A Topological Approach for Semi-Supervised Learning

Anonymous

Keywords: Semi-Supervised learning, Persistence Diagrams, Structured data

TL;DR: A new TDA method for semi-supervised learning based on homological properties of data

Abstract: 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 a new semi-supervised learning method based on techniques from Topological Data Analysis. In particular, we have used a homological approach that consists in studying the persistence diagrams associated with data from binary classification tasks using the bottleneck and Wasserstein distances. In addition, we have carried out a thorough analysis of the developed method using 5 structured datasets. The results show that the semi-supervised method developed in this work outperforms both the results obtained with models trained with only manually labelled data, and those obtained with classical semi-supervised learning methods, improving the models up to a 16%.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2205.09617/code)