{"paper":{"title":"The NMF problem and lattice-subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.RA","authors_text":"Ioannis A. Polyrakis","submitted_at":"2019-06-11T21:15:01Z","abstract_excerpt":"Suppose that $A$ is a nonnegative $n\\times m$ real matrix. The NMF problem is the determination of two nonnegative real matrices $F$, $V$ so that $A=FV$ with intermediate dimension $p$ smaller than $min\\{ n,m\\}$. In this article we present a general mathematical method for the determination of two nonnegative real factors $F,V$ of $A$. During the first steps of this process the intermediate dimension $p$ of $F,V$ is determined, therefore we have an easy criterion for $p$. This study is based on the theory of lattice-subspaces and positive bases. Also we give the matlab program for the computat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05730","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"}