{"paper":{"title":"Co-clustering of Response and Covariate Variables by Tri-Factorizing Their Non-negative Regression Coefficient Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"(2) Faculty of Education, Kenichi Satoh (1), Shiga University, Shiga University), Yomei Tokuda (2) ((1) Faculty of Data Science","submitted_at":"2026-07-29T21:27:17Z","abstract_excerpt":"Two-block data---two sets of variables measured on the same individuals, such as microbial taxa and metabolites---raise the question of how \\emph{groups} of covariate variables relate to \\emph{groups} of response variables. Co-clustering answers this for a single matrix, not for two variable blocks; existing two-block methods either cluster only one side or return signed factors rather than clusters. Starting from the multivariate linear regression $Y_1\\approx M Y_2$, we give its non-negative coefficient matrix a tri-factorization $M=X_1\\Theta X_2$ (a tri-NMF), so that $X_1$ softly clusters th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27474","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.27474/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"}