# A partial clustering algorithm with automatic estimation of the number of clusters and identification of outliers This function performs the CrossClustering algorithm. This method combines the Ward's minimum variance and Complete-linkage (default, useful for finding spherical clusters) or Single-linkage (useful for finding elongated clusters) algorithms, providing automatic estimation of a suitable number of clusters and identification of outlier elements. ```r cc_crossclustering( dist, k_w_min = 2, k_w_max = attr(dist, "Size") - 2, k2_max = k_w_max + 1, out = TRUE, method = c("complete", "single") ) ## S3 method for class 'crossclustering' print(x, ...) ``` ## Arguments - `dist`: A dissimilarity structure as produced by the function `dist` - `k_w_min`: (int) Minimum number of clusters for the Ward's minimum variance method. By default is set equal 2 - `k_w_max`: (int) Maximum number of clusters for the Ward's minimum variance method (see details) - `k2_max`: (int) Maximum number of clusters for the Complete/Single-linkage method. It can not be equal or greater than the number of elements to cluster (see details) - `out`: (lgl) If `TRUE` (default) outliers must be searched (see details) - `method`: (chr) "complete" (default) or "single". CrossClustering combines Ward's algorithm with Complete-linkage if method is set to "complete", otherwise (if method is set to 'single') Single-linkage will be used. - `x`: an object used to select a method. - `...`: further arguments passed to or from other methods. ## Returns A list of objects describing characteristics of the partitioning as follows: - **Optimal_cluster**: number of clusters - **cluster_list_elements**: a list of clusters; each element of this lists contains the indices of the elements belonging to the cluster - **Silhouette**: the average silhouette width over all the clusters - **n_total**: total number of input elements - **n_clustered**: number of input elements that have actually been clustered ## Details See cited document for more details. ## Functions * `print(crossclustering)`: ## Examples ```r library(CrossClustering) #### Example of Cross-Clustering as in reference paper #### method = "complete" data(toy) ### toy is transposed as we want to cluster samples (columns of the ### original matrix) toy_dist <- t(toy) |> dist(method = "euclidean") ### Run CrossClustering cc_crossclustering( toy_dist, k_w_min = 2, k_w_max = 5, k2_max = 6, out = TRUE ) #### Simulated data as in reference paper #### method = "complete" set.seed(10) sg <- c(500, 250, 700, 300, 100) # 5 clusters t <- matrix(0, nrow = 5, ncol = 5) t[1, ] <- rep(6, 5) t[2, ] <- c( 0, 5, 12, 13, 15) t[3, ] <- c(15, 11, 9, 5, 0) t[4, ] <- c( 6, 12, 15, 10, 5) t[5, ] <- c(12, 17, 3, 7, 10) t_mat <- NULL for (i in seq_len(nrow(t))) { t_mat <- rbind( t_mat, matrix(rep(t[i, ], sg[i]), nrow = sg[i], byrow = TRUE) ) } data_15 <- matrix(NA, nrow = 2000, ncol = 5) data_15[1:1850, ] <- matrix( abs(rnorm(sum(sg) * 5, sd = 1.5)), nrow = sum(sg), ncol = 5 ) + t_mat set.seed(100) # simulate outliers data_15[1851:2000, ] <- matrix( runif(n = 150 * 5, min = 0, max = max(data_15, na.rm = TRUE)), nrow = 150, ncol = 5 ) ### Run CrossClustering cc_crossclustering( dist(data_15), k_w_min = 2, k_w_max = 19, k2_max = 20, out = TRUE ) #### Correlation-based distance is often used in gene expression time-series ### data analysis. Here there is an example, using the "complete" method. data(nb_data) nb_dist <- as.dist(1 - abs(cor(t(nb_data)))) cc_crossclustering(dist = nb_dist, k_w_max = 20, k2_max = 19) #### method = "single" ### Example on a famous shape data set ### Two moons data data(twomoons) moons_dist <- twomoons[, 1:2] |> dist(method = "euclidean") cc_moons <- cc_crossclustering( moons_dist, k_w_max = 9, k2_max = 10, method = 'single' ) moons_col <- cc_get_cluster(cc_moons) plot( twomoons[, 1:2], col = moons_col, pch = 19, xlab = "", ylab = "", main = "CrossClustering-Single" ) ### Worms data data(worms) worms_dist <- worms[, 1:2] |> dist(method = "euclidean") cc_worms <- cc_crossclustering( worms_dist, k_w_max = 9, k2_max = 10, method = "single" ) worms_col <- cc_get_cluster(cc_worms) plot( worms[, 1:2], col = worms_col, pch = 19, xlab = "", ylab = "", main = "CrossClustering-Single" ) ### CrossClustering-Single is not affected to chain-effect problem data(chain_effect) chain_dist <- chain_effect |> dist(method = "euclidean") cc_chain <- cc_crossclustering( chain_dist, k_w_max = 9, k2_max = 10, method = "single" ) chain_col <- cc_get_cluster(cc_chain) plot( chain_effect, col = chain_col, pch = 19, xlab = "", ylab = "", main = "CrossClustering-Single" ) ``` ## References Tellaroli P, Bazzi M., Donato M., Brazzale A. R., Draghici S. (2016). Cross-Clustering: A Partial Clustering Algorithm with Automatic Estimation of the Number of Clusters. PLoS ONE 11(3): e0152333. doi:10.1371/journal.pone.0152333 #' Tellaroli P, Bazzi M., Donato M., Brazzale A. R., Draghici S. (2017). E1829: Cross-Clustering: A Partial Clustering Algorithm with Automatic Estimation of the Number of Clusters. CMStatistics 2017, London 16-18 December, Book of Abstracts (ISBN 978-9963-2227-4-2) ## Author(s) Paola Tellaroli, ;; Marco Bazzi, ; Michele Donato,

cc_crossclustering function