I am interested in subspace identification and tracking.
Given a set of data points and information about the content of the data (for example, the data set may be images of human faces, or surveillance footage of a known location), what factors would one consider before deciding, say, between a union of subspace model and a low dimensional subspace embedding to fit the given data? By a low dimensional subspace embedding, I mean using $k$ largest singular values to approximate the underlying subspace and solving a regularization problem that penalizes large variations in the subspaces.
Apart from the nature of data, what other factors could motivate choosing one model over the other?
Thanks!