# Determination the stability of k Prototypes Clustering Calculating the stability for a k-Prototypes clustering with k clusters or computing the stability-based optimal number of clusters for k-Prototype clustering. Possible stability indices are: `Jaccard`, `Rand`, `Fowlkes \& Mallows` and `Luxburg`. ```r stability_kproto( object, method = c("rand", "jaccard", "luxburg", "fowlkesmallows"), B = 100, verbose = FALSE, ... ) ``` ## Arguments - `object`: Object of class `kproto` resulting from a call with `kproto(..., keep.data=TRUE)` - `method`: character specifying the stability, either one or more of `luxburg`, `fowlkesmallows`, `rand` or/and `jaccard`. - `B`: numeric, number of bootstrap samples - `verbose`: Logical whether information about the bootstrap procedure should be given. - `...`: Further arguments passed to `kproto`, like: * `nstart`: If \> 1 repetitive computations of `kproto` with random initial prototypes are computed. * `lambda`: Factor to trade off between Euclidean distance of numeric variables and simple matching coefficient between categorical variables. ## Returns The output contains the stability for a given k-Prototype clustering in a list with two elements: - **kp_stab**: stability values for the given clustering - **kp_bts_stab**: stability values for each bootstrap samples ## Examples ```r ## Not run: # generate toy data with factors and numerics n <- 10 prb <- 0.99 muk <- 2.5 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, keep.data = TRUE) # calculate cluster stability stab <- stability_kproto(method = c("luxburg","fowlkesmallows"), object = kpres) ## End(Not run) ``` ## References * Aschenbruck, R., Szepannek, G., Wilhelm, A.F.X (2023): Stability of mixed-type cluster partitions for determination of the number of clusters. **Submitted**. * von Luxburg, U. (2010): Clustering stability: an overview. **Foundations and Trends in Machine Learning, Vol 2, Issue 3**. tools:::Rd_expr_doi("10.1561/2200000008") . * Ben-Hur, A., Elisseeff, A., Guyon, I. (2002): A stability based method for discovering structure in clustered data. **Pacific Symposium on Biocomputing**. tools:::Rd_expr_doi("10/bhfxmf") . ## Author(s) Rabea Aschenbruck

stability_kproto function