Learning from geometrical data

The class of geometrical data is an interesting class as one encounters them in real world applications, e.g., the representation of images, geographic information systems, traffic networks, etc. Despite the interest in this type of data, there has been no in-depth study of the theory of learning related to geometrical data. In this presentation, we will look closer to two subtasks in this area: Firstly, we present a number of learnability results for plane and planar graphs and we list a number of important prediction applications in the context of applications such as image recognition and spatial reasoning. Secondly, we take first steps towards analyzing the learnability tasks when considering projections of solid objects. In particular we consider the learning tasks where the input is a set of random generated orthogonal projections of polygons. We examine unique reconstructability of the projected model and present probably approximately correct techniques to learn the model. Finally we outline the future research needed to acquire a good understanding of these tasks, as well as possible solution methods.This presentation was given as part of a DTAI-seminar at the KU Leuvenstatus: publishe