A topological approach for semi-supervised learning

Nowadays, Machine Learning and Deep Learning methods have become the state-of-the-art approach to solve data classification tasks. In order to use those methods, it is necessary to acquire and label a considerable amount of data; however, this is not straightforward in some fields, since data annotation is time consuming and might require expert knowledge. This challenge can be tackled by means of semi-supervised learning methods that take advantage of both labelled and unlabelled data. In this work, we present new semi-supervised learning methods based on techniques from Topological Data Analysis (TDA). In particular, we have created two semi-supervised learning methods following two topological approaches. In the former, we have used a homological approach that consists in studying the persistence diagrams associated with the data using the bottleneck and Wasserstein distances. In the latter, we have considered the connectivity of the data. In addition, we have carried out a thorough analysis of the developed methods using 9 tabular datasets with low and high dimensionality. The results show that the developed semi-supervised methods outperform the results obtained with models trained with only manually labelled data, and are an alternative to other classical semi-supervised learning algorithms.