Generalized Principal Component Analysis (GPCA)

Understand

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 reduced to classifying one point per subspace.
• We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data.