multiplier of support vector v and rf,v is the normalized value of feature f in support vector v (37). For the compatibility of features measured in different units, feature values are normalized in SVMs since SVMlight (38) and similar implementations limit feature values to the [0,1] interval. In constrained optimization, we standardize feature values to zero mean and unit SD. Standardization is less sensitive to a few outliers than the above normalization. For nonlinear SVMs, the effect of leaving out a feature on the objective function is more informative than the weight itself (39). This justiﬁes the computationally much more intensive recursive feature elimination (RFE) (33) method. Basically, in every iteration, a leave-one-out procedure is performed for each for the surviving features. The feature with the smallest effect on the objective function is removed. Validation Ten independent cross-validation experiments were used. In each experiment, the Novartis data were divided into a training set and a test set of equal size using a random number generator. siRNAs with 16 or more identities were eliminated. Blind tests were performed using a large enough dataset (either the Novartis or the Dharmacon data) for training and any other set for testing. RESULTS Predictions with 92.3% accuracy were achieved by SVMs with a polynomial kernel using WFE (28) in 10· cross- validation experiments (Figures 2 and 3). This accuracy is deﬁned as 100 minus the average percentage difference bet- ween predicted and observed knockdown activities. SVMs with Gaussian radial basis function or linear kernel provided for less accurate predictions than the polynomial kernel. BC between <60% and >70% active siRNAs was 94% accurate. Here we set the parameter l to 0.35 to reduce false positives. The subsequent MVR on the >70% active molecules is 95% accurate. Altogether, the BC-MVR combination predicted 89% of the >90% active siRNAs with a 12% false-positive rate. Regressing 19mers [from the Dharmacon (3), Holen’s (15) and Sætrom’s (17) sets] by any method trained on 21mers with deoxynucleotide overhangs in the Novartis set (1) or vice versa reduced the accuracy to 78% or lower (data not shown). Supplementing the missing two nucleotides did not lead to signiﬁcant improvement. BC and MVR automatically reduced the number of fea- tures at the ﬁrst iteration to 72 and 86, respectively. At ident- ical feature numbers, WFE led to quite unexpected results: basically similar features were selected by constrained optim- ization methods and linear SVMs. This observation increases the conﬁdence for ﬁnding the biological and thermodynamic signature for RNAi. As a rule, either identical or analogous features are selected by WFE over linear methods and by RFE using a polynomial kernel (Supplementary Table S1). Although WFE requires as many as 142 features to reach maximal accuracy compared to 68 features with RFE/polynomial kernel, 30 features are shared between these two sets. More importantly, several remaining features form analogous combinations (Figure 4). As an example, the selection against AAA starting at 18 is Nucleic Acids Research, 2007, Vol. 35, No. 2 437 Figure 2. The accuracy of SVM using different kernels and constrained optimization methods as functions of the number of features. Results of 10· cross-validation experiments (see Materials and Methods) are shown. Note that constrained optimization eliminated all but 72 features in the first iteration. Figure 3. Observed versus predicted activities in the Novartis dataset (1). Predictions were performed by the polynomial kernel SVM using 142 features shown on Supplementary Table 1. expressed in WFE by selection against AA at positions 18 and 19. Analogously, RFE indicates selection against A at 18 and AA at 19. Another example is the negative preference for CC at 12, which is expressed in RFE by that single fea- ture. However, WFE uses two features, AC at 11 and CC at 13, to the same effect. Yet another example is disfavoring C at 9 and CC at 10 in RFE, which is expressed by selection against AC at 8 and CC at 8, 9 and 10 in WFE. As a more complex example, the global G + C content is selected by the polynomial kernels used in RFE, whereas WFE chooses a wide-array of local mono- and dinucleotide features that are clearly related to the global G + C content. We postulated that the features selected by WFE account for