Recently, a novel flow for computing the eigenvectors associated with the smallest eigenvalues of a symmetric but not necessarily positive definite matrix was introduced. This meant that the eigenvectors associated with the smallest eigenvalues could be found simply by reversing the sign of the matrix. The current paper derives a cost function and the corresponding negative gradient flow which ...

We present an approach to the determination of the stabilizing solution of Lur’e matrix equations. We show that the knowledge of a certain deflating subspace of an even matrix pencil may lead to Lur’e equations which are defined on some subspace, the so-called “projected Lur’e equations.” These projected Lur’e equations are shown to be equivalent to projected Riccati equations, if the deflating...

As a classical subspace learning method, Probabilistic PCA (PPCA) has been extended to several bilinear variants for dealing with matrix observations. However, they are all based on the Tucker model, leading to a restricted subspace representation and the problem of rotational ambiguity. To address these problems, this paper proposes a bilinear PPCA method named as Probabilistic Rank-One Matrix...

Subspace clustering is the problem of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This type of structure occurs naturally in many applications ranging from bioinformatics, image/text clustering to semi-supervised learning. The companion paper [3] shows that robust and tractable subspace clustering is possible with minimal re...

We show that noncommutative Lp-spaces satisfy the axioms of the (nonunital) operator system with a dominating constant 2 1 p . Therefore, noncommutative Lpspaces can be embedded into BpHq 2 1 p -completely isomorphically and complete order isomorphically. 1. Introducton A unital involutive subspace of BpHq had been abstractly characterized by Choi and Effros [CE]. Their axioms are based on obse...

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

Subspace fitting has become a well known method to identify FIR Single Input Multiple Output (SIMO) systems, only resorting to second-order statistics. The main drawback of this method is its computational cost, due to the eigendecomposition of the sample covariance matrix. We propose a scheme that solves the subspace fitting problem without using the eigendecomposition of the cited matrix. The...

We consider the problem of clustering incomplete data drawn from a union of subspaces. Classical subspace clustering methods are not applicable to this problem because the data are incomplete, while classical low-rank matrix completion methods may not be applicable because data in multiple subspaces may not be low rank. This paper proposes and evaluates two new approaches for subspace clusterin...