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Stochastic approximation of eigenvectors and eigenvalues of the Q-symmetric expectation of a random matrix

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  • Jean-Marie Monnez

Abstract

We establish an almost sure convergence theorem of the stochastic approximation process of Oja for estimating eigenvectors of the Q-symmetric expectation of a random matrix, under a correlation model between the incoming random matrices. This theorem generalizes previous theorems and extends them to the case where the metric Q is unknown and estimated online in parallel. We apply it to streaming principal component analysis of a random vector Z, when a mini-batch of observations of Z is used at each step or all the observations up to the current step. We deal with the case of streaming generalized canonical correlation analysis, with a metric estimated online in parallel.

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  • Jean-Marie Monnez, 2024. "Stochastic approximation of eigenvectors and eigenvalues of the Q-symmetric expectation of a random matrix," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(5), pages 1669-1683, March.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:5:p:1669-1683
    DOI: 10.1080/03610926.2022.2107225
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