot(outPCAMIX)data(diamond) #Mixed Reduced K-means solution with 3 clusters in 2 dimensions #after 10 random starts outmixedRKM = cluspcamix(diamond, 3, 2, method = "mixedRKM", nstart = 10, seed = 1234) outmixedRKM #A graph with the categories and a biplot of the continuous variables (dimensions 1 and 2) plot(outmixedRKM) #Tandem analysis: PCAMIX or FAMD followed by K-means solution #with 3 clusters in 2 dimensions after 10 random starts outTandem = cluspcamix(diamond, 3, 2, alpha = 1, nstart = 10, seed = 1234) outTandem #Scatterplot (dimensions 1 and 2) plot(outTandem) #nclus = 1 just gives the PCAMIX or FAMD solution #outPCAMIX = cluspcamix(diamond, 1, 2) #outPCAMIX #Biplot (dimensions 1 and 2) #plot(outPCAMIX)
Data of married women in Indonesia who were not pregnant (or did not know they were pregnant) at the time of the survey. The dataset contains demographic and socio-economic characteristics of the women along with their preferred method of contraception (no use, long-term methods, short-term methods).
data(cmc)data(cmc)
A data frame containing 1,437 observations on the following 10 variables.
W_AGEwife's age in years.
W_EDUordered factor indicating wife's education, with levels "low", "2", "3" and "high".
H_EDUordered factor indicating wife's education, with levels "low", "2", "3" and "high".
NCHILDnumber of children.
W_RELfactor indicating wife's religion, with levels "non-Islam" and "Islam".
W_WORKfactor indicating if the wife is working.
H_OCCfactor indicating husband's occupation, with levels "1", "2", "3" and "4". The labels are not known.
SOLordered factor indicating the standard of living index with levels "low", "2", "3" and "high".
MEDEXPfactor indicating media exposure, with levels "good" and "not good".
CMfactor indicating the contraceptive method used, with levels "no-use", "long-term" and "short-term".
This dataset is part of the 1987 National Indonesia Contraceptive Prevalence Survey and was created by Tjen-Sien Lim. It has been taken from the UCI Machine Learning Repository at http://archive.ics.uci.edu/ml/.
Lim, T.-S., Loh, W.-Y. & Shih, Y.-S. (1999). A Comparison of Prediction Accuracy, Complexity, and Training Time of Thirty-three Old and New Classification Algorithms. Machine Learning, 40(3), 203-228.
data(cmc)data(cmc)
Data on 308 diamond stones sold in Singapore. The main attributes are diamond weight, colour, clarity, certification body and price in Singapore $. The weight of a diamond stone is indicated in terms of carat units. Since stones may be divided into 3 clusters due to their size, namely small (less than 0.5 carats), medium (0.5 to less than 1 carat) and large (1 carat and over), following Chu (2001), three binary variables have been built representing the three caratage ranges, and three quantitative variables (denoted Small, Medium, Large) have been derived by multiplying such binary variables by carats. So, the "Small" variable has nonzero values (i.e., the carat values) only for the smallest diamonds (less than 0.5 carats), and likewise for the other two variables. Thus, these variables are weighted binary variables. The colour of a diamond is graded from D (completely colourless), E, F, G, ..., to I (almost colorless). Clarity refers to the diamond's internal and external imperfections. Clarity is graded on a scale from IF (internally flawless), to very very slightly imperfect (VVS1 or VVS2), and very slightly imperfect, VS1 or VS2. Three certification bodies were used: New York based Gemmological Institute of America (GIA), Antwerp based International Gemmological Institute (IGI) and Hoge Raad Voor Diamant (HRD).
data(diamond)data(diamond)
A data frame with 308 observations on the following 7 variables.
Smallweighted binary variable with nonzero values (i.e., the carat values) for diamonds with less than 0.5 carats.
Mediumweighted binary variable with nonzero values (i.e., the carat values) for diamonds from 0.5 to less than 1 carat.
Largeweighted binary variable with nonzero values (i.e., the carat values) for diamonds from 1 carat and over.
Colourthe color of the diamond with a factor with levels (D, E, F, G, H, I).
Claritythe clarity of the diamond with a factor with levels (IF, VVS1, VVS2, VS1, VS2).
Certificationthe certification body with a factor with levels (GIA, IGI, HRD).
Pricethe price of a diamond in Singapore $.
Chu, S. (2001). Pricing the C's of Diamond Stones, Journal of Statistics Education, 9(2).
