M@CBETH: a microarray classification benchmarking tool.

Microarray classification can be useful to support clinical management decisions for individual patients in, for example, oncology. However, comparing classifiers and selecting the best for each microarray dataset can be a tedious and non-straightforward task. The M@CBETH (a MicroArray Classification BEnchmarking Tool on a Host server) web service offers the microarray community a simple tool for making optimal two-class predictions. M@CBETH aims at finding the best prediction among different classification methods by using randomizations of the benchmarking dataset. The M@CBETH web service intends to introduce an optimal use of clinical microarray data classification.

Systematic benchmarking of microarray data classification: assessing the role of non-linearity and dimensionality reduction.

MOTIVATION: Microarrays are capable of determining the expression levels of thousands of genes simultaneously. In combination with classification methods, this technology can be useful to support clinical management decisions for individual patients, e.g. in oncology. The aim of this paper is to systematically benchmark the role of non-linear versus linear techniques and dimensionality reduction methods. RESULTS: A systematic benchmarking study is performed by comparing linear versions of standard classification and dimensionality reduction techniques with their non-linear versions based on non-linear kernel functions with a radial basis function (RBF) kernel. A total of 9 binary cancer classification problems, derived from 7 publicly available microarray datasets, and 20 randomizations of each problem are examined. CONCLUSIONS: Three main conclusions can be formulated based on the performances on independent test sets. (1) When performing classification with least squares support vector machines (LS-SVMs) (without dimensionality reduction), RBF kernels can be used without risking too much overfitting. The results obtained with well-tuned RBF kernels are never worse and sometimes even statistically significantly better compared to results obtained with a linear kernel in terms of test set receiver operating characteristic and test set accuracy performances. (2) Even for classification with linear classifiers like LS-SVM with linear kernel, using regularization is very important. (3) When performing kernel principal component analysis (kernel PCA) before classification, using an RBF kernel for kernel PCA tends to result in overfitting, especially when using supervised feature selection. It has been observed that an optimal selection of a large number of features is often an indication for overfitting. Kernel PCA with linear kernel gives better results.

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.