# Generalized Principal Component Analysis (GPCA)

Data segmentation is usually though of as a chicken-and-egg problem. In order to estimate a mixture of models one needs to first segment the data, and in order to segment the data one needs to know the model parameters. Therefore, data segmentation is usually solved in two stages

1. Data clustering and 2. Model fitting.

Other iterative methods use, e.g. the Expectation Maximization (EM) algorithm. This talk will show that for a wide class of segmentation problems with multi-linear structure (including clustering subspaces of unknown and varying dimensions), the chicken-and-egg dilemma can be tackled as follows:

1. Fit a set of polynomials to all data points, without clustering the data 2. Obtain the model parameters for each group from the derivatives of these polynomials.

Applications of GPCA to image/video/motion segmentation, face clustering, and identification of hybrid dynamical models systems will also be presented.

*Author: Rene Vidal, John Hopkins University*