Kernel methods in orthogonalization of multi- and hypervariate data

Allan Aasbjerg Nielsen (Invited author)

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    345 Downloads (Pure)


    A kernel version of maximum autocorrelation factor (MAF) analysis is described very briefly and applied to change detection in remotely sensed hyperspectral image (HyMap) data. The kernel version is based on a dual formulation also termed Q-mode analysis in which the data enter into the analysis via inner products in the Gram matrix only. In the kernel version the inner products are replaced by inner products between nonlinear mappings into higher dimensional feature space of the original data. Via kernel substitution also known as the kernel trick these inner products between the mappings are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of this kernel function. This means that we need not know the nonlinear mappings explicitly. Kernel PCA and MAF analysis handle nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via the kernel function and then performing a linear analysis in that space. An example shows the successful application of kernel MAF analysis to change detection in HyMap data covering a small agricultural area near Lake Waging-Taching, Bavaria, Germany.
    Original languageEnglish
    Title of host publicationIEEE International Conference on Image Processing, ICIP
    Publication date2009
    ISBN (Print)978-1-4244-5653-6
    Publication statusPublished - 2009
    EventIEEE 16th International Conference on Image Processing ICIP 2009 - Cairo, Egypt
    Duration: 7 Nov 200910 Nov 2009


    ConferenceIEEE 16th International Conference on Image Processing ICIP 2009
    Internet address

    Bibliographical note

    Copyright 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.


    Dive into the research topics of 'Kernel methods in orthogonalization of multi- and hypervariate data'. Together they form a unique fingerprint.

    Cite this