orclass {orclus}

Subspace clustering based local classification using ORCLUS.

Description

Function to perform local classification where the subclasses are concentrated in different subspaces of the data.

Usage

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.

Value

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.

Author(s)

Gero Szepannek

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.

See Also

predict.orclass, orclus, predict.orclus

Examples

# 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)