eb6fdc36b281b7d5eabf33396c2683a2-Reviews.html

The paper introduces probabilistic principal component analysis on Riemannian manifolds, extending earlier non-probabilistic versions to a probabilistic latent variable model, and derives maximum likelihood estimation procedures for a broad class of manifolds. The methods are demonstrated on toy data (maniold is a sphere) and shape analysis on images. This is a very interesting advancement, and the paper is well written, making it reasonably accessible in spite of the difficult topic. I have a set of interrelated questions; explicating and clarifying them would clarify the potential impact of the paper to the reader: - Is essential generality lost by assuming an Euclidean latent space? Locally on a tangent space it makes sense, and may be practically necessary, of course.