# INCA index `INCAindex` helps to estimate the number of clusters in a dataset. ```r INCAindex(d, pert_clus) ``` ## Arguments - `d`: a distance matrix or a `dist` object with distance information between units. - `pert_clus`: an n-vector that indicates which group each unit belongs to. Note that the expected values of `pert` are numbers greater than or equal to 1 (for instance 1,2,3,4..., k). The default value indicates the presence of only one group in data. ## Returns Returns an object of class `incaix` which is a list containing the following components: - **well_class**: a vector indicating the number of well classified units. - **Ni_cluster**: a vector indicating each cluster size. - **Total**: percentage of objects well classified in the partition defined by `pert_clus`. ## References Arenas, C. and Cuadras, C.M. (2002). Some recent statistical methods based on distances.**Contributions to Science**, 2 , 183--191. Irigoien, I. and Arenas, C. (2008). INCA: New statistic for estimating the number of clusters and identifying atypical units. **Statistics in Medicine**, 27 (15), 2948--2973. ## Author(s) Itziar Irigoien itziar.irigoien@ehu.eus ; Konputazio Zientziak eta Adimen Artifiziala, Euskal Herriko Unibertsitatea (UPV/EHU), Donostia, Spain. Conchita Arenas carenas@ub.edu ; Departament d'Estadistica, Universitat de Barcelona, Barcelona, Spain. ## Note For a correct geometrical interpretation it is convenient to verify whether the distance matrix d is Euclidean. It admits the associated methods summary and plot. The first simply returns the percentage of well-classified units and the second offers a barchart with the percentages of well classified units for each group in the given partition. ## See Also `estW`, `INCAtest` ## Examples ```r #generate 3 clusters, each of them with 20 objects in dimension 5. mu1 <- sample(1:10, 5, replace=TRUE) x1 <- matrix(rnorm(20*5, mean = mu1, sd = 1),ncol=5, byrow=TRUE) mu2 <- sample(1:10, 5, replace=TRUE) x2 <- matrix(rnorm(20*5, mean = mu2, sd = 1),ncol=5, byrow=TRUE) mu3 <- sample(1:10, 5, replace=TRUE) x3 <- matrix(rnorm(20*5, mean = mu3, sd = 1),ncol=5, byrow=TRUE) x <- rbind(x1,x2,x3) # Euclidean distance between units. d <- dist(x) # given the right partition, calculate the percentage of well classified objects. partition <- c(rep(1,20), rep(2,20), rep(3,20)) INCAindex(d, partition) # In order to estimate the number of cluster in data, try several # partitions and compare the results library(cluster) T <- rep(NA, 5) for (l in 2:5){ part <- pam(d,l)$clustering T[l] <- INCAindex(d,part)$Total } plot(T, type="b",xlab="Number of clusters", ylab="INCA", xlim=c(1.5, 5.5)) ```

INCAindex function