{"paper":{"title":"Dimensionality-Dependent Generalization Bounds for $k$-Dimensional Coding Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Dacheng Tao, Dong Xu, Tongliang Liu","submitted_at":"2016-01-03T01:17:04Z","abstract_excerpt":"The $k$-dimensional coding schemes refer to a collection of methods that attempt to represent data using a set of representative $k$-dimensional vectors, and include non-negative matrix factorization, dictionary learning, sparse coding, $k$-means clustering and vector quantization as special cases. Previous generalization bounds for the reconstruction error of the $k$-dimensional coding schemes are mainly dimensionality independent. A major advantage of these bounds is that they can be used to analyze the generalization error when data is mapped into an infinite- or high-dimensional feature sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00238","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"}