  Principal component analysis (PCA) is recognised as a quintessential data
analysis technique when it comes to describing linear relationships between the
features of a dataset. However, the well-known sensitivity of PCA to
non-Gaussian samples and/or outliers often makes it unreliable in practice. To
this end, a robust formulation of PCA is derived based on the maximum
correntropy criterion (MCC) so as to maximise the expected likelihood of
Gaussian distributed reconstruction errors. In this way, the proposed solution
reduces to a generalised power iteration, whereby: (i) robust estimates of the
principal components are obtained even in the presence of outliers; (ii) the
number of principal components need not be specified in advance; and (iii) the
entire set of principal components can be obtained, unlike existing approaches.
The advantages of the proposed maximum correntropy power iteration (MCPI) are
demonstrated through an intuitive numerical example.
