mch: Maximum Clusteriability Hyperplane
In DavidHofmeyr/PPCI: Projection Pursuit for Cluster Identification

Description Usage Arguments Value References Examples

Finds maximum clusterability hyperplane(s) for clustering.

1	mch(X, v0, minsize, verb, labels, maxit, ftol)

`X`	a numeric matrix (num_data x num_dimensions); the dataset to be clustered.
`v0`	(optional) initial projection direction(s). a matrix with ncol(X) rows. each column of v0 is used as an initialisation for projection pursuit. if omitted then a single initialisation is used; the vector joining the cluster means from a 2-means solution.
`minsize`	(optional) the minimum cluster size allowable. if omitted then minsize = 1.
`verb`	(optional) verbosity level of optimisation procedure. verb==0 produces no output. verb==1 produces plots illustrating the progress of projection pursuit via plots of the projected data. verb==2 adds to these plots additional information about the progress. verb==3 creates a folder in working directory and stores all plots for verb==2. if omitted then verb==0.
`labels`	(optional) vector of class labels. not used in the actual clustering procedure. only used for illustrative purposes for values of verb>0.
`maxit`	(optional) maximum number of iterations in optimisation. if omitted then maxit=50.
`ftol`	(optional) tolerance level for convergence of optimisation, based on relative function value improvements. if omitted then ftol = 1e-8.

a named list with class ppci_hyperplane_solution with the following components

`$cluster`	cluster assignment vector.
`$v`	the optimal projection vector.
`$b`	the value of b making H(v, b) the minimum normalised cut hyperplane.
`$fitted`	data projected into two dimensional subspace defined by $v and the principal component in the null space of $v.
`$data`	the input data matrix.
`$fval`	the variance ratio clusterability across H(v, b).
`$method`	=="MCDC".
`$params`	list of parameters used to find H(v, b).
`$alternatives`	an unnamed list. If more than one initilisation is considered, the alternatives to the best are stored in this field.

Hofmeyr, D., Pavlidis, N. (2015) Maximum Clusterability Divisive Clustering. Computational Intelligence, 2015 IEEE Symposium Series on, pp. 780–786.

## generate dataset with elongated clusters for which variance ratio in
## both dimensions is misleading for clustering
set.seed(1)
S <- matrix(c(1, .7, .7, 1), 2, 2)
X <- matrix(rnorm(2000), ncol = 2)%*%S
X[,1] <- X[,1] + rep(c(.8, -.8), each = 500)
X[,2] <- X[,2] + rep(c(-.8, .8), each = 500)

## find the optimal variance ratio hyperplane solution
sol <- mch(X)

## visualise the solution
plot(X, col = sol$cluster)