{"paper":{"title":"Multimapper: Data Density Sensitive Topological Visualization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"math.AT","authors_text":"Akash Rupela, Ankita Sarkar, Balaji Krishnamurthy, Bishal Deb, Nupur Kumari, Piyush Gupta","submitted_at":"2019-03-07T07:32:24Z","abstract_excerpt":"Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibly high-dimensional, a filter function on it and an open cover on the range of the function. It returns the nerve simplicial complex of the pullback of the cover. Mapper can be considered a discrete approximation of the topological construct called Reeb space, as analysed in the $1$-dimensional case by [Carriere et al.,2018]. Despite its success in obtaining insights in various fields such as in [Kamruzzaman et al., 2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02755","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}