143 citations · 581 across the 51 of their papers we have counts for
9 papers · 1 filter
Robust Hierarchical Clustering for Directed Networks: An Axiomatic Approach
Gunnar Carlsson, Facundo Mémoli, Santiago Segarra
We provide a complete taxonomic characterization of robust hierarchical clustering methods for directed networks following an axiomatic approach. We begin by introducing three prac…
Topological Deep Learning
Ephy R. Love, Benjamin Filippenko, Vasileios Maroulas +1
This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image…
A Topology Layer for Machine Learning
Rickard Brüel-Gabrielsson, Bradley J. Nelson, Anjan Dwaraknath +3
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topolog…
Topological Approaches to Deep Learning
Gunnar Carlsson, Rickard Brüel Gabrielsson
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this u…
Excisive Hierarchical Clustering Methods for Network Data
Gunnar Carlsson, Facundo Mémoli, Alejandro Ribeiro +1
We introduce two practical properties of hierarchical clustering methods for (possibly asymmetric) network data: excisiveness and linear scale preservation. The latter enforces imp…
Admissible Hierarchical Clustering Methods and Algorithms for Asymmetric Networks
Gunnar Carlsson, Facundo Mémoli, Alejandro Ribeiro +1
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms…