413 citations · 934 across the 23 of their papers we have counts for
26 papers
ALBATROSS: Cheap Filtration Based Geometry via Stochastic Sub-Sampling
Andrew J. Stier, Naichen Shi, Raed Al Kontar +2
Topological data analysis (TDA) detects geometric structure in biological data. However, many TDA algorithms are memory intensive and impractical for massive datasets. Here, we int…
Computing homology of -complexes from their quotients
Christine Escher, Chad Giusti, Chung-Ping Lai
In this paper, we investigate the question of how one can recover the homology of a simplicial complex equipped with a regular action of a finite group from the structure o…
Eulerian magnitude homology: subgraph structure and random graphs
Chad Giusti, Giuliamaria Menara
In this paper we explore the connection between the ranks of the magnitude homology groups of a graph and the structure of its subgraphs. To this end, we introduce variants of magn…
Persistent Extension and Analogous Bars: Data-Induced Relations Between Persistence Barcodes
Iris H. R. Yoon, Robert Ghrist, Chad Giusti
A central challenge in topological data analysis is the interpretation of barcodes. The classical algebraic-topological approach to interpreting homology classes is to build maps t…
A Topological Approach to Mapping Space Signatures
Chad Giusti, Darrick Lee, Vidit Nanda +1
A common approach for describing classes of functions and probability measures on a topological space is to construct a suitable map from into a vec…
U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology
Haibin Hang, Chad Giusti, Lori Ziegelmeier +1
Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological -- and indeed, linear -- algebra. However, matrices in…