Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces

A Note on the Structure of Affine Subspaces of

This paper investigates the structure of general affine subspaces of ( )  L . For a d × d expansive matrix A, it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is generated by dilating some shift invariant space in this affine subspace, and every non-zero and non-reducing affine subspace is the orthogonal direct sum of a reducing subspace and a ...

A Bollobás-type theorem for affine subspaces

Barycentric Subspaces and Affine Spans in Manifolds

This paper addresses the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. Current methods like Principal Geodesic Analysis (PGA) and Geodesic PCA (GPCA) minimize the distance to a ”Geodesic subspace”. This allows to build sequences of nested subspaces which are consistent with a forward component analysis approach. However, these methods cannot be adapted to a backw...

Clustering Affine Subspaces: Hardness and Algorithms

We study a generalization of the famous k-center problem where each object is an affinesubspace of dimension ∆, and give either the first or significantly improved algorithms andhardness results for many combinations of parameters. This generalization from points (∆ = 0)is motivated by the analysis of incomplete data, a pervasive challenge in statistics: incompletedata objects i...

Clustering Affine Subspaces: Algorithms and Hardness

We study a generalization of the famous k-center problem where each object is an affine subspace of dimension ∆, and give either the first or significantly improved algorithms and hardness results for many combinations of parameters. This generalization from points (∆ = 0) is motivated by the analysis of incomplete data, a pervasive challenge in statistics: incomplete data objects in R can be m...