clustMixType (version 0.1-16)

kproto: k prototypes clustering

Description

Computes k prototypes clustering for mixed type data.

Usage

kproto(x, ...)
"kproto"(x, k, lambda = NULL, iter.max = 100, nstart = 1, ...)

Arguments

x

Data frame with both mumerics and factors.

k

Either the number of clusters or a vector specifying indices of initial prototypes.

lambda

Parameter > 0 to trade off between Euclidean distance of numeric variables and simple matching coefficient between categorical variables.

iter.max

Maximum number of iterations if no convergence before.

nstart

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

...

Currently not used.

Value

kmeans like object of class kproto:

cluster

Vector of cluster memberships.

centers

Data frame of cluster prototypes.

lambda

Distance parameter lambda.

size

Vector of cluster sizes.

withinss

Vector of summed distances to the cluster prototype per cluster.

tot.withinss

Target function: sum of all distances to clsuter prototype.

dists

Matrix with distances of observations to all cluster prototypes.

iter

Prespecified maximum number of iterations.

trace

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

Details

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).

References

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.

Examples

# 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 prototyps
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)