Runs joint dimension and clustering algorithms repeatedly for different numbers of clusters on bootstrap replica of the original data and returns corresponding cluster assignments, and cluster agreement indices comparing pairs of partitions.
global_bootclus(data, nclusrange = 3:4, ndim = NULL, method = c("RKM","FKM","mixedRKM","mixedFKM","clusCA","MCAk","iFCB"), nboot = 10, alpha = NULL, alphak = NULL, center = TRUE, scale = TRUE, nstart = 100, smartStart = NULL, seed = NULL)global_bootclus(data, nclusrange = 3:4, ndim = NULL, method = c("RKM","FKM","mixedRKM","mixedFKM","clusCA","MCAk","iFCB"), nboot = 10, alpha = NULL, alphak = NULL, center = TRUE, scale = TRUE, nstart = 100, smartStart = NULL, seed = NULL)
data |
Continuous, Categorical ot Mixed data set |
nclusrange |
An integer or an integer vector with the number of clusters or a range of numbers of clusters (should be greater than one) |
ndim |
Dimensionality of the solution; if |
method |
Specifies the method. Options are RKM for Reduced K-means, FKM for Factorial K-means, mixedRKM for Mixed Reduced K-means, mixedFKM for Mixed Factorial K-means, MCAk for MCA K-means, iFCB for Iterative Factorial Clustering of Binary variables and clusCA for Cluster Correspondence Analysis. |
nboot |
Number of bootstrap pairs of partitions |
alpha |
Adjusts for the relative importance of (mixed) RKM and FKM in the objective function; |
alphak |
Non-negative scalar to adjust for the relative importance of MCA ( |
center |
A logical value indicating whether the metric variables should be shifted to be zero centered (default = |
scale |
A logical value indicating whether the metric variables should be scaled to have unit variance before the analysis takes place (default = |
nstart |
Number of random starts (default = 100) |
smartStart |
If |
seed |
An integer that is used as argument by |
The algorithm for assessing global cluster stability is similar to that in Dolnicar and Leisch (2010) and can be summarized in three steps:
Step 1. Resampling: Draw bootstrap samples S_i and T_i of size n from the data and use the original data, X, as evaluation set E_i = X. Apply the clustering method of choice to S_i and T_i and obtain C^S_i and C^T_i.
Step 2. Mapping: Assign each observation x_i to the closest centers of C^S_i and C^T_i using Euclidean distance, resulting in partitions C^XS_i and C^XT_i, where C^XS_i is the partition of the original data, X, predicted from clustering bootstrap sample S_i (same for T_i and C^XT_i).
Step 3. Evaluation: Use the Adjusted Rand Index (ARI, Hubert & Arabie, 1985) or the Measure of Concordance (MOC, Pfitzner 2008) as measure of agreement and stability.
Inspect the distributions of ARI/MOC to assess the global reproducibility of the clustering solutions.
While nboot = 100 is recommended, smaller run numbers could give quite informative results as well, if computation times become too high.
Note that the stability of a clustering solution is assessed, but stability is not the only important validity criterion - clustering solutions obtained by very inflexible clustering methods may be stable but not valid, as discussed in Hennig (2007).
nclusrange |
An integer or an integer vector with the number of clusters or a range of numbers of clusters |
clust1 |
Partitions, C^XS_i of the original data, X, predicted from clustering bootstrap sample S_i (see Details) |
clust2 |
Partitions, C^XT_i of the original data, X, predicted from clustering bootstrap sample T_i (see Details) |
index1 |
Indices of the original data rows in bootstrap sample S_i |
index2 |
Indices of the original data rows in bootstrap sample T_i |
rand |
Adjusted Rand Index values |
moc |
Measure of Concordance values |
Hennig, C. (2007). Cluster-wise assessment of cluster stability. Computational Statistics and Data Analysis, 52, 258-271.
Pfitzner, D., Leibbrandt, R., & Powers, D. (2009). Characterization and evaluation of similarity measures for pairs of clusterings. Knowledge and Information Systems, 19(3), 361-394.
Dolnicar, S., & Leisch, F. (2010). Evaluation of structure and reproducibility of cluster solutions using the bootstrap. Marketing Letters, 21(1), 83-101.
