UNIVERSITY OF BENIN, NIGERIA

DEPT: GEOGRAPHY AND REGIONAL PLANNING

NAME: OSAZUWA OSAZE SUNDAY

MATRICULATION NUMBER: SSC1205599

LEVEL: 300L

COURSE CODE: GEO 326

COURSE TITLE: ADVANCE QUANTITATIVE

TECHNIQUES

TITLE: NEAREST NEIGHBORS ANALYSIS

20, JULY

INTRODUCTIONGeography deals with the study of spatial distribution in space. This is to say that

although phenomena occur in individual location they are distributed in space forming a

pattern. Phenomena do not only locate in space but also interacts with one another.

Knowing the pattern of occurrence that some particular phenomena in space is a major

geographical problem which required analysis. Thus to know the pattern of occurrence of

phenomena in space we study the relationship between individual phenomena using

various methods. An example of the method used in the search for pattern in landscape of

geographical area is the nearest neighbor analysis. The question then arise 'what is nearest

neighbor analysis?'.

NEAREST NEIGHBOR ANALYSISGeographers for a long time have been interest in how features are distributed in

space and this interest made them study the patterns of the phenomena in space which is

known as pattern analysis. Pattern analysis in this case may be defined or described as the

mean distance or distances between an array of points in space. The aspect of pattern

analysis which is usually used un the point pattern analysis of which the nearest neighbor

is a part. Different scholars has defined nearest neighbor analysis and one of this

definition was given by Upton. Nearest Neighbor Analysis according to Upton (1985), is

a method of exploring pattern in locational data by comparing graphically the observed

distribution of functions of event-to-event or random point-to-event nearest neighbor

distances, either with each other or with those that may be theoretically expected from

various hypothesized models, in particular that of spatial randomness. That is Nearest

Neighbor Analysis uses the distance between each location (points) in a layer to

determine if the point pattern are clustered, random or regular.

The Nearest Neighbor Analysis technique was devised by a botanist who wished

to describe and provide a quantitative description of the patterns of plant distribution

especially the distribution of trees. The early beginnings of nearest neighbor analysis can

be attributed to the pioneering works of P.J Clark and F.C Evans in 1954 is their attempt

to describe and analyze the pattern and distribution of trees and other plants in the forest.

However since geographers are interested in the study of the pattern of distribution of

phenomenon over space the techniques of the nearest neighbor has since been adapted for

geographical studies. As such the nearest neighbor analysis has since evolved to it been

used to identify a tendency towards or calculate the degree of nucleation (clustering) or

dispersion of phenomena in space. The nearest neighbor analysis can be used to analyze

the distribution of schools, hospitals, buildings, settlement and a myriad of physical

features such as wells, springs mountains, hills etc on the earth surface.

The nearest neighbor analysis since its introduction into geographical studies has

found more application in settlement system analysis. On maps settlements often appears

as dots. Dot patterns are difficult to describe even though they are highly useful in

portraying distribution of phenomenon in geographical studies. Nearest neighbor analysis

attempt to find the order of arrangement of this settlements on the map. This attempts to

measure the distributions according to whether they are clustered, random or regular. As

such settlement are expected to be either clustered, random or regular. Nearest neighbor

analysis allows us to compare and contrast between distribution and also help to monitor

and compare changes occurring over a period of time.

DESCRIPTION OF NEAREST NEIGHBOR STATISTICS

As I have said before nearest neighbor analysis attempts to measure distribution

according to whether they are clustered, random or regular but these pattern appear on

map in such a way that they are judged or analyze subjectively using guess work in the

course of analyzing the map manually. These is where the nearest neighbor statistic

comes in. The nearest neighbor statistics is the method or formula used in nearest

neighbor analysis and is a means of standardizing the assessment of a distribution either

on map or ground objectively that is using the scientific method and calculations to

determine whether phenomenon are clustered, random or regular.

The nearest neighbor statistics produce a figure (expressed as Rn) which measures

the extent to which a particular distribution on map or land is clustered, random or

regular. After calculations the nearest neighbor formula will produce results between

zero(0) and 2.15 where the patterns of the distribution forms a continuum. These pattern

are explained below for clarity.

CLUSTERED PATTERN: A cluster patterns occur when all distribution (in this

case represented by dot) converge closely to a point. Another name for clustered

distribution is nucleated distribution. For example in settlements, nucleated

settlements are made up of buildings clustered together in an area. These areas are

usually the meeting point of transport routes, such as rivers, roads and railway lines.

