{"paper":{"title":"An information theoretic formulation of the Dictionary Learning and Sparse Coding Problems on Statistical Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Baba C. Vemuri, Monami Banerjee, Rudrasis Chakraborty, Victoria Crawford","submitted_at":"2016-04-23T19:15:42Z","abstract_excerpt":"In this work, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions). Unlike the traditional DL and SC framework, our new formulation {\\it does not explicitly incorporate any sparsity inducing norm in the cost function but yet yields SCs}. Moreover, we extend this framework to the manifold of symmetric positive definite matrices, $\\mathcal{P}_n$. Our algorithm approximates the data points, which are probability distributions, by the weighted Kullback-Leibeler center (KL-center)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06939","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"}