## 3 bootstrap replicates and nstart = 1 for speed in example, ## use at least 20 replicates for real applications data(diamond) boot_mixedRKM = global_bootclus(diamond[,-7], nclusrange = 3:4, method = "mixedRKM", nboot = 3, nstart = 1, seed = 1234) boxplot(boot_mixedRKM$rand, xlab = "Number of clusters", ylab = "adjusted Rand Index") ## 5 bootstrap replicates and nstart = 10 for speed in example, ## use more for real applications #data(macro) #boot_RKM = global_bootclus(macro, nclusrange = 2:5, #method = "RKM", nboot = 5, nstart = 10, seed = 1234) #boxplot(boot_RKM$rand, xlab = "Number of clusters", ylab = #"adjusted Rand Index") ## 5 bootstrap replicates and nstart = 1 for speed in example, ## use more for real applications #data(bribery) #boot_cluCA = global_bootclus(bribery, nclusrange = 2:5, #method = "clusCA", nboot = 5, nstart = 1, seed = 1234) #boxplot(boot_cluCA$rand, xlab = "Number of clusters", ylab = #"adjusted Rand Index")## 3 bootstrap replicates and nstart = 1 for speed in example, ## use at least 20 replicates for real applications data(diamond) boot_mixedRKM = global_bootclus(diamond[,-7], nclusrange = 3:4, method = "mixedRKM", nboot = 3, nstart = 1, seed = 1234) boxplot(boot_mixedRKM$rand, xlab = "Number of clusters", ylab = "adjusted Rand Index") ## 5 bootstrap replicates and nstart = 10 for speed in example, ## use more for real applications #data(macro) #boot_RKM = global_bootclus(macro, nclusrange = 2:5, #method = "RKM", nboot = 5, nstart = 10, seed = 1234) #boxplot(boot_RKM$rand, xlab = "Number of clusters", ylab = #"adjusted Rand Index") ## 5 bootstrap replicates and nstart = 1 for speed in example, ## use more for real applications #data(bribery) #boot_cluCA = global_bootclus(bribery, nclusrange = 2:5, #method = "clusCA", nboot = 5, nstart = 1, seed = 1234) #boxplot(boot_cluCA$rand, xlab = "Number of clusters", ylab = #"adjusted Rand Index")
The dataset was collected with an interactive online version of the Humor Styles Questionnaire (HSQ) which assesses four independent ways in which people express and appreciate humor (Martin et al. 2003): affiliative (items with prefix AF), defined as the benign uses of humor to enhance one's relationships with others; self-enhancing (SE), indicating uses of humor to enhance the self; aggressive (AG), the use of humor to enhance the self at the expense of others; self-defeating (SD), the use of humor to enhance relationships at the expense of oneself. The main part of the questionnaire consisted of 32 statements rated from 1 to 5 according to the respondents' level of agreement. The number of respondents is 993.
data("hsq")data("hsq")
A data frame with 993 observations on 32 Likert-type variables (statements) with 5 response categories, ranging from 1 (strong agreement) to 5 (strong disagreement).
AF1I usually don't laugh or joke around much with other people
SE2If I am feeling depressed, I can usually cheer myself up with humor
AG3If someone makes a mistake, I will often tease them about it
SD4I let people laugh at me or make fun at my expense more than I should
AF5I don't have to work very hard at making other people laugh - I seem to be a naturally humorous person
SE6Even when I'm by myself, I'm often amused by the absurdities of life
AG7People are never offended or hurt by my sense of humor
SD8I will often get carried away in putting myself down if it makes my family or friends laugh
AF9I rarely make other people laugh by telling funny stories about myself
SE10If I am feeling upset or unhappy I usually try to think of something funny about the situation to make myself feel better
AG11When telling jokes or saying funny things, I am usually not very concerned about how other people are taking it
SD12I often try to make people like or accept me more by saying something funny about my own weaknesses, blunders, or faults
AF13I laugh and joke a lot with my closest friends
SE14My humorous outlook on life keeps me from getting overly upset or depressed about things
AG15I do not like it when people use humor as a way of criticizing or putting someone down
SD16I don't often say funny things to put myself down
AF17I usually don't like to tell jokes or amuse people
SE18If I'm by myself and I'm feeling unhappy, I make an effort to think of something funny to cheer myself up
AG19Sometimes I think of something that is so funny that I can't stop myself from saying it, even if it is not appropriate for the situation
SD20I often go overboard in putting myself down when I am making jokes or trying to be funny
AF21I enjoy making people laugh
SE22If I am feeling sad or upset, I usually lose my sense of humor
AG23I never participate in laughing at others even if all my friends are doing it
SD24When I am with friends or family, I often seem to be the one that other people make fun of or joke about
AF25I don't often joke around with my friends
SE26It is my experience that thinking about some amusing aspect of a situation is often a very effective way of coping with problems
AG27If I don't like someone, I often use humor or teasing to put them down
SD28If I am having problems or feeling unhappy, I often cover it up by joking around, so that even my closest friends don't know how I really feel
AF29I usually can't think of witty things to say when I'm with other people
SE30I don't need to be with other people to feel amused - I can usually find things to laugh about even when I'm by myself
AG31Even if something is really funny to me, I will not laugh or joke about it if someone will be offended
SD32Letting others laugh at me is my way of keeping my friends and family in good spirits
Martin, R. A., Puhlik-Doris, P., Larsen, G., Gray, J., & Weir, K. (2003). Individual differences in uses of humor and their relation to psychological well-being: Development of the Humor Styles Questionnaire. Journal of Research in Personality, 37(1), 48-75.
data(hsq)data(hsq)
Assessment of the cluster-wise stability of a joint dimension and clustering method. The data is resampled using bootstrapping and the Jaccard similarities of the original clusters to the most similar clusters in the resampled data are computed. The mean over these similarities is used as an index of the stability of a cluster. The method is similar to the one described in Hennig (2007).
