This paper presents an algebro-geometric solution to the problem of segmenting an
unknown number of subspaces of unknown and varying dimensions from sample data
points. We represent the subspaces with a set of homogeneous polynomials whose degree
is the number of subspaces and whose derivatives at a data point give normal vectors to the
subspace passing through the point. When the number of subspaces is known, we show that
these polynomials can be estimated linearly from data; hence, subspace segmentation is …

This thesis presents a novel algebraic geometric framework for simultaneous data
segmentation and model estimation, with the hope of providing a theoretical footing for the
problem as well as an algorithm for initializing iterative techniques. The algebraic geometric
approach presented in this thesis is based on eliminating the data segmentation part
algebraically and then solving the model estimation part directly using all the data and
without having to iterate between data segmentation and model estimation. The algebraic …