  Principal Component Analysis (PCA) is a fundamental tool for data
visualization, denoising, and dimensionality reduction. It is widely popular in
Statistics, Machine Learning, Computer Vision, and related fields. However, PCA
is well-known to fall prey to outliers and often fails to detect the true
underlying low-dimensional structure within the dataset. Following the Median
of Means (MoM) philosophy, recent supervised learning methods have shown great
success in dealing with outlying observations without much compromise to their
large sample theoretical properties. This paper proposes a PCA procedure based
on the MoM principle. Called the \textbf{M}edian of \textbf{M}eans
\textbf{P}rincipal \textbf{C}omponent \textbf{A}nalysis (MoMPCA), the proposed
method is not only computationally appealing but also achieves optimal
convergence rates under minimal assumptions. In particular, we explore the
non-asymptotic error bounds of the obtained solution via the aid of the
Rademacher complexities while granting absolutely no assumption on the outlying
observations. The derived concentration results are not dependent on the
dimension because the analysis is conducted in a separable Hilbert space, and
the results only depend on the fourth moment of the underlying distribution in
the corresponding norm. The proposal's efficacy is also thoroughly showcased
through simulations and real data applications.
