# Estimation of Number of Clusters in Data `INCAnumclu` helps to estimate the number of clusters in a dataset. The INCA index associated to different partitions with different number of clusters is calculated. ```r INCAnumclu(d, K, method = "pam", pert, L= NULL, noise=NULL) ``` ## Arguments - `d`: a distance matrix or a `dist` object with distance information between units. - `K`: the maximum number of cluster to be considered. For each k value ( k=2,..,K) a partition with k clusters is calculated. - `method`: character string defining the clustering method in order to obtain the partitions. The hierarchical aglomerative clustering methods are perfomed via `hclust` function in package `fastcluster`. Other clustering methods are performed via the functions in package `cluster`, such as: `pam`, `diana` and `fanny`. The available clustering methods are `pam` (default method), `average` (UPGMA), `single` (single linkage), `complete` (complete linkage), `ward.D2` (Ward's method), `ward.D`, `centroid`, `median`, `diana` (hierarchical divisive) and `fanny` (fuzzy clustering). Nevertheless, the user can introduce particular or custom partitions indicating `method="partition"` and specifying the partitions in argument `pert`. - `pert`: only useful when parameter `method`="partition"; it is a matrix and each column contains a partition of the units. That means that each column is an n-vector that indicates which group each unit belongs to. Note that the expected values of each column of `pert` are numbers greater than or equal to 1 (for instance 1,2,3,4..., k). - `L`: default value NULL, but when some units are considered by the user as noise units, `L` must be specified as follows: (a) `L` is greater than or equal to 1 and all units in clusters with a cardinal <= L are considered noise units; (b) `L="custom"` when the user wants to specify which units are considered noise units. These units must be specified in argument `noise`. - `noise`: when `L="custom"`, it is a logical vector indicating the units considered by the user as noise units. ## Returns Returns an object of class `incanc` which is a numeric vector containing the INCA index associated to each of the k (k=2,...,K) partitions. When `noise` is no null, the function returns a list with the INCA index for each partition, which is calculated without noise units as well as with noise units. The associated `plot` returns INCA index plot, both, with and without noise. ## References 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. Arenas, C. and Cuadras, C.M. (2002). Some recent statistical methods based on distances.**Contributions to Science**, 2 , 183--191. ## 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. ## See Also `INCAindex`, `estW` ## Examples ```r #------- Example 1 -------------------------------------- #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) # calculte euclidean distance between them d <- dist(x) # calculate the INCA index associated to partitions with k=2, ..., k=5 clusters. INCAnumclu(d, K=5) out <- INCAnumclu(d, K=5) plot(out) #------- Example 1 cont. -------------------------------- # With hypothetical noise elements noiseunits <- rep(FALSE, 60) noiseunits[sample(1:60, 20)] <- TRUE out <- INCAnumclu(d, K=5, L="custom", noise=noiseunits) plot(out) ```

INCAnumclu function