{"paper":{"title":"HOID: Higher Order Interpolatory Decomposition for tensors based on Tucker representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Arvind K. Saibaba","submitted_at":"2015-11-16T22:36:26Z","abstract_excerpt":"We derive a CUR-type factorization for tensors in the Tucker format based on interpolatory decomposition, which we will denote as Higher Order Interpolatory Decomposition (HOID). Given a tensor $\\mathcal{X}$, the algorithm provides a set of column vectors $\\{ \\mathbf{C}_n\\}_{n=1}^d$ which are columns extracted from the mode-$n$ tensor unfolding, along with a core tensor $\\mathcal{G}$ and together, they satisfy some error bounds. Compared to the Higher Order SVD (HOSVD) algorithm, the HOID provides a decomposition that preserves certain important features of the original tensor such as sparsity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05208","kind":"arxiv","version":3},"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"}