Reconstruction based subspace clustering methods compute a self reconstruction matrix over the samples and use it for spectral clustering to obtain the final clustering result. Their success largely relies on the assumption that the underlying subspaces are independent, which, however, does not always hold in the applications with increasing number of subspaces. In this paper, we propose a nove...

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 ...

Subspace identification techniques are reinterpreted via classical realization theory to formulate a wide class of subspace identification methods. Re-formulating subspace identification in terms of a low rank decomposition of a weighted Hankel matrix allows special cases such as impulse-based and step-based input signals, but also realization based on arbitrary input signals and correlation fu...

The Rational Krylov Sequence (RKS) method can be seen as a generalisation of Arnoldi's method. It projects a matrix pencil onto a smaller subspace; this projection results in a small upper Hessenberg pencil. As for the Arnoldi method, RKS can be restarted implicitly, using the QR decomposition of a Hessenberg matrix. This restart comes with a projection of the subspace using a rational function...