local_bootclus(data, nclus, ndim = NULL, method = c("RKM","FKM","mixedRKM","mixedFKM","clusCA","MCAk","iFCB"), scale = TRUE, center= TRUE, alpha = NULL, nstart=100, nboot=10, alphak = .5, seed = NULL)local_bootclus(data, nclus, ndim = NULL, method = c("RKM","FKM","mixedRKM","mixedFKM","clusCA","MCAk","iFCB"), scale = TRUE, center= TRUE, alpha = NULL, nstart=100, nboot=10, alphak = .5, seed = NULL)
data |
Continuous, Categorical ot Mixed data set |
nclus |
Number of clusters |
ndim |
Dimensionality of the solution |
method |
Specifies the method. Options are RKM for Reduced K-means, FKM for Factorial K-means, mixedRKM for Mixed Reduced K-means, mixedFKM for Mixed Factorial K-means, MCAk for MCA K-means, iFCB for Iterative Factorial Clustering of Binary variables and clusCA for Cluster Correspondence Analysis. |
scale |
A logical value indicating whether the metric variables should be scaled to have unit variance before the analysis takes place (default = |
center |
A logical value indicating whether the metric variables should be shifted to be zero centered (default = |
alpha |
Adjusts for the relative importance of (mixed) RKM and FKM in the objective function; |
nstart |
Number of random starts (default = 100) |
nboot |
Number of bootstrap pairs of partitions |
alphak |
Non-negative scalar to adjust for the relative importance of MCA ( |
seed |
An integer that is used as argument by |
The algorithm for assessing local cluster stability is similar to that in Hennig (2007) and can be summarized in three steps:
Step 1. Resampling: Draw bootstrap samples S_i and T_i of size n from the data and use the original data as evaluation set E_i = X. Apply a joint dimension reduction and clustering method to S_i and T_i and obtain C^S_i and C^T_i.
Step 2. Mapping: Assign each observation x_i to the closest centers of C^S_i and C^T_i using Euclidean distance, resulting in partitions C^XS_i and C^XT_i.
Step 3. Evaluation: Obtain the maximum Jaccard agreement between each original cluster C_k and each one of the two bootstrap clusters, C_^k'XS_i and C_^k'XT_i as measure of agreement and stability, and take the average of each pair.
Inspect the distributions of the maximum Jaccard coefficients to assess the cluster level (local) stability of the solution.
Here are some guidelines for interpretation. Generally, a valid, stable cluster should yield a mean Jaccard similarity value of 0.75 or more. Between 0.6 and 0.75, clusters may be considered as indicating patterns in the data, but which points exactly should belong to these clusters is highly doubtful. Below average Jaccard values of 0.6, clusters should not be trusted. "Highly stable" clusters should yield average Jaccard similarities of 0.85 and above.
While B = 100 is recommended, smaller run numbers could give quite informative results as well, if computation times become too high.
Note that the stability of a cluster is assessed, but stability is not the only important validity criterion - clusters obtained by very inflexible clustering methods may be stable but not valid, as discussed in Hennig (2007).
nclus |
An integer with the number of clusters |
clust1 |
Partitions, C^XS_i of the original data, X, predicted from clustering bootstrap sample S_i (see Details) |
clust2 |
Partitions, C^XT_i of the original data, X, predicted from clustering bootstrap sample T_i (see Details) |
index1 |
Indices of the original data rows in bootstrap sample S_i |
index2 |
Indices of the original data rows in bootstrap sample T_i |
Jaccard |
Mean Jaccard similarity values |
Hennig, C. (2007). Cluster-wise assessment of cluster stability. Computational Statistics and Data Analysis, 52, 258-271.
## 5 bootstrap replicates and nstart = 10 for speed in example, ## use more for real applications data(iris) bootres = local_bootclus(iris[,-5], nclus = 3, ndim = 2, method = "RKM", nboot = 5, nstart = 1, seed = 1234) boxplot(bootres$Jaccard, xlab = "cluster number", ylab = "Jaccard similarity") ## 5 bootstrap replicates and nstart = 5 for speed in example, ## use more for real applications #data(diamond) #bootres = local_bootclus(diamond[,-7], nclus = 4, ndim = 3, #method = "mixedRKM", nboot = 5, nstart = 10, seed = 1234) #boxplot(bootres$Jaccard, xlab = "cluster number", ylab = #"Jaccard similarity") ## 5 bootstrap replicates and nstart = 1 for speed in example, ## use more for real applications #data(bribery) #bootres = local_bootclus(bribery, nclus = 5, ndim = 4, #method = "clusCA", nboot = 10, nstart = 1, seed = 1234) #boxplot(bootres$Jaccard, xlab = "cluster number", ylab = #"Jaccard similarity")## 5 bootstrap replicates and nstart = 10 for speed in example, ## use more for real applications data(iris) bootres = local_bootclus(iris[,-5], nclus = 3, ndim = 2, method = "RKM", nboot = 5, nstart = 1, seed = 1234) boxplot(bootres$Jaccard, xlab = "cluster number", ylab = "Jaccard similarity") ## 5 bootstrap replicates and nstart = 5 for speed in example, ## use more for real applications #data(diamond) #bootres = local_bootclus(diamond[,-7], nclus = 4, ndim = 3, #method = "mixedRKM", nboot = 5, nstart = 10, seed = 1234) #boxplot(bootres$Jaccard, xlab = "cluster number", ylab = #"Jaccard similarity") ## 5 bootstrap replicates and nstart = 1 for speed in example, ## use more for real applications #data(bribery) #bootres = local_bootclus(bribery, nclus = 5, ndim = 4, #method = "clusCA", nboot = 10, nstart = 1, seed = 1234) #boxplot(bootres$Jaccard, xlab = "cluster number", ylab = #"Jaccard similarity")
Data on the macroeconomic performance of national economies of 20 countries, members of the OECD (September 1999). The performance of the economies reflects the interaction of six main economic indicators (percentage change from the previous year): gross domestic product (GDP), leading indicator (LI), unemployment rate (UR), interest rate (IR), trade balance (TB), net national savings (NNS).
