Homology has been gaining traction as a tool for studying patterns in real-world datasets. During the past year, I have sought to understand a slight variant on the typical computation of homology of a metric space which we term antihomology. This exposition will survey that work. In section 2, I begin with findings from computations on samples from common spaces (the circle, the disc, and the square). Section 3 presents one conjecture and one lemma regarding 1-dimensional cycles on the circle with evenly space points and the circle with random sampling. In section 4, I applied antihomology to power grid datasets and compared results with more traditional data reduction techniques. Lastly, section 5 reveals the connection between antihomology and location covering problems.
Revised: August 20, 2018 |
Published: September 30, 2017