Feature selection is an essential problem in many fields such as computer vision. In this paper we introduce a supervised feature selection criterion based on Partial Least Squares regression (PLS). We find an optimal feature subset by applying the theory of Optimal Experiment Design to optimize the eigenvalues of the loadings matrix obtained from PLS. Since PLS extracts components such that th...

A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer m ≥ 2, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least −m, diameter at least three and intersection number c2 ≥ 2.

We classify the distance-regular Cayley graphs with least eigenvalue −2 and diameter at most three. Besides sporadic examples, these comprise of the lattice graphs, certain triangular graphs, and line graphs of incidence graphs of certain projective planes. In addition, we classify the possible connection sets for the lattice graphs and obtain some results on the structure of distance-regular C...

We prove the following conjecture recently formulated by Jakobson, Nadirashvili and Polterovich [12]: For any Riemannian metric g on the Klein bottle K one has λ1(K, g)A(K, g) ≤ 12πE(2 √ 2/3), where λ1(K, g) and A(K, g) stand for the least positive eigenvalue of the Laplacian and the area of (K, g), respectively, and E is the complete elliptic integral of the second kind. Moreover, the equality...

The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact constraint and as such, is a convex problem with polynomial time complexity. Moreover, as a main pratical advantage of this relaxation over the standard Sem...

This paper presents a new computational approach for solving the Regularized Total Least Squares problem. The problem is formulated by adding a quadratic constraint to the Total Least Square minimization problem. Starting from the fact that a quadratically constrained Least Squares problem can be solved via a quadratic eigenvalue problem, an iterative procedure for solving the regularized Total...

We continue our investigation of graphsG for which the least eigenvalue λ(G) is minimal among the connected graphs of prescribed order and size. We provide structural details of the bipartite graphs that arise, and study the behaviour of λ(G) as the size increases while the order remains constant. The non-bipartite graphs that arise were investigated in a previous paper [F.K. Bell, D. Cvetković...

An inverse eigenvalue problem where a matrix is to be constructed from some or all of its eigenvalues may not have a real valued solution at all An approximate solution in the sense of least squares is sometimes desirable Two types of least squares problems are formulated and explored in this paper In spite of their di erent appearance the two problems are shown to be equivalent Thus one new nu...

Let S be a certain set of graphs. A graph is called a minimizing graph in the set S if its least eigenvalue attains the minimum among all graphs in S . In this paper, we determine the unique minimizing graph in Gn, where Gn denotes the set of connected graphs of order n with cut vertices.