Simplicial Regularization

Jose Gallego-Posada, Patrick Forré

Keywords: simplicial complex, regularization, mixup, fuzzy topology, umap

TL;DR: We propose a regularization framework based on the preservation of the simplicial complex structure of the data.

Abstract: Inspired by the fuzzy topological representation of a dataset employed in UMAP (McInnes et al., 2018), we propose a regularization principle for supervised learning based on the preservation of the simplicial complex structure of the data. We analyze the behavior of our proposal in contrast with the mixup (Zhang et al., 2018) framework on dimensionality reduction and classification tasks. Our experiments show how simplicial regularization induces more appropriate learning biases and alleviates some of the shortcomings of state-of-the art methods for regularization based on data augmentation.