Generative Manifold Learning for the Exploration of Partially Labeled Data

In many real-world application problems, the availability of data labels for supervised learning is rather limited and incompletely labeled datasets are commonplace in some of the currently most active areas of research. A manifold learning model, namely Generative Topographic Mapping (GTM), is the basis of the methods developed in the thesis reported in this paper. A variant of GTM that uses a graph approximation to the geodesic metric is first defined. This model is capable of representing data of convoluted geometries. The standard GTM is here modified to prioritize neighbourhood relationships along the generated manifold. This is accomplished by penalizing the possible divergences between the Euclidean distances from the data points to the model prototypes and the corresponding geodesic distances along the manifold. The resulting Geodesic GTM (Geo-GTM) model is shown to improve the continuity and trustworthiness of the representation generated by the model, as well as to behave robustly in the presence of noise. We then proceed to define a novel semi-supervised model, SS-Geo-GTM, that extends Geo-GTM to deal with semi-supervised problems. In SS-Geo-GTM, the model prototypes obtained from Geo-GTM are linked by the nearest neighbour to the data manifold. The resulting proximity graph is used as the basis for a class label propagation algorithm. The performance of SS-Geo-GTM is experimentally assessed via accuracy and Matthews correlation coefficient, comparing positively with an Euclidean distance-based counterpart and the alternative Laplacian Eigenmaps and semi-supervised Gaussian mixture models.