{"paper":{"title":"A Unified Framework for Sampling, Clustering and Embedding Data Points in Semi-Metric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SI","authors_text":"Cheng-Shang Chang, Chia-Tai Chang","submitted_at":"2017-08-01T13:47:39Z","abstract_excerpt":"In this paper, we propose a unified framework for sampling, clustering and embedding data points in semi-metric spaces. For a set of data points $\\Omega=\\{x_1, x_2, \\ldots, x_n\\}$ in a semi-metric space, we consider a complete graph with $n$ nodes and $n$ self edges and then map each data point in $\\Omega$ to a node in the graph with the edge weight between two nodes being the distance between the corresponding two points in $\\Omega$. By doing so, several well-known sampling techniques can be applied for clustering data points in a semi-metric space. One particularly interesting sampling techn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00316","kind":"arxiv","version":1},"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"}