## 3.4      Nearest Neighbor Analysis

### Introduction

Nearest neighbour analysis examines the distances between each point and the closest point to it (Fotheringham, et al 1994 and Wulder, 1999). The Nearest neighbour is a method of exploring pattern in Locational data by comparing graphically the observed distribution functions of event-to-event or random point-to-event nearest neighbour distances, either with each other or with those that may be theoretically expected from various hypothesized models, in particular that of spatial randomness (Upton, 1985), i.e. it describe distribution of points according to their spacing.

### The Nearest neighbour index

The Nearest neighbour index measures the degree of spatial dispersion in the distribution based on the minimum of the inter-feature distances (Chou, 1997), i.e. it is based on the distance between adjacent point features. Such that the distance between point features in a clustered pattern will be smaller than in a scattered (uniform) distribution with random falling between the two. The equation for the nearest neighbour is computed through the following steps

 Ad = (åidi)/n. di is the distance from point i to its nearest neighbour; Ad is the average of nearest neighbour distance of the point pattern; n is the total number of points in the chosen map area. Ed=1/2sqr(A/n) Expresses the expected value of the average nearest distance; A denotes the map area NNI=Ad/Ed Equation for the nearest neighbour index, it is defined as the ratio of Ad to Ed

The values of NNI range between two theoretical extremes, 0 and 2.1491. When all the points in a pattern fall at the same location, the pattern represents the theoretical extreme of spatial concentration, in this case, Ad = 0 and NNI = 0. The more closely the points are clustered together, the closer to 0 NNI will be, since the average nearest neighbour distance decreases. The closer NNI gets to 1, the more randomly spaced the points are. The value of NNI approaches 2.1491 for perfectly uniformly spaced points. Hence, the closer NNI is to 2.1491, the more uniformly spaced the data are.

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