True Dimensionality: Linear how many dimensions is enough? > 2 or 3? knee in error curve example: measured materials from graphics linear PCA: 25 can get physically impossible intermediate points [A Data-Driven Reflectance Model, SIGGRAPH 2003, W Matusik, H. Pfister M. Brand and L. McMillan, graphics.lcs.mit.edu/~wojciech/pubs/sig2003.pdf] 43