{"id":32355,"date":"2026-01-21T17:01:48","date_gmt":"2026-01-21T17:01:48","guid":{"rendered":"https:\/\/lamarr-institute.org\/publication\/kernel-k-medoids-as-general-vector-quantization\/"},"modified":"2026-11-13T11:05:00","modified_gmt":"2026-11-13T11:05:00","slug":"kernel-k-medoids-as-general-vector-quantization","status":"publish","type":"publication","link":"https:\/\/lamarr-institute.org\/de\/publication\/kernel-k-medoids-as-general-vector-quantization\/","title":{"rendered":"Kernel k-Medoids as General Vector Quantization"},"content":{"rendered":"<p>Vector Quantization (VQ) is a widely used technique in machine learning and data compression, valued for its simplicity and interpretability. Among hard VQ methods, k-medoids clustering and Kernel Density Estimation (KDE) approaches represent two prominent yet seemingly unrelated paradigms&#8212;one distance-based, the other rooted in probability density matching. In this paper, we investigate their connection through the lens of Quadratic Unconstrained Binary Optimization (QUBO). We compare a heuristic QUBO formulation for k-medoids, which balances centrality and diversity, with a principled QUBO derived from minimizing Maximum Mean Discrepancy in KDE-based VQ. Surprisingly, we show that the KDE-QUBO is a special case of the k-medoids-QUBO under mild assumptions on the kernel&#8217;s feature map. This reveals a deeper structural relationship between these two approaches and provides new insight into the geometric interpretation of the weighting parameters used in QUBO formulations for VQ.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vector Quantization (VQ) is a widely used technique in machine learning and data compression, valued for its simplicity and interpretability. Among hard VQ methods, k-medoids clustering and Kernel Density Estimation (KDE) approaches represent two prominent yet seemingly unrelated paradigms&#8212;one distance-based, the other rooted in probability density matching. In this paper, we investigate their connection through the lens of Quadratic Unconstrained Binary Optimization (QUBO). We compare a heuristic QUBO formulation for [&hellip;]<\/p>\n","protected":false},"author":14,"featured_media":0,"template":"","meta":{"_acf_changed":false,"footnotes":""},"publication-type":[32],"publication-year":[1681],"class_list":["post-32355","publication","type-publication","status-publish","hentry","publication-type-inproceedings","publication-year-1681"],"acf":[],"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/32355","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication"}],"about":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/types\/publication"}],"author":[{"embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":1,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/32355\/revisions"}],"predecessor-version":[{"id":44283,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication\/32355\/revisions\/44283"}],"wp:attachment":[{"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/media?parent=32355"}],"wp:term":[{"taxonomy":"publication-type","embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication-type?post=32355"},{"taxonomy":"publication-year","embeddable":true,"href":"https:\/\/lamarr-institute.org\/de\/wp-json\/wp\/v2\/publication-year?post=32355"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}