Abstract: Persistent homology has been gaining traction as a tool for studying patterns in real-world data-sets. We have sought to understand a slight variant on the typical computation of homology of a metric space. This exposition will survey that work. We include early findings from computations on samples from common spaces (the circle, the disc, and the square), one conjecture and one lemma regarding 1-dimensional cycles, and an application to simulated data.
Speaker’s Bio: Dr. Brett Jefferson has expertise in cognitive modelling and topological data analysis methods. As a perception modeler, Dr. Jefferson takes a systems approach to accounting for visual and perceptual processes. Resulting, dimensions of visual perception previously believed to be independent now have evidence that suggest large-scale dependencies. In addition to work in perception, the relatively new analysis techniques in TDA provide a robust approach to capturing qualitative trends in data. From cyclical patterns in numerical data to assessing consistency throughout a corpora, topological methods are proving useful to extending pattern recognition beyond classic statistical approaches. Dr. Jefferson is interested in comparing the methodologies across domains and datasets to discover new insights offered by the combination of tools.
Last Updated: February 15, 2021 - 7:57 am