DeepAI AI Chat
Log In Sign Up

Deriving Two Sets of Bounds of Moran's Index by Conditional Extremum Method

by   Yanguang Chen, et al.

Moran's index used to be considered to come between -1 and 1. However, in recent years, some scholars argued that the boundary value of Moran's index is determined by the minimum and maximum eigenvalues of spatial weight matrix . This paper is devoted to exploring the bounds of Moran's index from a new prospective. The main analytical processes are quadratic form transformation and the method of finding conditional extremum based on quadratic form. The results show that there are at least two sets of boundary values for Moran's index. One is determined by the eigenvalues of spatial weight matrix, and the other is determined by the quadratic form of spatial autocorrelation coefficient (-1<Moran's I<1). The intersection of these two sets of boundary values gives four possible numerical ranges of Moran's index. A conclusion can be reached that the bounds of Moran's index is determined by size vector and spatial weight matrix, and the basic boundary values are -1 and 1. The eigenvalues of spatial weight matrix represent the maximum extension length of then eigenvector axes of n geographical elements at different directions.


page 1

page 2

page 3

page 4


Spatial Autocorrelation Equation Based on Moran's Index

Based on standardized vector and globally normalized weight matrix, Mora...

On the degree-Kirchhoff index, Gutman index and the Schultz index of pentagonal cylinder/ Möbius chain

The degree-Kirchhoff index of a graph is given by the sum of inverses of...

Approximation of the zero-index transmission eigenvalues with a conductive boundary and parameter estimation

In this paper, we present a Spectral-Galerkin Method to approximate the ...

Derivation of an Inverse Spatial Autoregressive Model for Estimating Moran's Index

Spatial autocorrelation measures such as Moran's index can be expressed ...

On equipathenergetic graphs and new bounds on path energy

The path eigenvalues of a graph G are the eigenvalues of its path matrix...

Computation of Laplacian eigenvalues of two-dimensional shapes with dihedral symmetry

We numerically compute the lowest Laplacian eigenvalues of several two-d...

Hands-off Model Integration in Spatial Index Structures

Spatial indexes are crucial for the analysis of the increasing amounts o...