clustMixType (version 0.2-15)

kproto: k-Prototypes Clustering


Computes k-prototypes clustering for mixed-type data.


kproto(x, ...)

# S3 method for default kproto( x, k, lambda = NULL, iter.max = 100, nstart = 1, na.rm = TRUE, = TRUE, verbose = TRUE, ... )



Data frame with both numerics and factors.

Currently not used.


Either the number of clusters, a vector specifying indices of initial prototypes, or a data frame of prototypes of the same columns as x.


Parameter > 0 to trade off between Euclidean distance of numeric variables and simple matching coefficient between categorical variables. Also a vector of variable specific factors is possible where the order must correspond to the order of the variables in the data. In this case all variables' distances will be multiplied by their corresponding lambda value.


Maximum number of iterations if no convergence before.


If > 1 repetetive computations with random initializations are computed and the result with minimum tot.dist is returned.


A logical value indicating whether NA values should be stripped before the computation proceeds.

Logical whether original should be included in the returned object.


Logical whether information about the cluster procedure should be given. Caution: If verbose=FALSE, the reduction of the number of clusters is not mentioned.


kmeans like object of class kproto:


Vector of cluster memberships.


Data frame of cluster prototypes.


Distance parameter lambda.


Vector of cluster sizes.


Vector of within cluster distances for each cluster, i.e. summed distances of all observations belonging to a cluster to their respective prototype.


Target function: sum of all observations' distances to their corresponding cluster prototype.


Matrix with distances of observations to all cluster prototypes.


Prespecified maximum number of iterations.


List with two elements (vectors) tracing the iteration process: tot.dists and moved number of observations over all iterations.


The algorithm like k-means iteratively recomputes cluster prototypes and reassigns clusters. Clusters are assigned using \(d(x,y) = d_{euclid}(x,y) + \lambda d_{simple\,matching}(x,y)\). Cluster prototypes are computed as cluster means for numeric variables and modes for factors (cf. Huang, 1998). In case of na.rm = FALSE: for each observation variables with missings are ignored (i.e. only the remaining variables are considered for distance computation). In consequence for observations with missings this might result in a change of variable's weighting compared to the one specified by lambda. Further note: For these observations distances to the prototypes will typically be smaller as they are based on fewer variables.


  • Szepannek, G. (2018): clustMixType: User-Friendly Clustering of Mixed-Type Data in R, The R Journal 10/2, 200-208, 10.32614/RJ-2018-048.

  • Z.Huang (1998): Extensions to the k-Means Algorithm for Clustering Large Data Sets with Categorical Variables, Data Mining and Knowledge Discovery 2, 283-304.


# generate toy data with factors and numerics

n   <- 100
prb <- 0.9
muk <- 1.5 
clusid <- rep(1:4, each = n)

x1 <- sample(c("A","B"), 2*n, replace = TRUE, prob = c(prb, 1-prb))
x1 <- c(x1, sample(c("A","B"), 2*n, replace = TRUE, prob = c(1-prb, prb)))
x1 <- as.factor(x1)

x2 <- sample(c("A","B"), 2*n, replace = TRUE, prob = c(prb, 1-prb))
x2 <- c(x2, sample(c("A","B"), 2*n, replace = TRUE, prob = c(1-prb, prb)))
x2 <- as.factor(x2)

x3 <- c(rnorm(n, mean = -muk), rnorm(n, mean = muk), rnorm(n, mean = -muk), rnorm(n, mean = muk))
x4 <- c(rnorm(n, mean = -muk), rnorm(n, mean = muk), rnorm(n, mean = -muk), rnorm(n, mean = muk))

x <- data.frame(x1,x2,x3,x4)

# apply k-prototypes
kpres <- kproto(x, 4)
clprofiles(kpres, x)

# in real world clusters are often not as clear cut
# by variation of lambda the emphasize is shifted towards factor / numeric variables    
kpres <- kproto(x, 2)
clprofiles(kpres, x)

kpres <- kproto(x, 2, lambda = 0.1)
clprofiles(kpres, x)

kpres <- kproto(x, 2, lambda = 25)
clprofiles(kpres, x)

# }