data(macro)data(macro)
A data frame with 20 observations on the following 6 variables.
GDPnumeric
LInumeric
URnumeric
IRnumeric
TBnumeric
NNSnumeric
Vichi, M. & Kiers, H. A. (2001). Factorial k-means analysis for two-way data. Computational Statistics & Data Analysis, 37(1), 49-64.
The data set refers to 26 James Bond films produced up to 2021, based on 10 film characteristics: 7 continuous (year of release, production budget, box office gross in the USA and worldwide, running time, IMDB average rating, Rotten Tomatoes rating) and 3 categorical (Bond actor, native country of the actor playing the villain, native country of the actor playing the Bond girl). All figures in USD are adjusted for inflation. Most of the data was compiled from the Wikipedia page: https://en.wikipedia.org/wiki/List_of_James_Bond_films.
data("mybond")data("mybond")
A data frame with 26 observations on the following 10 variables.
yearYear of release
budgetOfficial production budget (in million USD)
grossusaBox office gross in the USA (in million USD)
grosswrldBox office gross worldwide (in million USD)
rtimeRunning time in minutes
IMDBIMDB rating
rottentomatoesRotten Tomatoes rating
actorBond actor
villaincntNative country of the actor playing the villain
bondgirlcntNative country of the actor playing the Bond girl
data(mybond)data(mybond)
clusmca() output.
Plotting function that creates a scatterplot of the object scores and/or the attribute scores and the cluster centroids. Optionally, the function returns a series of barplots showing the standardized residuals per attribute for each cluster.
## S3 method for class 'clusmca' plot(x, dims = c(1,2), what = c(TRUE,TRUE), cludesc = FALSE, topstdres = 20, objlabs = FALSE, attlabs = NULL, subplot = FALSE, max.overlaps=10, ...)## S3 method for class 'clusmca' plot(x, dims = c(1,2), what = c(TRUE,TRUE), cludesc = FALSE, topstdres = 20, objlabs = FALSE, attlabs = NULL, subplot = FALSE, max.overlaps=10, ...)
x |
Object returned by |
dims |
Numerical vector of length 2 indicating the dimensions to plot on horizontal and vertical axes respectively; default is first dimension horizontal and second dimension vertical |
what |
Vector of two logical values specifying the contents of the plots. First entry indicates whether a scatterplot of the objects is displayed in principal coordinates. Second entry indicates whether a scatterplot of the attribute categories is displayed in principal coordinates. Cluster centroids are always displayed. The default is |
cludesc |
A logical value indicating whether a series of barplots is produced showing the largest (in absolute value) standardized residuals per attribute for each cluster (default = |
topstdres |
Number of largest standardized residuals used to describe each cluster (default = 20). Works only in combination with |
objlabs |
A logical value indicating whether object labels will be plotted; if |
attlabs |
Vector of custom attribute labels; if not provided, default labeling is applied |
subplot |
A logical value indicating whether a subplot with the full distribution of the standardized residuals will appear at the bottom left corner of the corresponding plots. Works only in combination with |
max.overlaps |
Maximum number of text labels allowed to overlap. Defaults to 10 |
... |
Further arguments to be transferred to |
The function returns a ggplot2 scatterplot of the solution obtained via clusmca() that can be further customized using the ggplot2 package. When cludesc = TRUE the function also returns a series of ggplot2 barplots showing the largest (or all) standardized residuals per attribute for each cluster.
Hwang, H., Dillon, W. R., and Takane, Y. (2006). An extension of multiple correspondence analysis for identifying heterogenous subgroups of respondents. Psychometrika, 71, 161-171.
