Persistent homology, a technique from computational topology, has recently shown strong
empirical performance in the context of graph classification. Being able to capture long …

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold
of low intrinsic dimension, is a staple of modern machine learning research. However, recent …

There is a growing body of work that leverages features extracted via topological data
analysis to train machine learning models. While this field, sometimes known as topological …

The presence of some amino acid mutations in the amino acid sequence that determines a
protein's structure can significantly affect that 3D structure and its biological function …

In general, the critical points of the distance function $ d_ {\mathsf {M}} $ to a compact
submanifold $\mathsf {M}\subset\mathbb {R}^ D $ can be poorly behaved. In this article, we …

In this paper we present a novel method, Knowledge Persistence (), for faster evaluation of
Knowledge Graph (KG) completion approaches. Current ranking-based evaluation is …

Building outline extraction from segmented point clouds is a critical step of building footprint
generation. Existing methods for this task are often based on the convex hull and α-shape …

We consider the problem of learning the dynamics in the topology of time-evolving point
clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such …

Abstract As Artificial Intelligent (AI) technologies become ubiquitous, humans will have to
contend with many benefits and disadvantages of these advancements. Particularly, in …

Persistent homology is a popular computational tool for detecting non-trivial topology of
point clouds, such as the presence of loops or voids. However, many real-world datasets …