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Statistical strategies for scaling and weighting variables for cluster analysis
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Statistical strategies for scaling and weighting variables for cluster analysis
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Maloor
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Srinivas P.
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Srinivas P. Maloor
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Madigan
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David
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Advisory Committee
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David Madigan
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Orfanidis
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Sophocles Orfanidis
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Wilder
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Joseph
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Joseph Wilder
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Kettenring
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Jon
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Jon Kettenring
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outside member
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Gnanadesikan
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Ramanathan
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Advisory Committee
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Ramanathan Gnanadesikan
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Rutgers University
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Graduate School - New Brunswick
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theses
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2007
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2007
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English
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electronic
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xvii, 156 pages
Abstract
Cluster 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.
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.
Note
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Ph.D.
Note
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Includes bibliographical references (p. 149-154).
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Electrical and Computer Engineering
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Cluster analysis
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Multivariate analysis
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Graduate School - New Brunswick Electronic Theses and Dissertations
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16739
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doi:10.7282/T3BZ66D0
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ETD doctoral
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Copyright protected
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Open
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Srinivas Maloor
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Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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