38 citations · 199 across the 44 of their papers we have counts for
6 papers · 1 filter
Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic Structures
Mustafa Hajij, Ghada Zamzmi, Matthew Dawson +1
One of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from…
Cocycle Invariants and Oriented Singular Knots
Jose Ceniceros, Indu R. Churchill, Mohamed Elhamdadi +1
We extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called \emph{oriented singquandles} and assigning weight functions at both r…
Cell Complex Neural Networks
Mustafa Hajij, Kyle Istvan, Ghada Zamzmi
Cell complexes are topological spaces constructed from simple blocks called cells. They generalize graphs, simplicial complexes, and polyhedral complexes that form important domain…
A Topological Framework for Deep Learning
Mustafa Hajij, Kyle Istvan
We utilize classical facts from topology to show that the classification problem in machine learning is always solvable under very mild conditions. Furthermore, we show that a soft…
PageRank and The K-Means Clustering Algorithm
Mustafa Hajij, Eyad Said, Robert Todd
We utilize the PageRank vector to generalize the -means clustering algorithm to directed and undirected graphs. We demonstrate that PageRank and other centrality measures can be…
Fast and Scalable Complex Network Descriptor Using PageRank and Persistent Homology
Mustafa Hajij, Elizabeth Munch, Paul Rosen
The PageRank of a graph is a scalar function defined on the node set of the graph which encodes nodes centrality information of the graph. In this article, we use the PageRank func…