sparcl (version 1.0.3)

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)
"plot"(x,...) 
"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="" objective="" function="" with="" tuning="" parameter="" s:="" i.e.="" $o(s)="sum_j" w_j="" sum_ii'="" d_ii'j="" u_ii'$.<="" p="">

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

  # 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)