Widening the scope of an eigenvector stochastic approximation process and application to streaming PCA and related methods - Archive ouverte HAL Access content directly
Journal Articles Journal of Multivariate Analysis Year : 2021

Widening the scope of an eigenvector stochastic approximation process and application to streaming PCA and related methods

(1, 2) , (3, 2)
1
2
3

Abstract

We prove the almost sure convergence of Oja-type processes to eigenvectors of the expectation B of a random matrix while relaxing the i.i.d. assumption on the observed random matrices (B n) and assuming either (B n) converges to B or (E[B n |T n ]) converges to B where T n is the sigma-field generated by the events before time n. As an application of this generalization, the online PCA of a random vector Z can be performed when there is a data stream of i.i.d. observations of Z, even when both the metric M used and the expectation of Z are unknown and estimated online. Moreover, in order to update the stochastic approximation process at each step, we are no longer bound to using only a mini-batch of observations of Z, but all previous observations up to the current step can be used without having to store them. This is useful not only when dealing with streaming data but also with Big Data as one can process the latter sequentially as a data stream. In addition the general framework of this process, unlike other algorithms in the literature, also covers the case of factorial methods related to PCA.
Fichier principal
Vignette du fichier
article_monnez_skiredj_20201118.pdf (229.81 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03038206 , version 1 (03-12-2020)

Identifiers

Cite

Jean-Marie Monnez, Abderrahman Skiredj. Widening the scope of an eigenvector stochastic approximation process and application to streaming PCA and related methods. Journal of Multivariate Analysis, 2021, 182, pp.104694. ⟨10.1016/j.jmva.2020.104694⟩. ⟨hal-03038206⟩
138 View
204 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More