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.