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Found 6 papers, 4 papers with code
Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures
Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space.
Toroidal Coordinates: Decorrelating Circular Coordinates With Lattice Reduction
The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a $1$-dimensional hole in the data; the output is a map from the data into the circle that captures this hole, and that is of minimum energy in a suitable sense.
FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms.
Stable and consistent density-based clustering via multiparameter persistence
However, we prove that degree-Rips, as a multiparameter object, is stable, and we propose an alternative approach for taking slices of degree-Rips, which yields a one-parameter hierarchical clustering algorithm with better stability properties.
Visualization tools for parameter selection in cluster analysis
We propose an algorithm, HPREF (Hierarchical Partitioning by Repeated Features), that produces a hierarchical partition of a set of clusterings of a fixed dataset, such as sets of clusterings produced by running a clustering algorithm with a range of parameters.
Localization in Homotopy Type Theory
Our main result is that for a pointed, simply connected type $X$, the natural map $X \to X_{(p)}$ induces algebraic localizations on all homotopy groups.
Algebraic Topology Category Theory 55P60 (Primary), 18E35, 03B15 (Secondary)
