Uniform TitleStatistical strategies for scaling and weighting variables for cluster analysis
NameMaloor, Srinivas P. (author), Madigan, David (chair), Orfanidis, Sophocles (internal member), Wilder, Joseph (internal member), Kettenring, Jon (outside member), Gnanadesikan, Ramanathan (outside member), Rutgers University, Graduate School - New Brunswick,
SubjectElectrical and Computer Engineering,
DescriptionCluster analysis (CA) is a generic name for an array of quantitative methods, the applications of which are found in numerous fields ranging from astronomy and biology to finance and psychology. Though the intuitive idea of clustering is clear enough, the details of actually carrying out such an analysis entail many unresolved conceptual problems. Multivariate data, often poses a problem, in that the variables are not commensurate. Since the outcome of a CA is sensitive to the scales of measurement of the input data, many practitioners resort to standardizing the data prior to the analysis. Hence, the scaling of such multivariate data prior to CA is important as a preprocessing step. Autoscaling, is one such naive approach. Although it is a widely used procedure to standardize variables in some major point and click statistical software packages, it ignores the inherent cluster structure and actually proves counterproductive.
This dissertation is broadly divided into two parts - Univariate and Multivariate strategies. The first part addresses some univariate scaling and weighting approaches. In an attempt to put all variables on the same footing, we propose some intuitive strategies which we call equalizers. In addition, we consider letting the data suggest weights or highlighters that emphasize those variables with most promise for revealing the latent cluster structure. The methods vary in degree of complexity from simple weights based on order statistics to more complicated iterative ones. The results indicate that, in a variety of chosen simulated data as well as real data sets, the new methods are much better than the most popular method, autoscaling. Although these strategies are computationally appealing, they are at best suboptimal in their ability to unearth the latent clusters embedded in the multivariate structure of the data. Hence, the next part of this dissertation is devoted to multivariate scaling and weighting approaches. We perform a systematic study of the characteristics of a multivariate equalizer in both the null-cluster scenario and for a variety of cluster structures. In addition, we present a multivariate approach to perform variable highlighting that is validated by results from many simulated data sets as well as some real data sets. Taken together, our results indicate that simple and intuitive strategies to preprocess data sets render them amenable to superior cluster recovery.
NoteIncludes bibliographical references (p. 149-154).
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.