Bounds for the Distance to the Nearest Correlation Matrix

Bounds for the Distance to the Nearest Correlation Matrix

In a wide range of practical problems correlation matrices are formed in such a way that, while symmetry and a unit diagonal are assured, they may lack semidefiniteness. We derive a variety of new upper bounds for the distance from an arbitrary symmetric matrix to the nearest correlation matrix. The bounds are of two main classes: those based on the eigensystem and those based on a modified Cho...

Bounds for the Componentwise Distance to the Nearest Singular Matrix

The normwise distance of a matrix A to the nearest singular matrix is well known to be equal to ‖A‖/cond(A) for norms being subordinate to a vector norm. However, there is no hope to find a similar formula or even a simple algorithm for computing the componentwise distance to the nearest singular matrix for general matrices. This is because Rohn and Poljak [7] showed that this is an NP -hard pr...

Computing the Nearest Correlation Matrix

Nearest Neighbour Distance Matrix Classification

A distance based classification is one of the popular methods for classifying instances using a point-to-point distance based on the nearest neighbour or k-NEAREST NEIGHBOUR (k-NN). The representation of distance measure can be one of the various measures available (e.g. Euclidean distance, Manhattan distance, Mahalanobis distance or other specific distance measures). In this paper, we propose ...

Structure method for solving the nearest Euclidean distance matrix problem

*Correspondence: [email protected] Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia Abstract A matrix with zero diagonal is called a Euclidean distance matrix when the matrix values are measurements of distances between points in a Euclidean space. Because of data errors such a matrix may not be exactly Euclidean and it is desira...