A Cure for Variance Inflation in High Dimensional Kernel Principal Component Analysis

Trine Julie Abrahamsen, Lars Kai Hansen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    Small sample high-dimensional principal component analysis (PCA) suffers from variance inflation and lack of generalizability. It has earlier been pointed out that a simple leave-one-out variance renormalization scheme can cure the problem. In this paper we generalize the cure in two directions: First, we propose a computationally less intensive approximate leave-one-out estimator, secondly, we show that variance inflation is also present in kernel principal component analysis (kPCA) and we provide a non-parametric renormalization scheme which can quite efficiently restore generalizability in kPCA. As for PCA our analysis also suggests a simplified approximate expression. © 2011 Trine J. Abrahamsen and Lars K. Hansen.
    Original languageEnglish
    JournalJournal of Machine Learning Research
    Volume12
    Pages (from-to)2027-2044
    ISSN1532-4435
    Publication statusPublished - 2011

    Keywords

    • Kernel PCA
    • Generalizability
    • Variance renormalization
    • PCA

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