sparcl (version 1.0.4)

HierarchicalSparseCluster.permute: Choose tuning parameter for sparse hierarchical clustering

Description

The tuning parameter controls the L1 bound on w, the feature weights. A permutation approach is used to select the tuning parameter.

Usage

HierarchicalSparseCluster.permute(x, nperms = 10, wbounds = NULL,
dissimilarity=c("squared.distance",
"absolute.value"),standardize.arrays=FALSE)
# S3 method for HierarchicalSparseCluster.permute
plot(x,...) 
# S3 method for HierarchicalSparseCluster.permute
print(x,...)

Arguments

x

A nxp data matrix, with n observations and p feaures.

nperms

The number of permutations to perform.

wbounds

The sequence of tuning parameters to consider. The tuning parameters are the L1 bound on w, the feature weights. If NULL, then a default sequence will be used. If non-null, should be greater than 1.

dissimilarity

How should dissimilarity be computed? Default is squared.distance.

standardize.arrays

Should the arrays first be standardized? Default is FALSE.

…

not used.

Value

gaps

The gap statistics obtained (one for each of the tuning parameters tried). If O(s) is the objective function evaluated at the tuning parameter s, and O*(s) is the same quantity but for the permuted data, then Gap(s)=log(O(s))-mean(log(O*(s))).

sdgaps

The standard deviation of log(O*(s)), for each value of the tuning parameter s.

nnonzerows

The number of features with non-zero weights, for each value of the tuning parameter.

wbounds

The tuning parameters considered.

bestw

The value of the tuning parameter corresponding to the highest gap statistic.

Details

Let $d_ii'j$ denote the dissimilarity between observations i and i' along feature j.

Sparse hierarchical clustering seeks a p-vector of weights w (one per feature) and a nxn matrix U that optimize $maximize_U,w sum_j w_j sum_ii' d_ii'j U_ii'$ subject to $||w||_2 <= 1, ||w||_1 <= s, w_j >= 0, sum_ii' U_ii'^2 <= 1$, where s is a value for the L1 bound on w. Let O(s) denote the objective function with tuning parameter s: i.e. $O(s)=sum_j w_j sum_ii' d_ii'j U_ii'$.

We permute the data as follows: within each feature, we permute the observations. Using the permuted data, we can run sparse hierarchical clustering with tuning parameter s, yielding the objective function O*(s). If we do this repeatedly we can get a number of O*(s) values.

Then, the Gap statistic is given by $Gap(s)=log(O(s))-mean(log(O*(s)))$. The optimal s is that which results in the highest Gap statistic. Or, we can choose the smallest s such that its Gap statistic is within $sd(log(O*(s)))$ of the largest Gap statistic.

References

Witten and Tibshirani (2009) A framework for feature selection in clustering.

See Also

HierarchicalSparseCluster, KMeansSparseCluster, KMeansSparseCluster.permute

Examples

# NOT RUN {
  # Generate 2-class data
  set.seed(1)
  x <- matrix(rnorm(100*50),ncol=50)
  y <- c(rep(1,50),rep(2,50))
  x[y==1,1:25] <- x[y==1,1:25]+2
  # Do tuning parameter selection for sparse hierarchical clustering
  perm.out <- HierarchicalSparseCluster.permute(x, wbounds=c(1.5,2:6),
nperms=5)
  print(perm.out)
  plot(perm.out)
  # Perform sparse hierarchical clustering
  sparsehc <- HierarchicalSparseCluster(dists=perm.out$dists, wbound=perm.out$bestw, 
method="complete")
  par(mfrow=c(1,2))
  plot(sparsehc)
  plot(sparsehc$hc, labels=rep("", length(y)))
  print(sparsehc)
  # Plot using knowledge of class labels in order to compare true class
  #   labels to clustering obtained
  par(mfrow=c(1,1))
  ColorDendrogram(sparsehc$hc,y=y,main="My Simulated
Data",branchlength=.007)
# }