Monthly
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6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

August 15, 1998, Vol. 10, No. 6, Pages 1435-1444
(doi: 10.1162/089976698300017241)
© 1998 Massachusetts Institute of Technology
The Influence Function of Principal Component Analysis by Self-Organizing Rule
Article PDF (95.04 KB)
Abstract

This article is concerned with a neural network approach to principal component analysis (PCA). An algorithm for PCA by the self-organizing rule has been proposed and its robustness observed through the simulation study by Xu and Yuille (1995). In this article, the robustness of the algorithm against outliers is investigated by using the theory of influence function. The influence function of the principal component vector is given in an explicit form. Through this expression, the method is shown to be robust against any directions orthogonal to the principal component vector. In addition, a statistic generated by the self-organizing rule is proposed to assess the influence of data in PCA.