https://cvc-lab.github.io/component---src-pages-projects-scalable-…an-co-clustering-js-fbadf1fb4f50d955d498.js

1"use strict";(self.webpackChunkcvc_website=self.webpackChunkcvc_website||[]).push([[576],{7528:function(e,t,a){var r=a(6540),n=a(4794);t.A=function(e){let{description:t="",lang:a="en",meta:c=[],title:s,pathname:l,image:i}=e;const{site:o}=(0,n.useStaticQuery)("3764592887"),m=o.siteMetadata.title,d=(o.siteMetadata.siteUrl||"").replace(/\/+$/,""),u=t||o.siteMetadata.description,p=s&&s!==m?`${s} | ${m}`:m,v=l&&d?`${d}${l}`:void 0,h=d?`${d}${i||"/og-image.jpg"}`:void 0;return r.createElement(r.Fragment,null,r.createElement("html",{lang:a}),r.createElement("title",null,p),r.createElement("meta",{name:"description",content:u}),v&&r.createElement("link",{rel:"canonical",href:v}),r.createElement("meta",{property:"og:site_name",content:m}),r.createElement("meta",{property:"og:title",content:p}),r.createElement("meta",{property:"og:description",content:u}),r.createElement("meta",{property:"og:type",content:"website"}),v&&r.createElement("meta",{property:"og:url",content:v}),h&&r.createElement("meta",{property:"og:image",content:h}),r.createElement("meta",{name:"twitter:card",content:h?"summary_large_image":"summary"}),r.createElement("meta",{name:"twitter:title",content:p}),r.createElement("meta",{name:"twitter:description",content:u}),h&&r.createElement("meta",{name:"twitter:image",content:h}),c.map((e=>{let{name:t,content:a,property:n}=e;return n?r.createElement("meta",{key:n,property:n,content:a}):r.createElement("meta",{key:t,name:t,content:a})})))}},8952:function(e,t,a){a.r(t),a.d(t,{Head:function(){return h}});var r=a(6540),n=a(8027),c=a(3514),s=a(7528);const l="https://arxiv.org/pdf/2504.04079",i=[{title:"Fully variational co-clustering",body:"Learns row and column clusters directly in latent space, replacing separate post-hoc clustering with a generative, end-to-end objective."},{title:"Compositional ELBOs",body:"Combines row-side, column-side, and joint cell-level variational objectives so each part of the matrix contributes structured evidence."},{title:"Noise and missing-input robustness",body:"Regularized reconstruction, KL structure, and noise learning are designed to keep cluster assignments stable under corrupted or sparse data."},{title:"Coherent row-column partitions",body:"A mutual-information cross-loss encourages row and column assignments to preserve dependence in the original matrix."}],o=[["Input matrix","Rows are instances; columns are features."],["Row and column VAEs","Separate encoders learn probabilistic latent spaces for each axis."],["GMM priors","Mixture components provide soft cluster anchors in both latent spaces."],["Joint cell latent space","A third latent variable models row-column interaction and local deviations."],["MI cross-loss","Soft row and column partitions are coupled through mutual information."],["Co-cluster structure","Rows and columns reorder into interpretable blocks."]],m=[["Fashion-MNIST-test","68.2 +/- 1.8","65.0 +/- 1.6","Strong image benchmark gain over DeepCC"],["WebKB4","83.2 +/- 1.6","42.3 +/- 1.2","Large accuracy gain on sparse text/web data"],["Yale","58.1 +/- 1.7","61.0 +/- 1.5","Improved facial-image latent separation"],["WebKB wisconsin","81.6 +/- 2.2","51.5 +/- 1.6","Best reported result in both ACC and NMI table columns"],["IMDb movies actors","26.2 +/- 2.4","19.4 +/- 1.8","Modest gain on a harder sparse movie-feature split"]],d=[["Fashion-MNIST-test","Feature only","62.1 / 58.2","DREG helps, but without the joint stage it remains weaker."],["Fashion-MNIST-test","Simple cascade","64.4 / 59.6","Better than feature-only, still below two-stage ELBO."],["Fashion-MNIST-test","Two-stage ELBO","68.2 / 65.0","Best reported ACC and NMI for this ablation."],["WebKB wisconsin","Two-stage ELBO","81.6 / 51.5","Best reported ACC and NMI under DREG."]],u=[{title:"Mild outlier profile",body:"One near-singleton group shows low motor burden, high MoCA, early Hoehn and Yahr stage, and mild or near-normal imaging values."},{title:"Older heterogeneous group",body:"An older cluster displays wider motor severity and comparatively preserved DaTSCAN signals, suggesting non-linear relationships among age, imaging, and symptoms."