  Data analysis often requires methods that are invariant with respect to
specific transformations, such as rotations in case of images or shifts in case
of images and time series. While principal component analysis (PCA) is a
widely-used dimension reduction technique, it lacks robustness with respect to
these transformations. Modern alternatives, such as autoencoders, can be
invariant with respect to specific transformations but are generally not
interpretable. We introduce General Transform-Invariant Principal Component
Analysis (GT-PCA) as an effective and interpretable alternative to PCA and
autoencoders. We propose a neural network that efficiently estimates the
components and show that GT-PCA significantly outperforms alternative methods
in experiments based on synthetic and real data.
