Multivariate decision trees through margin maximization principle and topological organization of clusters

This thesis explores two different ways of inducing multivariate decision tree classifiers, in order to take into account the correlation between the attributes when defining the splits in the tree nodes. The first part of the thesis proposes to use the margin maximization principle in order to create efficient multivariate splits at each node of an ensemble of decision trees. The objective of this method, called support vector trees forest (SVTF), is to assess the performance of multivariate trees forest on multicategory and/or high dimensional classification problems. A new decision scheme is also presented as a substitute to the common averaging schemes (i.e. like majority voting), which is used to infer a unique decision vote from the outputs of every tree. In our proposal, the trees decisions are weighted according to the confidence of each tree towards its own output decision. To do so, fuzzy logic principles are exploited, allowing to compute a confidence score in each node based on where the new data sample fall from the decision boundaries in the SVM features space. The second part of the thesis focuses on visual events from video surveillance sequences, which is a specific case of topologically structured data. In this context, our goal is to conceive an automated method, flexible and accurate, for recognizing the visual events. This is done by defining a three stages system. The first one aims at defining and building a set of relevant features describing the shape and movements of the foreground objects in the scene. To this aim, we introduce new motion descriptors based on space-time volumes. Second, an unsupervised learning-based method is used to cluster the objects, thereby defining a set of coarse to fine local patterns of features, representing primitive events in the video sequences. Finally, events are modeled as a spatio-temporal organization of patterns based on an ensemble of randomized trees. In particular, we want this classifier to discover the temporal and causal correlations between the most discriminative patterns.(FSA 3) -- UCL, 201