Efficient Sparsification of Simplicial Complexes via Local Densities of States
SIAM Journal on Mathematics of Data Science, 2026
Simplicial complexes (SCs), a generalization of graph models for relational data that account for higher-order relations between data items, have become a popular abstraction for analyzing complex data using tools from topological data analysis or topological signal processing. However, the analysis of many real-world …
Cholesky-like Preconditioner for Hodge Laplacians via Heavy Collapsible Subcomplex
SIAM Journal on Matrix Analysis and Applications, 2024
Techniques based on $k$-th order Hodge Laplacian operators $L_k$ are widely used to describe the topology as well as the governing dynamics of high-order systems modeled as simplicial complexes. In all of them, it is required to solve a number of least square problems with $L_k$ as coefficient matrix, for example in …
Quantifying the structural stability of simplicial homology
Journal of Scientific Computing, vol. 97, 2023
The homology groups of a simplicial complex reveal fundamental properties of the topology of the data or the system and the notion of topological stability naturally poses an important yet not fully investigated question. In the current work, we study the stability in terms of the smallest perturbation sufficient to …