Generalized principal component analysis (gpca): an algebraic geometric approach to subspace clustering and motion segmentation

Abstract

Simultaneous data segmentation and model estimation refers to the problem of estimating a collection of models from sample data points, without knowing which points correspond to which model. This is a challenging problem in many disciplines, such as machine learning, computer vision, robotics and control, that is usually regarded as "chicken-and-egg". This is because if the segmentation of the data was known, one could easily fit a single model to each group of points. Conversely, if the models were known, one could easily find the data points that best fit each model. Since in practice neither the models nor the segmentation of the data are known, most of the existing approaches start with an initial estimate for the either the segmentation of the data or the model parameters and then iterate between data segmentation and model estimation. However, the convergence of iterative algorithms to the global optimum is in general very sensitive to initialization of both the number of models and the model parameters. Finding a good initialization remains a challenging problem. This thesis