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Published in:
2012 | OriginalPaper | Chapter
Principal Components Analysis
Authors : Wolfgang Karl Härdle, Léopold Simar
Published in: Applied Multivariate Statistical Analysis
Publisher: Springer Berlin Heidelberg
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Chapter
9
presented the basic geometric tools needed to produce a lower dimensional description of the rows and columns of a multivariate data matrix. Principal components analysis has the same objective with the exception that the rows of the data matrix
${{\mathcal{X}}}$
will now be considered as observations from a
p
-variate random variable
X
. The principle idea of reducing the dimension of
X
is achieved through linear combinations. Low dimensional linear combinations are often easier to interpret and serve as an intermediate step in a more complex data analysis. More precisely one looks for linear combinations which create the largest spread among the values of
X
. In other words, one is searching for linear combinations with the largest variances.