Database Reference
In-Depth Information
Principal Components Analysis
PCA operates on a data matrix
X
and seeks to extract a set of
k
principal components from
X
. The principal components are each uncorrelated to each other and are computed such
that the first principal component accounts for the largest variation in the input data. Each
subsequent principal component is, in turn, computed such that it accounts for the largest
variation, provided that it is independent of the principal components computed so far.
In this way, the
k
principal components returned are guaranteed to account for the highest
amount of variation in the input data possible. Each principal component, in fact, has the
same feature dimensionality as the original data matrix. Hence, a projection step is required
in order to actually perform dimensionality reduction, where the original data is projected
into the
k-dimensional
space represented by the principal components.
