Treffer: Convergence of a normed eigenvector stochastic approximation process and application to online principal component analysis of a data stream

Title:
Convergence of a normed eigenvector stochastic approximation process and application to online principal component analysis of a data stream
Authors:
Monnez, Jean-Marie, Skiredj, Abderrahman
Contributors:
Centre d'investigation clinique plurithématique Pierre Drouin Nancy (CIC-P), Centre d'investigation clinique Nancy (CIC), Centre Hospitalier Régional Universitaire de Nancy (CHRU Nancy)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Lorraine (UL)-Centre Hospitalier Régional Universitaire de Nancy (CHRU Nancy)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Lorraine (UL), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), IUT Nancy Charlemagne, Université de Lorraine (UL), Biology, genetics and statistics (BIGS), Centre Inria de l'Université de Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Ecole Nationale Supérieure des Mines de Nancy (ENSMN), Institut Mines-Télécom Paris (IMT)-Université de Lorraine (UL), Results incorporated in this article received funding from the investments for the Future program under grant agreement No ANR-15-RHU-0004., IECL, ANR-15-RHUS-0004,FIGHT-HF,Combattre l'insuffisance cardiaque(2015)
Source:
https://hal.science/hal-01844419 ; [Research Report] IECL. 2019.
Publisher Information:
CCSD
Publication Year:
2019
Collection:
Université de Lorraine: HAL
Subject Terms:
Stochastic approximation algorithms, Big Data, Principal Component Analysis, Online Estimation, Data Stream, Stochastic Ap- proximation, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Document Type:
Report report
Language:
English
Availability:
https://hal.science/hal-01844419
https://hal.science/hal-01844419v2/document
https://hal.science/hal-01844419v2/file/Basic%20CV%20of%20a%20normed%20eigen%20SA%20process2.pdf
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edsbas.33B4FA4
Database:
BASE

Weitere Informationen

Many articles were devoted to the problem of estimating recursively the eigenvectors and eigenvalues in decreasing order of the expectation of a random matrix using an i.i.d. sample of it. The present study makes the following contributions. The convergence of a normed process is proved under more general assumptions: the random matrices are not supposed i.i.d. and a new data mini-batch or all data until the current step are taken into account at each step without storing them; three types of processes are studied; this is applied to online principal component analysis of a data stream, assuming that data are realizations of a random vector Z whose expectation is unknown and must be estimated online, as well as possibly the metrics used when it depends on unknown characteristics of Z.