Recent literature [1] suggests that embedding a graph on an unit sphere leads to better generalization for graph transduction. However, the choice of optimal embedding and an efficient algorithm to compute the same remains open. In this paper, we show that orthonormal representations, a class of unit-sphere graph embeddings are PAC learnable. Existing PAC-based analysis do not apply as the VC d...

The stabilization and robustification of a time-delay system is the topic of this paper. More precisely, we want to minimize theH2 norm of the transfer function corresponding to this class of linear time-invariant input-output systems with fixed time delays in the states. Due to the presence of the delays, the transfer function is a nonrational, nonlinear function, and the classical procedure w...

Barabanov norms have been introduced in Barabanov (Autom. Remote Control, 49 (1988), pp. 152–157) and constitute an important instrument in analyzing the joint spectral radius of a family of matrices and related issues. However, although they have been studied extensively, even in very simple cases it is very difficult to construct them explicitly (see, e.g., Kozyakin (Discrete Contin. Dyn. Sys...

A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different basis? In this paper, we propose a new spectral clustering algorithm. It can recover a k-partition such that the subspace corresponding to the span of its ind...

In this work an innovative unsupervised change detection technique for multispectral and hyperspectral images is proposed. It consists in the comparison between two co-registered and radiometrically correct multispectral images, carried out by comparing pixels’ spectral signatures. Supposing a change is occurred, we can state that the spectral vector associated to a pixel in the “changed image”...

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...

Let A = ( H1 E ∗ E H2 ) and à = ( H1 O O H2 ) be Hermitian matrices with eigenvalues λ1 ≥ · · · ≥ λk and λ̃1 ≥ · · · ≥ λ̃k, respectively. Denote by ‖E‖ the spectral norm of the matrix E, and η the spectral gap between the spectra of H1 and H2. It is shown that |λi − λ̃i| ≤ 2‖E‖ η + √ η2 + 4‖E‖2 , which improves all the existing results. Similar bounds are obtained for singular values of matrices u...

We extend, in the context of connected noncompact semisimple Lie group, two results of Antezana, Massey, and Stojanoff: Given 0 < λ < 1, (a) the limit points of the sequence {∆λ (X)}m∈N are normal, and (b) lim m→∞‖∆ m λ (X)‖ = r(X), where ‖X‖ is the spectral norm and r(X) is the spectral radius of X ∈ Cn×n and ∆λ(X) is the λ-Aluthge transform of X.

Some authors studied the matrix ] [ ij a A  which entries depend on j i, . In [6] Solak and Bahsi studied the matrix of the form ] [ ij b B  where 1 ) , max(    j i a bij . They studied some properties of this matrix. Bozkort in [3] computed the spectral norms of the matrices related with integer sequences. In [2] Solak and Bozkort determined bounds for the spectral and p l norm of Cauchy-...