Convergence study of principal component analysis algorithms | IEEE Conference Publication | IEEE Xplore

Convergence study of principal component analysis algorithms


Abstract:

We investigate the convergence properties of two different principal component analysis algorithms, and analytically explain some commonly observed experimental results. ...Show More

Abstract:

We investigate the convergence properties of two different principal component analysis algorithms, and analytically explain some commonly observed experimental results. We use two different methodologies to analyze the two algorithms. The first methodology uses the fact that both algorithms are stochastic approximation procedures. We use the theory of stochastic approximation, in particular the results of Fabian (1968), to analyze the asymptotic mean square errors (AMSEs) of the algorithms. This analysis reveals the conditions under which the algorithms produce smaller AMSEs, and also the conditions under which one algorithm has a smaller AMSE than the other. We next analyze the asymptotic mean errors (AMEs) of the two algorithms in the neighborhood of the solution. This analysis establishes the conditions under which the AMEs of the minor eigenvectors go to zero faster. Furthermore, the analysis makes explicit that increasing the gain parameter up to an upper bound improves the convergence of all eigenvectors. We also show that the AME of one algorithm goes to zero faster than the other. Experiments with multi-dimensional Gaussian data corroborate the analytical findings presented here.
Date of Conference: 12-12 June 1997
Date Added to IEEE Xplore: 06 August 2002
Print ISBN:0-7803-4122-8
Conference Location: Houston, TX, USA

References

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