HierarchicalSparseCluster.permute {sparcl} | R Documentation |
The tuning parameter controls the L1 bound on w, the feature weights. A permutation approach is used to select the tuning parameter.
HierarchicalSparseCluster.permute(x, nperms = 10, wbounds = NULL, dissimilarity=c("squared.distance", "absolute.value"),standardize.arrays=FALSE) ## S3 method for class 'HierarchicalSparseCluster.permute' plot(x,...) ## S3 method for class 'HierarchicalSparseCluster.permute' print(x,...)
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. |
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.
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. |
Daniela M. Witten and Robert Tibshirani
Witten and Tibshirani (2009) A framework for feature selection in clustering.
HierarchicalSparseCluster, KMeansSparseCluster, KMeansSparseCluster.permute
# 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)