{"paper":{"title":"On the Restricted Isometry Property of Centered Self Khatri-Rao Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexander Fengler, Peter Jung","submitted_at":"2019-05-22T17:09:30Z","abstract_excerpt":"In this work we establish the Restricted Isometry Property (RIP) of the centered column-wise self Khatri-Rao (KR) products of $n\\times N$ matrix with iid columns drawn either uniformly from a sphere or with iid sub-Gaussian entries. The self KR product is an $n^2\\times N$-matrix which contains as columns the vectorized (self) outer products of the columns of the original $n\\times N$-matrix. Based on a result of Adamczak et al. we show that such a centered self KR product with independent heavy tailed columns has small RIP constants of order $s$ with probability at least $1-C\\exp(-cn)$ provided"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09245","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"}