Iodice D'Enza, A., and Palumbo, F. (2013). Iterative factor clustering of binary data. Computational Statistics, 28(2), 789-807.
van de Velden M., Iodice D'Enza, A., and Palumbo, F. (2017). Cluster correspondence analysis. Psychometrika, 82(1), 158-185.
data("mybond") #Cluster Correspondence Analysis with 3 clusters in 2 dimensions after 10 random starts outclusCA = clusmca(mybond[,8:10], 3, 2, nstart = 100, seed = 234) #Save the ggplot2 scatterplot map = plot(outclusCA, max.overlaps = 40)$map #Customization (adding titles) map + ggtitle(paste("Cluster CA plot of the James bond categorical data: 3 clusters of sizes ", paste(outclusCA$size, collapse = ", "),sep = "")) + xlab("Dim. 1") + ylab("Dim. 2") + theme(plot.title = element_text(size = 10, face = "bold", hjust = 0.5)) data("mybond") #i-FCB with 3 clusters in 2 dimensions after 10 random starts outclusCA = clusmca(mybond[,8:10], 3, 2, method = "iFCB", nstart= 10) #Scatterlot with the observations only (dimensions 1 and 2) #and cluster description plots showing the 20 largest std. residuals #(with the full distribution showing in subplots) plot(outclusCA, dim = c(1,2), what = c(TRUE, FALSE), cludesc = TRUE, subplot = TRUE)data("mybond") #Cluster Correspondence Analysis with 3 clusters in 2 dimensions after 10 random starts outclusCA = clusmca(mybond[,8:10], 3, 2, nstart = 100, seed = 234) #Save the ggplot2 scatterplot map = plot(outclusCA, max.overlaps = 40)$map #Customization (adding titles) map + ggtitle(paste("Cluster CA plot of the James bond categorical data: 3 clusters of sizes ", paste(outclusCA$size, collapse = ", "),sep = "")) + xlab("Dim. 1") + ylab("Dim. 2") + theme(plot.title = element_text(size = 10, face = "bold", hjust = 0.5)) data("mybond") #i-FCB with 3 clusters in 2 dimensions after 10 random starts outclusCA = clusmca(mybond[,8:10], 3, 2, method = "iFCB", nstart= 10) #Scatterlot with the observations only (dimensions 1 and 2) #and cluster description plots showing the 20 largest std. residuals #(with the full distribution showing in subplots) plot(outclusCA, dim = c(1,2), what = c(TRUE, FALSE), cludesc = TRUE, subplot = TRUE)
cluspca() output.
Plotting function that creates a scatterplot of the objects, a correlation circle of the variables or a biplot of both objects and variables. Optionally, it returns a parallel coordinate plot showing cluster means.
## S3 method for class 'cluspca' plot(x, dims = c(1, 2), cludesc = FALSE, what = c(TRUE,TRUE), attlabs, max.overlaps=10, ...)## S3 method for class 'cluspca' plot(x, dims = c(1, 2), cludesc = FALSE, what = c(TRUE,TRUE), attlabs, max.overlaps=10, ...)
x |
Object returned by |
dims |
Numerical vector of length 2 indicating the dimensions to plot on horizontal and vertical axes respectively; default is first dimension horizontal and second dimension vertical |
what |
Vector of two logical values specifying the contents of the plots. First entry indicates whether a scatterplot of the objects and cluster centroids is displayed and the second entry whether a correlation circle of the variables is displayed. The default is |
cludesc |
A logical value indicating if a parallel coordinate plot showing cluster means is produced (default = |
attlabs |
Vector of custom attribute labels; if not provided, default labeling is applied |
max.overlaps |
Maximum number of text labels allowed to overlap. Defaults to 10 |
... |
Further arguments to be transferred to |
The function returns a ggplot2 scatterplot of the solution obtained via cluspca() that can be further customized using the ggplot2 package. When cludesc = TRUE
the function also returns a ggplot2 parallel coordinate plot.
De Soete, G., and Carroll, J. D. (1994). K-means clustering in a low-dimensional Euclidean space. In Diday E. et al. (Eds.), New Approaches in Classification and Data Analysis, Heidelberg: Springer, 212-219.
Vichi, M., and Kiers, H.A.L. (2001). Factorial K-means analysis for two-way data. Computational Statistics and Data Analysis, 37, 49-64.
data("macro") #Factorial K-means (3 clusters in 2 dimensions) after 100 random starts outFKM = cluspca(macro, 3, 2, method = "FKM", rotation = "varimax") #Scatterplot (dimensions 1 and 2) and cluster description plot plot(outFKM, cludesc = TRUE) data("iris", package = "datasets") #Compromise solution between PCA and Reduced K-means #on the iris dataset (3 clusters in 2 dimensions) after 100 random starts outclusPCA = cluspca(iris[,-5], 3, 2, alpha = 0.3, rotation = "varimax") table(outclusPCA$cluster,iris[,5]) #Save the ggplot2 scatterplot map = plot(outclusPCA)$map #Customization (adding titles) map + ggtitle(paste("A compromise solution between RKM and FKM on the iris: 3 clusters of sizes ", paste(outclusPCA$size, collapse = ", "),sep = "")) + xlab("Dimension 1") + ylab("Dimension 2") + theme(plot.title = element_text(size = 10, face = "bold", hjust = 0.5))data("macro") #Factorial K-means (3 clusters in 2 dimensions) after 100 random starts outFKM = cluspca(macro, 3, 2, method = "FKM", rotation = "varimax") #Scatterplot (dimensions 1 and 2) and cluster description plot plot(outFKM, cludesc = TRUE) data("iris", package = "datasets") #Compromise solution between PCA and Reduced K-means #on the iris dataset (3 clusters in 2 dimensions) after 100 random starts outclusPCA = cluspca(iris[,-5], 3, 2, alpha = 0.3, rotation = "varimax") table(outclusPCA$cluster,iris[,5]) #Save the ggplot2 scatterplot map = plot(outclusPCA)$map #Customization (adding titles) map + ggtitle(paste("A compromise solution between RKM and FKM on the iris: 3 clusters of sizes ", paste(outclusPCA$size, collapse = ", "),sep = "")) + xlab("Dimension 1") + ylab("Dimension 2") + theme(plot.title = element_text(size = 10, face = "bold", hjust = 0.5))
cluspcamix() output.
