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Boulesteix, Anne-Laure (2005): Dimension reduction and Classification with High-Dimensional Microarray Data. Dissertation, LMU München: Faculty of Mathematics, Computer Science and Statistics
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Abstract

Usual microarray data sets include only a handful of observations, but several thousands of predictor variables. Transforming the high-dimensional predictor space to make classification (for instance cancer diagnosis) possible is a major challenge. This thesis deals with various dimension reduction approaches which can handle such data. Chapter 2 gives an introduction into classification with microarray data as well as an overview of a few specific problems such as variable selection and comparison of classification methods. In Chapter 3, I discuss a particular class of interaction structures in the classification framework: "emerging patterns". I propose a new and more general definition referring to underlying probabilities and present a new simple method which is based on the CART algorithm to find the corresponding empirical patterns in concrete data sets. In addition, the detected patterns can be used to define new variables for classification. Thus, I propose a simple scheme to use the patterns to improve the performance of classification procedures. I implemented the search algorithm as well as the classification procedure in the language R. Some of these programs are publicly available from my homepage. Chapter 4 deals with classical linear dimension reduction methods. In the context of binary classification with continuous predictors, I prove two properties concerning the connections between Partial Least Squares (PLS) dimension reduction, between-group PCA and between linear discriminant analysis and between-group PCA. PLS dimension reduction for classification is examined thoroughly in Chapter 5. The classification procedure consisting of PLS dimension reduction and linear discriminant analysis on the new components is compared favorably with some of the best state-of-the-art classification methods using nine real microarray cancer data sets. Moreover, I apply a boosting algorithm to this classification method, which is a novel approach. In addition, I suggest a simple procedure to choose the number of PLS components. At last, I examine the connection between PLS dimension reduction and variable selection and prove a property concerning the equivalence between a common univariate selection criterion and a variable selection approach based on the first PLS component.