Visualisation of structured data through generative probabilistic modeling

This thesis is concerned with the construction of topographic maps of structured data. A probabilistic generative model-based approach is taken, inspired by the GTM algorithm. Depending on the data at hand, the form of a probabilistic generative model is specified that is appropriate for modelling the probability density of the data. A mixture of such models is formulated which is topographically constrained on a low-dimensional latent space. By constrained, we mean that each point in the latent space determines the parameters of one model via a smooth non-linear mapping; by topographic, we mean that neighbouring latent points generate similar parameters which address statistically similar models. The constrained mixture is trained to model the density of the structured data. A map is constructed by projecting each data item to a location on the latent space where the local latent points are associated with models that express a high probability of having generated the particular data item. We present three formulations for constructing topographic maps of structured data. Two of them are concerned with tree-structured data and employ hidden Markov trees and Markov trees as probabilistic generative models. The third approach is concerned with astronomical light curves from eclipsing binary stars and employs a physical-based model. The formulation of the all three models is accompanied by experiments and analysis of the resulting topographic maps. To my parents Mαρία and Σταμάτης