On the continuum a perfectly clustered distribution will have an Rn value of zero (0)

but since there are no perfectly clustered distribution the Rn values tend to be above 0

but below one(1).

RANDOM PATTERN: A distribution is termed random when it does not show a

pattern at all. In this situation the Rn value will be equal to 1.0. Another name for

random pattern is dispersed pattern. For example in settlement analysis a

random/dispersed settlement patterns are made up of individual buildings scattered

over a wide area. These buildings may be separated by large open spaces, farmlands,

forests or grasslands. The usual pattern of settlement is one which is predominantly

random with a tendency either towards clustering or regularity.

REGULAR PATTERN: When distribution exist in a perfectly uniform manner in

space or on the map we say the distribution has a regular pattern. Although a perfectly

regular pattern is not possible in reality but assuming it exist in reality, the Rn value

on the continuum will be 2.15 which will then be explained that each dot (settlement)

are equidistant from all its neighbors.

On the nearest neighbor statistics continuum the patterns above are arrange on the

continuum in such a way as shown below with zero(0) representing the clustered

pattern, one(1) representing the random pattern while 2.15 on the continuum

represents the regular patter

.

From the graph above the value of Rn=1.27 shows a distribution that is random but

tending toward the regular.

METHODOLOGY FOR CALCULATIONS OF THE NEAREST NEIGHBOR STATISTICS

The nearest neighbor formula used to calculate the nearest neighbor is given as:

Rn = 2đ√n/A

Where

Rn = is the nearest neighbor value describing the distribution.

đ = this is the mean distance between the nearest neighbors.(km)

n = this represent the total number of distribution(points) in the study area.

A = This represents the study area(km²).

The procedure to follow when calculating the nearest neighbor statistics is as follows

The first thing to do if one wants to calculate the nearest neighbor statistics is to first

locate the area where the distribution (houses in a settlement or settlements in a town

or any other phenomenon of interest) or get the map showing the distribution.

After getting the location or map of the distribution the next step is to find the mean

distance đ which is usually a straight line measure of the distance between each

phenomenon or settlement and its nearest neighbors. The mean distance is gotten by

calculating the sum if all the distance gotten and dividing it by the total number of the

distribution (points) under study. Using the formular below:

đ =Σd/nWhere:

Σ = sigma means to sum up the values of distance.

d = distance of phenomenon from the nearest neighbor.

n = total number of phenomenon.

The third procedure in computing nearest neighbor statistics is to determine the area

of the map or the area the phenomenon is occupying by multiplying the length by the

breath of the location in km².

The last step is to calculate the nearest neighbor statistics by inputting or substituting

all the elements unto the nearest neighbor formula and computing to the the nearest

neighbor value.

LIMITATIONS AND PROBLEMS OF NEAREST NEIGHBOR ANALYSIS

LIMITATIONS

Although the nearest neighbor has been variously applied and found to be useful in

geographical studies, care must be taken when using the technique. However the

following limitations affects the usefulness of the technique.

The first of the limitations is that of the size of the area chosen. If two regions are

under observation in nearest neighbor analysis, the two regions must have similarly

size if the comparison between the two regions is to be valid.

The size of the area of the chosen distribution must not be too large as this will reduce

or lower the Rn values(as it exaggerates the degree of clustering of the distributions)

nor must the area be be to small as this will increases the Rn values (as it exaggerates

the level of regularity).

The boundaries of the area under study is also critical most especially where the area

under study is part of a larger area or region. Hence delineating or choosing of such

boundaries must be done carefully. This kind of problem is called the area modification problem.

PROBLEMSAs useful as nearest neighbor analysis is its has some major problems of which the

following are common.

When carrying out a nearest neighbor analysis of a valley where the nearest neighbors

are separated by a river, distortions are likely to occur in such analysis.

The choice of distribution or features to be included in the nearest neighbor a

statistics race rises a lot of questions for example what size of area a acceptable, are

we to includes farmsteads or hamlets.

The nearest of a point or features maybe outside a study area.

How to determine the center of a settlement is a subjective decisions.

REFERENCESWaug .D (1995), geography an integrated approach, Thomas and son's limited

http://www.hbp.usm.my/Thesis/HeritageGIS/master%5Cthesis%5C3-Nearest

%20neighbor%20analysis.htm

http://ceadserv1.nku.edu/longa//geomed/ppa/doc/html/ppa.html

https://en.m.wikipedia.org/wiki/Nearest_neighbor_search?

_e_pi_=7%2CPAGE_ID10%2C5837470691

http://geographyfieldwork.com/nearest_neighbour_analysis.htm