2016/02/19 by Paul Bendich, Bendich, Paul, Ellen Gasparovic +5
Computer Science · #Computational Geometry (cs.CG) #Data Visualization and Analytics #FOS: Computer and information sciences #Image Retrieval and Classification Techniques #Topological and Geometric Data Analysis #cs.CG
paper · pdf · doi:10.48550/arxiv.1602.06245
14 pages
openalex publication_date 2016/02/19 · arxiv created 2016/02/27 · arxiv updated 2016/03/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We propose a flexible and multi-scale method for organizing, visualizing, and understanding datasets sampled from or near stratified spaces. The first part of the algorithm produces a cover tree using adaptive thresholds based on a combination of multi-scale local principal component analysis and topological data analysis. The resulting cover tree nodes consist of points within or near the same stratum of the stratified space. They are then connected to form a scaffolding graph, which is then simplified and collapsed down into a spine graph. From this latter graph the stratified structure becomes apparent. We demonstrate our technique on several synthetic point cloud examples and we use it to understand song structure in musical audio data.