},{title:"Moderate PD subgroups",body:"Several broader groups share moderate severity but differ by cognition, imaging spread, age at diagnosis, and ventricular or striatal measures."},{title:"Candidate biomarker families",body:"Putamen and caudate DaTSCAN ratios, ventricular and striatal MRI volumes, UPDRS-III, Hoehn and Yahr stage, and MoCA emerge as separating variables."}],p="@article{vinod2025scalable,\n  title={Scalable Robust Bayesian Co-Clustering with Compositional ELBOs},\n  author={Vinod, Ashwin and Bajaj, Chandrajit},\n  journal={arXiv preprint arXiv:2504.04079},\n  year={2025}\n}",v=()=>{const e=Array.from({length:64},((e,t)=>{const a=["srvcc-tone-a","srvcc-tone-b","srvcc-tone-c","srvcc-tone-d","srvcc-tone-e"];return a[(7*t+Math.floor(t/3))%a.length]})),t=Array.from({length:64},((e,t)=>{const a=Math.floor(t/8),r=t%8;return a<3&&r<4?"srvcc-tone-a":a<3&&r>=4?"srvcc-tone-c":a>=3&&a<6&&r<3?"srvcc-tone-d":a>=3&&a<6&&r>=3&&r<6?"srvcc-tone-b":"srvcc-tone-e"}));return r.createElement("figure",{className:"srvcc-matrix-sketch","aria-label":"Noisy matrix converted into co-cluster blocks"},r.createElement("div",{className:"srvcc-matrix-panel"},r.createElement("p",null,"Noisy input"),r.createElement("div",{className:"srvcc-matrix-grid","aria-hidden":"true"},e.map(((e,t)=>r.createElement("span",{key:`n-${t}`,className:e}))))),r.createElement("div",{className:"srvcc-matrix-arrow","aria-hidden":"true"},"→"),r.createElement("div",{className:"srvcc-matrix-panel"},r.createElement("p",null,"Co-clustered blocks"),r.createElement("div",{className:"srvcc-matrix-grid srvcc-matrix-grid--block","aria-hidden":"true"},t.map(((e,t)=>r.createElement("span",{key:`b-${t}`,className:e}))))))};t.default=()=>{const[e,t]=r.useState(!1);return r.createElement(c.A,{headerVariant:"compact"},r.createElement("main",{className:"srvcc-page"},r.createElement("section",{className:"srvcc-hero"},r.createElement("div",{className:"srvcc-shell srvcc-hero-grid"},r.createElement("div",{className:"srvcc-hero-copy"},r.createElement("p",{className:"srvcc-eyebrow"},"Preprint | arXiv:2504.04079v2"),r.createElement("h1",null,"Scalable Robust Bayesian Co-Clustering with Compositional ELBOs"),r.createElement("p",{className:"srvcc-authors"},"Ashwin Vinod, Chandrajit Bajaj"),r.createElement("p",{className:"srvcc-lead"},"A fully variational co-clustering framework that learns row clusters, column clusters, and cell-level interaction structure in one noise-robust training pipeline."),r.createElement("div",{className:"srvcc-actions"},r.createElement("a",{className:"srvcc-button srvcc-button--primary",href:l},r.createElement(n.hko,null)," Read full paper"),r.createElement("a",{className:"srvcc-button",href:"https://arxiv.org/abs/2504.04079"},"arXiv record"))),r.createElement(v,null))),r.createElement("section",{className:"srvcc-section"},r.createElement("div",{className:"srvcc-shell srvcc-summary-grid"},r.createElement("article",{className:"srvcc-summary-card"},r.createElement("p",{className:"srvcc-eyebrow"},"Problem"),r.createElement("h2",null,"Co-clustering rows and features under real-world noise"),r.createElement("p",null,"Co-clustering identifies homogeneous groups of both instances and features in a matrix. Traditional methods often depend on shallow factorizations, linear transformations, or assumptions that struggle with sparse, high-dimensional, corrupted, or missing data.")),r.createElement("article",{className:"srvcc-summary-card srvcc-summary-card--accent"},r.createElement("p",{className:"srvcc-eyebrow"},"Approach"),r.createElement("h2",null,"Variational row, column, and joint latent structure"),r.createElement("p",null,"SRVCC uses row-side and column-side VAEs with Gaussian mixture priors, adds a joint cell-level latent variable, and optimizes a compositional objective with mutual information coupling and doubly reparameterized gradients.")))),r.createElement("section",{className:"srvcc-section srvcc-section--muted",id:"contributions"},r.createElement("div",{className:"srvcc-shell"},r.createElement("div",{className:"srvcc-section-heading"},r.createElement("p",{className:"srvcc-eyebrow"},"Core contributions"),r.createElement("h2",null,"What the paper adds")),r.createElement("div",{className:"srvcc-card-grid"},i.map((e=>r.createElement("article",{className:"srvcc-card",key:e.title},r.createElement("h3",null,e.title),r.createElement("p",null,e.body))))))),r.createElement("section",{className:"srvcc-section",id:"method"},r.createElement("div",{className:"srvcc-shell"},r.createElement("div",{className:"srvcc-section-heading"},r.createElement("p",{className:"srvcc-eyebrow"},"Method"),r.createElement("h2",null,"Processing pipeline"),r.createElement("p",null,"The framework turns a raw matrix into soft row clusters, soft column clusters, and joint block labels while retaining uncertainty throughout the training objective.")),r.createElement("ol",{className:"srvcc-pipeline"},o.map((e=>

