Over the past two decades, we have seen tremendous advances on
the simultaneous segmentation and estimation of a collection of models
from sample data points, without knowing which points correspond to
which model. Most existing segmentation methods treat this problem as
"chicken-and-egg", and iterate between model estimation and data
segmentation. This lecture will show that for a wide variety of data
segmentation problems (e.g. mixtures of subspaces), the
"chicken-and-egg" dilemma can be tackled using an algebraic geometric
technique called Generalized Principal Component Analysis (GPCA). This
technique is a natural extension of classical PCA from one to multiple
subspaces. The lecture will touch upon a few motivating applications of
GPCA in computer vision, such as image/video segmentation, 3-D motion
segmentation or dynamic texture segmentation, but will mainly emphasize
the basic theory and algorithmic aspects of GPCA.