Swap, Shift and Trim to Edge Collapse a Flag Filtration

Explore an algorithm for reducing flag (or clique) complex filtrations to accelerate persistent homology computations in this 44-minute lecture. Delve into the edge collapse technique introduced by Boissonnat and Pritam, which operates solely on the 1-skeleton of the filtration. Gain a clear and intuitive understanding of the algorithm's underlying principles, and discover various extensions, including a zigzag filtration simplification method. Examine experimental results to gain insights into the algorithm's behavior and performance. Learn how this approach can significantly enhance the efficiency of persistent homology calculations in applied algebraic topology.