Text S3.dvi

Supervised learning requires a training set on which the classifier’s parameters are learnt. An independent test set is used to evaluate its performance. For each test sample the classifier returns a vector that estimates the probability that the sample belongs to any of the classes under consideration, in our case edges and non-edges. We employ the random forest classifier [1], a state-of-the-art supervised learning approach which was recently successfully used for link prediction [2]. A random forest consists of a set of decision trees. Each node of a decision tree contains a simple test of the form Is the value of the ith dimension di lower than threshold ti?, and all leave nodes contain a deterministic class label (in our case: edge, non-edge). Given a test sample, all trees of the forest are traversed from their roots to one of their leaves. Finally, the sample arrives in one of the leaves that, in our case, classifies this sample as an edge or a non-edge sample. The number of trees voting for a certain class are counted and the percentage of trees classifying the test sample as an edge defines its prediction value. The random forest is built (learnt) on a given set of training samples. For each tree, the following procedure is repeated: We start with the root node that contains all samples. At each node, the feature that best splits the samples in the node is selected among a randomly chosen subset of size mtry of the P available features and an adequate threshold is found. Subsequently, the node is split and the process is recursively repeated for each of the resulting subsets until a pure subset with samples from only one class is produced. Here we build ntree = 500 decision trees. We learn based on P = 15 features and at each node of the decision trees, the number of features sampled for splitting is mtry = √ P .