Plotting function that creates a scatterplot of the objects, a correlation circle of the variables or a biplot of both objects and variables. Optionally, for metric variables, it returns a parallel coordinate plot showing cluster means and for categorical variables, a series of barplots showing the standardized residuals per attribute for each cluster.
## S3 method for class 'cluspcamix' plot(x, dims = c(1, 2), cludesc = FALSE, topstdres = 20, objlabs = FALSE, attlabs = NULL, attcatlabs = NULL, subplot = FALSE, what = c(TRUE,TRUE), max.overlaps = 10, ...)## S3 method for class 'cluspcamix' plot(x, dims = c(1, 2), cludesc = FALSE, topstdres = 20, objlabs = FALSE, attlabs = NULL, attcatlabs = NULL, subplot = FALSE, what = c(TRUE,TRUE), max.overlaps = 10, ...)
x |
Object returned by |
dims |
Numerical vector of length 2 indicating the dimensions to plot on horizontal and vertical axes respectively; default is first dimension horizontal and second dimension vertical |
what |
Vector of two logical values specifying the contents of the plots. First entry indicates whether a scatterplot of the objects and cluster centroids is displayed and the second entry whether a correlation circle of the variables is displayed. The default is |
cludesc |
A logical value indicating if a parallel coordinate plot showing cluster means is produced (default = |
topstdres |
Number of largest standardized residuals used to describe each cluster (default = 20). Works only in combination with |
subplot |
A logical value indicating whether a subplot with the full distribution of the standardized residuals will appear at the bottom left corner of the corresponding plots. Works only in combination with |
objlabs |
A logical value indicating whether object labels will be plotted; if |
attlabs |
Vector of custom labels of continuous attributes; if not provided, default labeling is applied |
attcatlabs |
Vector of custom labels of categorical attributes (categories); if not provided, default labeling is applied |
max.overlaps |
Maximum number of text labels allowed to overlap. Defaults to 10 |
... |
Further arguments to be transferred to |
The function returns a ggplot2 scatterplot of the solution obtained via cluspcamix() that can be further customized using the ggplot2 package. When cludesc = TRUE, for metric variables, the function also returns a ggplot2 parallel coordinate plot and for categorical variables, a series of ggplot2 barplots showing the largest (or all) standardized residuals per attribute for each cluster.
van de Velden, M., Iodice D'Enza, A., & Markos, A. (2019). Distance-based clustering of mixed data. Wiley Interdisciplinary Reviews: Computational Statistics, e1456.
Vichi, M., Vicari, D., & Kiers, H. A. L. (2019). Clustering and dimension reduction for mixed variables. Behaviormetrika. doi:10.1007/s41237-018-0068-6.
data(diamond) #Mixed Reduced K-means solution with 3 clusters in 2 dimensions #after 10 random starts outmixedRKM = cluspcamix(diamond, 3, 2, method = "mixedRKM", nstart = 10) #Scatterplot (dimensions 1 and 2) plot(outmixedRKM, cludesc = TRUE)data(diamond) #Mixed Reduced K-means solution with 3 clusters in 2 dimensions #after 10 random starts outmixedRKM = cluspcamix(diamond, 3, 2, method = "mixedRKM", nstart = 10) #Scatterplot (dimensions 1 and 2) plot(outmixedRKM, cludesc = TRUE)
This function facilitates the selection of the appropriate number of clusters and dimensions for joint dimension reduction and clustering methods.
tuneclus(data, nclusrange = 3:4, ndimrange = 2:3, method = c("RKM","FKM","mixedRKM","mixedFKM","clusCA","iFCB","MCAk"), criterion = "asw", dst = "full", alpha = NULL, alphak = NULL, center = TRUE, scale = TRUE, rotation = "none", nstart = 100, smartStart = NULL, seed = NULL) ## S3 method for class 'tuneclus' print(x, ...) ## S3 method for class 'tuneclus' summary(object, ...) ## S3 method for class 'tuneclus' fitted(object, mth = c("centers", "classes"), ...)tuneclus(data, nclusrange = 3:4, ndimrange = 2:3, method = c("RKM","FKM","mixedRKM","mixedFKM","clusCA","iFCB","MCAk"), criterion = "asw", dst = "full", alpha = NULL, alphak = NULL, center = TRUE, scale = TRUE, rotation = "none", nstart = 100, smartStart = NULL, seed = NULL) ## S3 method for class 'tuneclus' print(x, ...) ## S3 method for class 'tuneclus' summary(object, ...) ## S3 method for class 'tuneclus' fitted(object, mth = c("centers", "classes"), ...)
