Abstracts Category : Other

A bootstrap procedure for unsupervised classificationbased on variable and observation resampling

by Junhong Liu

In this thesis, we first investigate theperformance of bagged sparse 2-means clustering using aconventional bagging procedure. We next propose a cross baggingprocedure, which bootstraps the variables and observationssimultaneously, for sparse unsupervised classification problems.Formulated under a general framework, the procedure admits avariety of plugged-in classifiers, which can be determined case bycase. Our procedure comprises two main stages. The main goal in thefirst stage is to collect class probabilities and variableimportance. Another round of modified bagging is implemented in thefollow-up stage, aiming to re-classify the original learning set sothat the final partition is more accurate than that obtained by asingle-round bagging. We illustrate the potential applicability ofcross bagging by studying its behavior when sparse 2-meansclustering is taken to be the sparse unsupervised classifier andk-nearest-neighbor classifier is taken as the supervisedclassifier. Several simulations are reported to demonstrate theperformances of cross bagged sparse 2-means clustering, which arecompared with those of sparse 2-means clustering and its baggedversion. The results show that, under the aforementioned setting,cross bagged sparse 2-means clustering approximates Bayes rule thebest when n is greater or close to p. However, this conclusion maynot be true if n is much smaller than p. published_or_final_version Statistics and Actuarial Science Master Master of Philosophy