In order to perform complex actions in human environments, an autonomous robot needs the ability to understand the environment, that is, to gather and maintain spatial knowledge. Topological map is commonly used for representing large scale, global maps such as floor plans. Although much work has been done in topological map extraction, we have found little previous work on the problem of learning the topological map using a probabilistic model. Learning a topological map means learning the structure of the large-scale space and dependency between places, for example, how the evidence of a group of places influence the attributes of other places. This is an important step towards planning complex actions in the environment. In this thesis, we consider the problem of using probabilistic deep learning model to learn the topological map, which is essentially a sparse undirected graph where nodes represent places annotated with their semantic attributes (e.g. place category). We propose to use a novel probabilistic deep model, Sum-Product Networks (SPNs), due to their unique properties. We present two methods for learning topological maps using SPNs: the place grid method and the template-based method. We contribute an algorithm that builds SPNs for graphs using template models. Our experiments evaluate the ability of our models to enable robots to infer semantic attributes and detect maps with novel semantic attribute arrangements. Our results demonstrate their understanding of the topological map structure and spatial relations between places.
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