Superregular matrices are a class of lower triangular Toeplitz matrices that arise in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that no submatrix has a zero determinant unless it is trivially zero due to the lower triangular structure. In this paper, we discuss how superregular matrices may be used to cons...

Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...

The objective of this paper is to design optimal signature matrices for binary inputs. For the determination of such optimal codes, we need certain measures as objective functions. The sum-channel capacity and Bit Error Rate (BER) measures are typical methods for the evaluation of signature matrices. In this paper, in addition to these measures, we use distance criteria to evaluate the optimali...

In this paper we present an efficient approach for comparing protein structures based on distance matrices. In the first step, the distance matrices are calculated and normalized in order to avoid the scaling distortion. Further, versions from these matrices are saved on different scales and for each two protein structures we compare their respective equal-scaled matrices. Thus, we avoid the pr...

Biologists frequently summarize multivariate data from n populations by computing some measure of distance between populations. The problem then arises of comparing two such pairwise distance matrices based on different characters. A permutation test for correlation between distance matrices is proposed. This test, based on Kendall's tau statistic, is compared to Pearson's product-moment and Sp...

It has been postulated that existing species have been linked in the past in a way that can be described using an additive tree structure. Any such tree structure reflecting species relationships is associated with a matrix of distances between the species considered which is called a distance matrix or a tree metric matrix. A circular order of elements of X corresponds to a circular (clockwise...

Over the past few years, symmetric positive definite matrices (SPD) have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the two most widely-used measures are affine-invariant distance and log-Euclidean distance. This is because these two measures are true geodesic distances induced...

It has been postulated that existing species have been linked in the past in a way that can be described using an additive tree structure. Any such tree structure reflecting species relationships is associated with a matrix of distances between the species considered and called a distance matrix or a tree metric matrix. A circular order of elements of X corresponds to a circular (clockwise) sca...

The set of Euclidean distance matrices has a well-known representation as a convex cone. The problems of representing the group averages of K distance matrices are discussed, but not fully resolved, in the context of SMACOF, Generalized Orthogonal Procrustes Analysis and Individual Differences Scaling. The polar (or dual) cone representation, corresponding to inner-products around a centroid, i...

This paper describes a structure tensor based method to characterize activity in videos. Based on the relationship observed between structure tensors and covariance matrices, the distance between structure tensor matrices is computed by either a generalized eigenvalue or a Riemannian manifold. A histogram of distances between structure tensor matrices is constructed to serve as a signature for ...