{"paper":{"title":"Two New Approaches to Compressed Sensing Exhibiting Both Robust Sparse Recovery and the Grouping Effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Mathukumalli Vidyasagar, Mehmet Eren Ahsen, Niharika Challapalli","submitted_at":"2014-10-30T01:47:09Z","abstract_excerpt":"In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the $\\ell_1$- and $\\ell_2$-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a convex combination of the $\\ell_1$- and $\\ell_2$-norm squared. It is shown that, in the context of compressed sensing, the EN formulation does not achieve robust recovery of sparse vectors, whereas the new CLOT formulation achieves robust recovery. Also, like EN but unlike LASSO"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8229","kind":"arxiv","version":4},"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"}