Let G be a weighted graph with Laplacian matrix L and signless Laplacian matrix Q. In this note, block representations for the group inverse of L and Q are given. The resistance distance in a graph can be obtained from the block representation of the group inverse of L.

Given a symmetric matrix what is the nearest correlation matrix, that is, the nearest symmetric positive semidefinite matrix with unit diagonal? This problem arises in the finance industry, where the correlations are between stocks. For distance measured in two weighted Frobenius norms we characterize the solution using convex analysis. We show how the modified alternating projections method ca...

In this paper we consider weighted nonnegative matrix factorizations and we show that the popular algorithms of Lee and Seung can incorporate such a weighting. We then prove that for appropriately chosen weighting matrices, the weighted Euclidean distance function and the weighted generalized Kullback-Leibler divergence function are essentially identical. We finally show that the weighting can ...

Volumetric, slice-based, 3-D atlases are invaluable tools for understanding complex cortical convolutions. We present a simple scheme to convert a slice-based atlas to a conceptual surface atlas that is easier to visualize and understand. The key idea is to unfold each slice into a one-dimensional vector, and concatenate a succession of these vectors--while maintaining as much spatial contiguit...

The spatial weighting matrix is very important to overview of the relationship between one location another in regression. In this study, authors compare queen contiguity and rook SAR SEM models stunting cases Bone Bolango Regency, Gorontalo Province. variables used are number IDL, percentage LBW, amount proper sanitation, exclusively breastfed babies, poor people. purpose study was determine f...

We show that Boolean matrix multiplication, computed as a sum of products of column vectors with row vectors, is essentially the same as Warshall’s algorithm for computing the transitive closure matrix of a graph from its adjacency matrix. Warshall’s algorithm can be generalized to Floyd’s algorithm for computing the distance matrix of a graph with weighted edges. We will generalize Boolean mat...

spatial distribution of thermal regions is dependent on local factors and circulation patterns in long terms. recognition of spatial distribution of temperature in geographical regions could be help on planning and environmental policies. the aim of this paper is recognition and detachment of thermal regions in iran. for this object, maximum daily temperature data have been provided using 620 s...

Making an informed decision with regards to a suitable business location or site selection for organizations is becoming challenging for business decision makers globally; and even more challenging in business environment that are saddled with uncertainties. The continues raise of multiple criteria variation of site preferences has also necessitated the application of advanced decision making t...

We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs [5], it takes into account all paths between vertices. Formally, it is defined as d(i, j) = qii+qjj−qij−qji [11], where qij is the (i, j)-entry of the relative forest accessibility matrix Q(ε) = (I + εL)−1, L is the Laplacian matrix of the (weighted) (multi)graph, and ε is a positive...

We propose a new graph metric and study its properties. In contrast to the standard distance in connected graphs [5], it takes into account all paths between vertices. Formally, it is defined as d(i, j) = qii+qjj−qij−qji [11], where qij is the (i, j)-entry of the relative forest accessibility matrix Q(ε) = (I + εL)−1, L is the Laplacian matrix of the (weighted) (multi)graph, and ε is a positive...