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tokens: g is a binary loss function and s j the scorefor learner j . The predicted class for x 0 is associated with the index k for which the vector Δ is minimal. Appendix C Description of classification algorithms: SVM – Ensemble methods Support-machine vectors The SVM method classifies the data by finding the best hyperplane separating the datapoints of one class from those of another category. Given a training set of M datapoints , where x i refers to the P-dimensional feature vector and y i the associated label that indicates whether the datapoint belongs to the positive class ( y i = +1) or the negative class ( y i = −1), the objective of SVM is to separate the data into distinct classes using a separating rule in form of a parametrized function f ( x ). For linearly separable data, the equation of the hyperplane is: where the scalar product w . x is equivalentto w ⊤ x . An infinity of hyperplanes verify Eq. ( C.1 ), but only one hyperplane maximizing the margins between the observationsand the hyperplane exists. This optimal hyperplane verify: To find the“best” linear hyperplane minimizing the margins , the SVM algorithm consists in solving a quadratic problem: For non-linearly separable data, the use of a kernel φ trick enables to map the distribution of the datapoints x into a projected space where φ ( x ) can be linearly separable, and defines, in the same approach as in Eq. ( C.2 ), a quadratic problem: where f ( x ) = f W , B ( x ) = W . φ ( x ) + B = 0. The selection of an adequate kernel K is determined by a list of criteria. By definition, a kernel must be symmetric, definite positive, square integrable and satisfy: Among commonly used kernels: Linear: K ( x i , x j ) = x i . x j Power: Gaussian (rbf): Further details about the SVMs are available in Vapnik (2000) and Cristianini Shawe-Taylor (2000) . C.2: Ensemble classifiers The principle of ensemble methodology is to combine a set of predictions from different learners in order to improve the accuracy of a single learner. Among the ensemble methods, two distinct approaches are identified: 1. Averaging methods: Bagging/ Random forests... 2. Boosting methods: AdaBoost/GentleBoost/RSBoost/... – AdaBoost AdaBoost, known also as “Adaptive Boosting” refers to a specific algorithm of boosted classifier defined as the sum of individual predictions from T weak learners. The algorithm aims to minimize the (weighted) classification error at each iteration: where: x i is the feature vector of the i th observation. y i is the true label of the i th observation. h t is the prediction of learner t . 1 is the indicator function. is the weight of the i th observation at step t . t the iteration step from 1 to T . At the first iteration, the weights are initialized (e.g., ) and the weak learner h t is obtained by minimizing the error ε t . For the next iteration, the weights of the learner ( t + 1) are adjusted according to the performance of the previous one ( t ): whether increase for misclassified