Semi-Supervised Machine Learning: a Homological Approach

Using techniques of Symbolic Computation and Computer Algebra, we apply the concept of persistent homology to obtain a new semi-supervised learning method. Machine Learning and Deep Learning methods have become the state-of-the-art approach for solving 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 may 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 our team we have applied this Machine Learning paradigm in various applied projects (e.g.