In this talk, we discuss the problem of modeling and segmenting multivariate mixed data. The basic idea is to generalize the classical Principal Component Analysis to the new situation in which the data are drawn from a mixture of models. We will discuss a new approach to model the data as an algebraic set, in particular, an arrangement of subspaces, and show how this approach leads to an effective non-iterative solution to the problem of estimating and segmenting mixed data. We will also discuss many fundamental mathematical and conceptual problems that arise from segmentation, as well as some applications in computer vision and image processing.