1{let[t,a]=e;return r.createElement("li",{key:t},r.createElement("h3",null,t),r.createElement("p",null,a))}))))),r.createElement("section",{className:"srvcc-section srvcc-section--muted",id:"results"},r.createElement("div",{className:"srvcc-shell"},r.createElement("div",{className:"srvcc-section-heading"},r.createElement("p",{className:"srvcc-eyebrow"},"Reported results"),r.createElement("h2",null,"Benchmarks across image, text, and web data"),r.createElement("p",null,"Selected values from the paper tables. ACC is clustering accuracy; NMI is normalized mutual information.")),r.createElement("div",{className:"srvcc-table-wrap"},r.createElement("table",{className:"srvcc-table"},r.createElement("thead",null,r.createElement("tr",null,r.createElement("th",null,"Dataset"),r.createElement("th",null,"SRVCC ACC"),r.createElement("th",null,"SRVCC NMI"),r.createElement("th",null,"Note"))),r.createElement("tbody",null,m.map((e=>r.createElement("tr",{key:e[0]},e.map((e=>r.createElement("td",{key:e},e))))))))))),r.createElement("section",{className:"srvcc-section",id:"ablation"},r.createElement("div",{className:"srvcc-shell srvcc-two-column"},r.createElement("div",{className:"srvcc-section-heading"},r.createElement("p",{className:"srvcc-eyebrow"},"Ablation"),r.createElement("h2",null,"Why the two-stage ELBO matters"),r.createElement("p",null,"The paper compares feature-only clustering, a simple cascade, and the two-stage compositional ELBO design. The two-stage version with DREG reports the strongest accuracy and NMI on the shown ablations.")),r.createElement("div",{className:"srvcc-mini-table"},d.map((e=>{let[t,a,n,c]=e;return r.createElement("article",{key:`${t}-${a}`},r.createElement("span",null,t),r.createElement("h3",null,a),r.createElement("strong",null,n),r.createElement("p",null,c))}))))),r.createElement("section",{className:"srvcc-section srvcc-section--muted",id:"biomedical"},r.createElement("div",{className:"srvcc-shell"},r.createElement("div",{className:"srvcc-section-heading"},r.createElement("p",{className:"srvcc-eyebrow"},"Biomedical appendix"),r.createElement("h2",null,"PPMI co-clustering as a Parkinson's exploration"),r.createElement("p",null,"The paper appendix applies the co-clustering approach to PPMI clinical and imaging variables. This section is exploratory and should be read as biomarker-discovery analysis, not diagnostic deployment.")),r.createElement("div",{className:"srvcc-card-grid srvcc-card-grid--two"},u.map((e=>r.createElement("article",{className:"srvcc-card",key:e.title},r.createElement("h3",null,e.title),r.createElement("p",null,e.body))))))),r.createElement("section",{className:"srvcc-section",id:"citation"},r.createElement("div",{className:"srvcc-shell"},r.createElement("article",{className:"srvcc-citation-card"},r.createElement("div",null,r.createElement("p",{className:"srvcc-eyebrow"},"Resources"),r.createElement("h2",null,"Paper and citation")),r.createElement("pre",null,r.createElement("code",null,p)),r.createElement("div",{className:"srvcc-actions"},r.createElement("button",{className:"srvcc-button srvcc-button--primary",onClick:async()=>{"undefined"!=typeof navigator&&navigator.clipboard&&(await navigator.clipboard.writeText(p),t(!0),window.setTimeout((()=>t(!1)),1800))},type:"button"},r.createElement(n.paH,null)," ",e?"Copied":"Copy citation"),r.createElement("a",{className:"srvcc-button",href:l},r.createElement(n.WCW,null)," Download PDF")))))))};const h=e=>{let{location:t}=e;return r.createElement(s.A,{pathname:t.pathname,title:"Scalable Robust Bayesian Co-Clustering",description:"A variational co-clustering framework for robust row and column structure discovery in noisy, sparse, and high-dimensional data."})}}}]);
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