clustMixType (version 0.3-9)

kproto_gower: k-Prototypes Clustering using Gower Dissimilarity

Description

Internal function. Computes k-prototypes clustering for mixed-type data using Gower dissimilarity.

Usage

kproto_gower(
  x,
  k,
  lambda = NULL,
  iter.max = 100,
  na.rm = "yes",
  keep.data = TRUE,
  verbose = TRUE
)

Value

kmeans like object of class kproto:

cluster

Vector of cluster memberships.

centers

Data frame of cluster prototypes.

lambda

Distance parameter lambda. For codetype = "gower" only a vector of variable specific weights is possible.

size

Vector of cluster sizes.

withinss

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

tot.withinss

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

dists

Matrix with distances of observations to all cluster prototypes.

iter

Prespecified maximum number of iterations.

stdization

List of standardized ranks for ordinal variables and and an additional element num_ranges with ranges of all numeric variables. Used by predict.kproto.

trace

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

Arguments

x

Data frame with both numerics and factors (also ordered factors are possible).

k

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

lambda

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.

iter.max

Maximum number of iterations if no convergence before.

na.rm

Character; passed from kproto. For "no" observations where all variables are missinf are assigned cluster membershim NA.

keep.data

Logical whether original should be included in the returned object.

verbose

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

Author

Details

Internal function called by kproto. Note that there is no nstart argument. Higher values than nstart = 1 can be specified within kproto which will call kproto_gower several times. For Gower dissimilarity range-normalized absolute distances from the cluster median are computed for the numeric variables (and for the ranks of the ordered factors respectively). For factors simple matching distance is used as in the original k prototypes algorithm. The prototypes are given by the median for numeric variables, the mode for factors and the level with the closest rank to the median rank of the corresponding cluster. In case of na.rm = "no": 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.

References

• Gower, J. C. (1971): A General Coefficient of Similarity and Some of Its Properties. Biometrics, 27(4), 857–871. tools:::Rd_expr_doi("10.2307/2528823").

• Podani, J. (1999): Extending Gower's general coefficient of similarity to ordinal characters. TAXON, 48, 331-340. tools:::Rd_expr_doi("10.2307/1224438").

Examples

datasim <- function(n = 100, k.ord = 2, muk = 1.5){
  clusid <- rep(1:4, each = n)
  # numeric
  mus <- c(rep(-muk, n),
           rep(-muk, n),
           rep(muk, n),
           rep(muk, n))
           x1 <- rnorm(4*n) + mus
 # ordered factor
  mus <- c(rep(-muk, n),
           rep(muk, n),
           rep(-muk, n),
           rep(muk, n))
 x2 <- rnorm(4*n) + mus
 # ordered factor
 
 quants <- quantile(x2, seq(0, 1, length.out = (k.ord+1)))
 quants[1] <- -Inf
 quants[length(quants)] <- Inf
 x2 <- as.ordered(cut(x2, quants))
 x <- data.frame(x1, x2)
 return(x)
 }
 
 n     <- 100
 x     <- datasim(n = n, k.ord = 10, muk = 2)
 truth <- rep(1:4, each = n)
 
 # calling the internal kproto_gower() directly 
 kgres <- kproto_gower(x, 4, verbose = FALSE)
 
 # calling kproto gower via kproto:
 kgres2 <- kproto(x, 4, verbose = FALSE, type = "gower", nstart = 10)
 
 table(kgres$cluster, truth)
 clprofiles(kgres, x)