L2-norm multiple kernel learning and its application to biomedical data fusion.

BACKGROUND: This paper introduces the notion of optimizing different norms in the dual problem of support vector machines with multiple kernels. The selection of norms yields different extensions of multiple kernel learning (MKL) such as L(infinity), L1, and L2 MKL. In particular, L2 MKL is a novel method that leads to non-sparse optimal kernel coefficients, which is different from the sparse kernel coefficients optimized by the existing L(infinity) MKL method. In real biomedical applications, L2 MKL may have more advantages over sparse integration method for thoroughly combining complementary information in heterogeneous data sources. RESULTS: We provide a theoretical analysis of the relationship between the L2 optimization of kernels in the dual problem with the L2 coefficient regularization in the primal problem. Understanding the dual L2 problem grants a unified view on MKL and enables us to extend the L2 method to a wide range of machine learning problems. We implement L2 MKL for ranking and classification problems and compare its performance with the sparse L(infinity) and the averaging L1 MKL methods. The experiments are carried out on six real biomedical data sets and two large scale UCI data sets. L2 MKL yields better performance on most of the benchmark data sets. In particular, we propose a novel L2 MKL least squares support vector machine (LSSVM) algorithm, which is shown to be an efficient and promising classifier for large scale data sets processing. CONCLUSIONS: This paper extends the statistical framework of genomic data fusion based on MKL. Allowing non-sparse weights on the data sources is an attractive option in settings where we believe most data sources to be relevant to the problem at hand and want to avoid a "winner-takes-all" effect seen in L(infinity) MKL, which can be detrimental to the performance in prospective studies. The notion of optimizing L2 kernels can be straightforwardly extended to ranking, classification, regression, and clustering algorithms. To tackle the computational burden of MKL, this paper proposes several novel LSSVM based MKL algorithms. Systematic comparison on real data sets shows that LSSVM MKL has comparable performance as the conventional SVM MKL algorithms. Moreover, large scale numerical experiments indicate that when cast as semi-infinite programming, LSSVM MKL can be solved more efficiently than SVM MKL. AVAILABILITY: The MATLAB code of algorithms implemented in this paper is downloadable from http://homes.esat.kuleuven.be/~sistawww/bioi/syu/l2lssvm.html.

A kernel-based integration of genome-wide data for clinical decision support.

BACKGROUND: Although microarray technology allows the investigation of the transcriptomic make-up of a tumor in one experiment, the transcriptome does not completely reflect the underlying biology due to alternative splicing, post-translational modifications, as well as the influence of pathological conditions (for example, cancer) on transcription and translation. This increases the importance of fusing more than one source of genome-wide data, such as the genome, transcriptome, proteome, and epigenome. The current increase in the amount of available omics data emphasizes the need for a methodological integration framework. METHODS: We propose a kernel-based approach for clinical decision support in which many genome-wide data sources are combined. Integration occurs within the patient domain at the level of kernel matrices before building the classifier. As supervised classification algorithm, a weighted least squares support vector machine is used. We apply this framework to two cancer cases, namely, a rectal cancer data set containing microarray and proteomics data and a prostate cancer data set containing microarray and genomics data. For both cases, multiple outcomes are predicted. RESULTS: For the rectal cancer outcomes, the highest leave-one-out (LOO) areas under the receiver operating characteristic curves (AUC) were obtained when combining microarray and proteomics data gathered during therapy and ranged from 0.927 to 0.987. For prostate cancer, all four outcomes had a better LOO AUC when combining microarray and genomics data, ranging from 0.786 for recurrence to 0.987 for metastasis. CONCLUSIONS: For both cancer sites the prediction of all outcomes improved when more than one genome-wide data set was considered. This suggests that integrating multiple genome-wide data sources increases the predictive performance of clinical decision support models. This emphasizes the need for comprehensive multi-modal data. We acknowledge that, in a first phase, this will substantially increase costs; however, this is a necessary investment to ultimately obtain cost-efficient models usable in patient tailored therapy.

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.