The Generative Simplicial Complex to extract Betti numbers from unlabelled data

Analysis of multidimensional data is challenging. Topological invariants can be used to summarize essential features of such data sets. In this work, we propose to compute the Betti numbers from a generative model based on a simplicial complex learnt from the data. The algorithm called a Generative Simplicial Complex can extract topological features from multidimensional datasets with non-trivial underlying topological structure, and from a real data set. We compare it to the Witness Complex, a geometric technique based on nearest neighbors.