In this paper, we study subspace embedding problem and obtain the following results: 1. We extend the results of approximate matrix multiplication from the Frobenius norm to the spectral norm. Assume matrices A and B both have at most r stable rank and r̃ rank, respectively. Let S be a subspace embedding matrix with l rows which depends on stable rank, then with high probability, we have ‖ASSB−A...

Principal eigenvectors of the data covariance matrix or the subspace spanned by them, called PCA subspace, provide optimal solutions to several information representation tasks. Recently, many neural approaches have been proposed for learning them (see, e.g., Hertz r t a/. 1991; Oja 1992). A well-known algorithm for learning the PCA subspace of the input vectors is so-called Op’s subspace rule ...

This talk addresses vector-valued subspace Gabor frames with rational time-frequency product. By introduction of a suitable Zak transform matrix, we characterize vector-valued subspace Gabor frames, Riesz bases and orthonorrmal bases, and the uniqueness of Gabor duals of type I and type II. Using the uniqueness results, we extend the classical Balian-Low theorem to vector-valued subspace Gabor ...

We study the underlying structure of data (approximately) generated from a union of independent subspaces. Traditional methods learn only one subspace, failing to discover the multi-subspace structure, while state-of-the-art methods analyze the multi-subspace structure using data themselves as the dictionary, which cannot offer the explicit basis to span each subspace and are sensitive to error...

Tracking the dominant subspace of a measured data matrix is an essential part of many signal processing algorithms. We present a modiication to the so-called spherical subspace tracking algorithm. This algorithm has a low computational complexity, but suuers from accumulation of numerical errors. We show that this numerical instability can be circumvented by using a minimal orthogonal parameter...

Suppose one approximates an invariant subspace of an n n matrix in C nn which in not necessarily self{adjoint. Suppose that one also has an approximation for the corresponding eigenvalues. We consider the question of how good the approximations are. Speciically, we develop bounds on the angle between the approximating subspace and the invariant subspace itself. These bounds are functions of the...

This letter addresses the problem of order estimation for uniform linear arrays (ULAs) with multi-switch antenna selection in small-sample regime. Multi-switch results a data matrix missing entries, scenario which existing methods that build on eigenvalues sample covariance do not perform well. A direct application Davis-Kahan theorem allows us to show signal subspace is quite robust presence e...

In this paper, a closed-loop subspace identification approach through an orthogonal projection and subsequent singular value decomposition is proposed. As a by-product of this development, it explains why some existing subspace methods may deliver a bias in the presence of the feedback control and suggests a remedy to eliminate the bias. Furthermore, as the proposed method is a projection based...

Efficient mode shape extraction of fluid-structure systems is of particular interest in engineering. An efficient modified version of unsymmetric Lanczos method is proposed in this paper. The original unsymmetric Lanczos method was applied to general form of unsymmetric matrices, while the proposed method is developed particularly for the fluid-structure matrices. The method provides us with si...

Subspace-based methods rely on singular value decomposition (SVD) of the sample covariance matrix (SCM) to compute the array signal or noise subspace. For large array, triditional subspace-based algorithms inevitably lead to intensive computational complexity due to both calculating SCM and performing SVD of SCM. To circumvent this problem, a NyströmBased algorithm for array subspace estimation...