Explore a 21-minute conference talk on adapting circular coordinate representation for high-dimensional datasets using generalized penalty functions in Topological Data Analysis. Delve into dimension reduction techniques, topological concepts, and the application of persistent cohomology for data visualization on a torus. Learn how this approach accommodates sparsity while preserving topological structures, supported by simulation experiments and real data analysis. Examine the two-loop example revisited and a high-dimensional example, based on joint research with Alice Pantania, Jisu Kim, and Mikael Vejdemo-Johansson.