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Article Dans Une Revue Communications in Statistics - Theory and Methods Année : 2024

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

Résumé

We establish an almost sure convergence theorem of the stochasticapproximation process of Oja for estimating eigenvectors of theQ-symmetric expectation of a random matrix, under a correlationmodel between the incoming random matrices. This theorem gener-alizes previous theorems and extends them to the case where themetricQis unknown and estimated online in parallel. We apply it tostreaming principal component analysis of a random vectorZ, whena mini-batch of observations ofZis used at each step or all theobservations up to the current step. We deal with the case ofstreaming generalized canonical correlation analysis, with a metricestimated online in parallel.
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Dates et versions

hal-03956687 , version 1 (25-01-2023)

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Jean-Marie Monnez. Stochastic approximation of eigenvectors and eigenvalues of the Q-symmetric expectation of a random matrix. Communications in Statistics - Theory and Methods, 2024, 53 (5), pp.1669-1683. ⟨10.1080/03610926.2022.2107225⟩. ⟨hal-03956687⟩
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