We present a method for binary on-line classification of triggered but temporally blurred events that are embedded in noisy time series in the context of on-line discrimination between left and right imaginary hand-movement. In particular the goal of the binary classification problem is to obtain the decision, as fast and as reliably as possible from the recorded EEG single trials. To provide a probabilistic decision at every time-point t the presented method gathers information from two distinct sequences of features across time. In order to incorporate decisions from prior time-points we suggest an appropriate weighting scheme, that emphasizes time instances, providing a higher discriminatory power between the instantaneous class distributions of each feature, where the discriminatory power is quantified in terms of the Bayes error of misclassification. The effectiveness of this procedure is verified by its successful application in the 3rd BCI competition. Disclosure of the data after the competition revealed this approach to be superior with single trial error rates as low as 10.7, 11.5 and 16.7% for the three different sub jects under study.

BACKGROUND: Support Vector Machines (SVMs)--using a variety of string kernels--have been successfully applied to biological sequence classification problems. While SVMs achieve high classification accuracy they lack interpretability. In many applications, it does not suffice that an algorithm just detects a biological signal in the sequence, but it should also provide means to interpret its solution in order to gain biological insight. RESULTS: We propose novel and efficient algorithms for solving the so-called Support Vector Multiple Kernel Learning problem. The developed techniques can be used to understand the obtained support vector decision function in order to extract biologically relevant knowledge about the sequence analysis problem at hand. We apply the proposed methods to the task of acceptor splice site prediction and to the problem of recognizing alternatively spliced exons. Our algorithms compute sparse weightings of substring locations, highlighting which parts of the sequence are important for discrimination. CONCLUSION: The proposed method is able to deal with thousands of examples while combining hundreds of kernels within reasonable time, and reliably identifies a few statistically significant positions.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for classification, leading to a convex quadratically constrained quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementations. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classification. Experimental results show that the proposed algorithm works for hundred thousands of examples or hundreds of kernels to be combined, and helps for automatic model selection, improving the interpretability of the learning result. In a second part we discuss general speed up mechanism for SVMs, especially when used with sparse feature maps as appear for string kernels, allowing us to train a string kernel SVM on a 10 million real-world splice data set from computational biology. We integrated multiple kernel learning in our machine learning toolbox SHOGUN for which the source code is publicly available at http://www.fml.tuebingen.mpg.de/raetsch/projects/shogun.

While classical kernel-based learning algorithms are based on a single kernel, in practice it is often desirable to use multiple kernels. Lankriet et al. (2004) considered conic combinations of kernel matrices for classi- fication, leading to a convex quadratically constraint quadratic program. We show that it can be rewritten as a semi-infinite linear program that can be efficiently solved by recycling the standard SVM implementa- tions. Moreover, we generalize the formulation and our method to a larger class of problems, including regression and one-class classifica- tion. Experimental results show that the proposed algorithm helps for automatic model selection, improving the interpretability of the learn- ing result and works for hundred thousands of examples or hundreds of kernels to be combined. f (x) = sign N Xi=1 αiyik(xi, x) + b! ,