On the Importance of Looking at the Manifold

Abstract

Data typically represented in regular domains, such as images, can have a higher level of relational information, either between data samples or even relations within samples. With this perspective our data points can be enriched by explicitly accounting for this connectivity. We analyze various approaches for unsupervised representation learning and investigate the importance of considering topological information. We show that each of the representations learned by these models may have critical importance for further downstream tasks, and that accounting for the topological features can improve the modeling capabilities for certain problems.

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