# Subspace clustering based local classification using ORCLUS. Function to perform local classification where the subclasses are concentrated in different subspaces of the data. ```r orclass(x, ...) ## Default S3 method: orclass(x, grouping, k, l, k0, a = 0.5, prior = NULL, inner.loops = 1, predict.train = "nearest", verbose = TRUE, ...) ## S3 method for class 'formula' orclass(formula, data = NULL, ...) ``` ## Arguments - `x`: A matrix or data frame containing the explanatory variables. The method is restricted to numerical data. - `grouping`: A factor specifying the class for each observation. - `formula`: A formula of the form `grouping ~ x1 + x2 + ...` That is, the response is the grouping factor and the right hand side specifies the (non-factor) discriminators. - `data`: Data frame from which variables specified in formula are to be taken. - `k`: Prespecifies the final number of clusters. - `l`: Prespecifies the dimension of the final cluster-specific subspaces (equal for all clusters). - `k0`: Initial number of clusters (that are computed in the entire data space). Must be greater than `k`. The number of clusters is iteratively decreased by factor `a` until the final number of `k` clusters is reached. - `a`: Prespecified factor for the cluster number reduction in each iteration step of the algorithm. - `prior`: Argument for optional specification of class prior probabilities if different from the relative class frequencies. - `inner.loops`: Number of repetitive iterations (i.e. recomputation of clustering and cluster-specific subspaces) while the number of clusters and the subspace dimension are kept constant. - `predict.train`: Character pecifying whether prediction of training data should be pursued. If `"nearest"` the class distribution in `orclus` cluster assignment is used for classification. - `verbose`: Logical indicating whether the iteration process sould be displayed. - ``...``: Currently not used. ## Details For each cluster the class distribution is computed. ## Returns Returns an object of class `orclass`. - **orclus.res**: Object of class `orclus` containing the resulting clusters. - **cluster.posteriors**: Matrix of clusterwise class posterior probabilities where clusters are rows and classes are coloumns. - **cluster.priors**: Vector of relative cluster frequencies weighted by class priors. - **purity**: Statistics indicating the discriminability of the identified clusters. - **prior**: Vector of class prior probabilities. - **predict.train**: Prediction of training data if specified. - **orclass.call**: (Matched) function call. ## References Aggarwal, C. and Yu, P. (2000): **Finding generalized projected clusters in high dimensional spaces**, Proceedings of ACM SIGMOD International Conference on Management of Data, pp. 70-81. ## Author(s) Gero Szepannek ## See Also `predict.orclass`, `orclus`, `predict.orclus` ## Examples ```r # definition of a function for parameterized data simulation sim.orclus <- function(k = 3, nk = 100, d = 10, l = 4, sd.cl = 0.05, sd.rest = 1, locshift = 1){ ### input parameters for data generation # k number of clusters # nk observations per cluster # d original dimension of the data # l subspace dimension where the clusters are concentrated # sd.cl (within cluster subspace) standard deviations for data generation # sd.rest standard deviations in the remaining space # locshift parameter of a uniform distribution to sample different cluster means x <- NULL for(i in 1:k){ # cluster centers apts <- locshift*matrix(runif(l*k), ncol = l) # sample points in original space xi.original <- cbind(matrix(rnorm(nk * l, sd = sd.cl), ncol=l) + matrix(rep(apts[i,], nk), ncol = l, byrow = TRUE), matrix(rnorm(nk * (d-l), sd = sd.rest), ncol = (d-l))) # subspace generation sym.mat <- matrix(nrow=d, ncol=d) for(m in 1:d){ for(n in 1:m){ sym.mat[m,n] <- sym.mat[n,m] <- runif(1) } } subspace <- eigen(sym.mat)$vectors # transformation xi.transformed <- xi.original %*% subspace x <- rbind(x, xi.transformed) } clids <- rep(1:k, each = nk) result <- list(x = x, cluster = clids) return(result) } # simulate data of 2 classes where class 1 consists of 2 subclasses simdata <- sim.orclus(k = 3, nk = 200, d = 15, l = 4, sd.cl = 0.05, sd.rest = 1, locshift = 1) x <- simdata$x y <- c(rep(1,400), rep(2,200)) res <- orclass(x, y, k = 3, l = 4, k0 = 15, a = 0.75) res # compare results table(res$predict.train$class, y) ```

orclass function