{"paper":{"title":"Guarantees for the Kronecker Fast Johnson-Lindenstrauss Transform Using a Coherence and Sampling Argument","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Osman Asif Malik, Stephen Becker","submitted_at":"2019-11-19T17:42:59Z","abstract_excerpt":"In the recent paper [Jin, Kolda & Ward, arXiv:1909.04801], it is proved that the Kronecker fast Johnson-Lindenstrauss transform (KFJLT) is, in fact, a Johnson-Lindenstrauss transform, which had previously only been conjectured. In this paper, we provide an alternative proof of this, for when the KFJLT is applied to Kronecker vectors, using a coherence and sampling argument. Our proof yields a different bound on the embedding dimension, which can be combined with the bound in the paper by Jin et al. to get a better bound overall. As a stepping stone to proving our result, we also show that the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.08424","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.08424/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}