I love this visualization - but I think there's a very different intuition you get from PCA in high dimensions. I prefer to think of the singular vectors in PC

I love this visualization - but I think there's a very different intuition you get from PCA in high dimensions. I prefer to think of the singular vectors in PCA as an ordering of "prototype signals" for which some linear combination best reconstructs the data. That explains, for example, why the largest singular vectors on natural time series data gives fourier like coefficients, and why the largest singular vectors on aligned faces gives variations in lighting.