Slide 13
Slide 13 text
DATA-DRIVEN DIMENSION REDUCTION
PRINCIPAL COMPONENTS
SUMMARISING THOUGHTS
*Candés, Li, Ma, Wright (2011) Robust principal component analysis? J. ACM.
*Schölkopf, Smola, Müller (1997) Kernel principal component analysis. Springer.
Rather than apply principal components to a single image, we can apply it to
numerous images to find dominant linear directions across all the images.
Utility is not restricted to images and videos, but to any matrix / vector database. More
robust and nonlinear variants also exist.
However, we can’t really use this if we are interested in input-output pairs. For
instance, computer experiments are usually carried out via a uniform design of
experiment.
Naïvely applying PCA to the inputs does not facilitate output-driven dimension
reduction.