no code implementations • 30 May 2024 • Shiv Bhatia, Yueqi Cao, Paul Lezeau, Anthea Monod
Our contributions are threefold: we provide a novel tropical geometric approach to selecting sampling domains among linear regions; an algebraic result allowing for a guided restriction of the sampling domain for network architectures with symmetries; and an open source library to analyze neural networks as tropical Puiseux rational maps.
1 code implementation • 18 Oct 2022 • Yueqi Cao, Prudence Leung, Anthea Monod
Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has recently gained much popularity from its myriad successful applications to many domains.
1 code implementation • 19 Apr 2022 • Yueqi Cao, Anthea Monod
We show that the mean of the persistence diagrams of subsamples -- taken as a mean persistence measure computed from the subsamples -- is a valid approximation of the true persistent homology of the larger dataset.
1 code implementation • 4 Apr 2021 • Yueqi Cao, Athanasios Vlontzos, Luca Schmidtke, Bernhard Kainz, Anthea Monod
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in a hierarchy-preserving manner using a variety of metrics.
1 code implementation • 26 May 2019 • Yueqi Cao, Didong Li, Huafei Sun, Amir H Assadi, Shiqiang Zhang
In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space.