{
  "abstract": "Accurate optimization of a supervised spectral objective need not produce an accurate population subspace or a better predictive representation. We investigate these distinctions for Online Kernel Supervised Principal Component Analysis (OKSPCA), which combines a centered cross-moment in finite random-feature coordinates with an Adam-style orthonormal basis update for an established objective. Fixed-map consistency, concentration and perturbation results describe the estimator and its exact subspace; same-target comparisons then assess the practical iterate separately. Across six predictive benchmarks, performance depends on the declared pipeline: replacing the tracker with the exact empirical target leaves the two regression deficits largely unchanged. Direct classification-rank models capture nearly all terminal objective energy on average, but a saved intermediate state exhibits substantial geometric deviation; a controlled sample-size study further separates empirical accuracy from population recovery. In distinct numerical-service workloads, exact on-request computation is faster in the tested classification settings, whereas Adam saves time relative to the tested full thin-SVD service for some dense wider-regression requests, alongside persistent geometric error. These diagnostics limit explanations based solely on terminal optimization accuracy and distinguish numerical cost from quality, rank coverage and freshness; they establish neither practical-tracker convergence nor predictive or deployment benefits from basis availability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20454",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhenlin Yao"
    },
    {
      "name": "Wei Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3btw3rahcavnn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20454",
  "fulltext_url": null,
  "id": "3btw3rahcavnn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20454",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Stochastic Gradient Optimization Techniques"
    ]
  ],
  "openalex": "W7213590409",
  "pdf_url": "https://arxiv.org/pdf/2609.20454",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3btw3rahcavnn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:29Z",
      "native_id": "2609.20454",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20454"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Online Supervised Dimension Reduction with Random Features: Diagnostics and Computational Trade-offs",
  "title_text": "Online Supervised Dimension Reduction with Random Features: Diagnostics and Computational Trade-offs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:29Z",
  "url": "https://research.draconitic.com/paper/3btw3rahcavnn",
  "venue": "arXiv",
  "versions": []
}