data |
Continuous, Categorical ot Mixed data set |
nclusrange |
An integer vector with the range of numbers of clusters which are to be compared by the cluster validity criteria. Note: the number of clusters should be greater than one |
ndimrange |
An integer vector with the range of dimensions which are to be compared by the cluster validity criteria |
method |
Specifies the method. Options are |
criterion |
One of |
dst |
Specifies the data used to compute the distances between objects. Options are |
alpha |
Adjusts for the relative importance of (mixed) RKM and FKM in the objective function; |
alphak |
Non-negative scalar to adjust for the relative importance of MCA ( |
center |
A logical value indicating whether the variables should be shifted to be zero centered (default = |
scale |
A logical value indicating whether the variables should be scaled to have unit variance before the analysis takes place (default = |
rotation |
Specifies the method used to rotate the factors. Options are none for no rotation, varimax for varimax rotation with Kaiser normalization and promax for promax rotation (default = |
nstart |
Number of starts (default = 100) |
smartStart |
If |
seed |
An integer that is used as argument by |
x |
For the |
object |
For the |
mth |
For the |
... |
Not used |
For the K-means part, the algorithm of Hartigan-Wong is used by default.
The hidden print and summary methods print out some key components of an object of class tuneclus.
The hidden fitted method returns cluster fitted values. If method is "classes", this is a vector of cluster membership (the cluster component of the "tuneclus" object). If method is "centers", this is a matrix where each row is the cluster center for the observation. The rownames of the matrix are the cluster membership values.
clusobjbest |
The output of the optimal run of |
nclusbest |
The optimal number of clusters |
ndimbest |
The optimal number of dimensions |
critbest |
The optimal criterion value for |
critgrid |
Matrix of size |
criterion |
"asw" for average Silhouette width or "ch" for "Calinski-Harabasz" |
cluasw |
Average Silhouette width values of each cluster, when criterion = "asw" |
Calinski, R.B., and Harabasz, J., (1974). A dendrite method for cluster analysis. Communications in Statistics, 3, 1-27.
Kaufman, L., and Rousseeuw, P.J., (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.
global_bootclus, local_bootclus
# Reduced K-means for a range of clusters and dimensions data(macro) # Cluster quality assessment based on the average silhouette width in the low dimensional space # nstart = 1 for speed in example # use more for real applications bestRKM = tuneclus(macro, 3:4, 2:3, method = "RKM", criterion = "asw", dst = "low", nstart = 1, seed = 1234) bestRKM #plot(bestRKM) # Cluster Correspondence Analysis for a range of clusters and dimensions data(bribery) # Cluster quality assessment based on the Callinski-Harabasz index in the full dimensional space bestclusCA = tuneclus(bribery, 4:5, 3:4, method = "clusCA", criterion = "ch", nstart = 20, seed = 1234) bestclusCA #plot(bestclusCA, cludesc = TRUE) # Mixed reduced K-means for a range of clusters and dimensions data(diamond) # Cluster quality assessment based on the average silhouette width in the low dimensional space # nstart = 5 for speed in example # use more for real applications bestmixedRKM = tuneclus(diamond[,-7], 3:4, 2:3, method = "mixedRKM", criterion = "asw", dst = "low", nstart = 5, seed = 1234) bestmixedRKM #plot(bestmixedRKM)# Reduced K-means for a range of clusters and dimensions data(macro) # Cluster quality assessment based on the average silhouette width in the low dimensional space # nstart = 1 for speed in example # use more for real applications bestRKM = tuneclus(macro, 3:4, 2:3, method = "RKM", criterion = "asw", dst = "low", nstart = 1, seed = 1234) bestRKM #plot(bestRKM) # Cluster Correspondence Analysis for a range of clusters and dimensions data(bribery) # Cluster quality assessment based on the Callinski-Harabasz index in the full dimensional space bestclusCA = tuneclus(bribery, 4:5, 3:4, method = "clusCA", criterion = "ch", nstart = 20, seed = 1234) bestclusCA #plot(bestclusCA, cludesc = TRUE) # Mixed reduced K-means for a range of clusters and dimensions data(diamond) # Cluster quality assessment based on the average silhouette width in the low dimensional space # nstart = 5 for speed in example # use more for real applications bestmixedRKM = tuneclus(diamond[,-7], 3:4, 2:3, method = "mixedRKM", criterion = "asw", dst = "low", nstart = 5, seed = 1234) bestmixedRKM #plot(bestmixedRKM)