2012

Analisis Spasial

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Deskripsi & AnalisisKonsep Proses, Pola &

AnalisisStatistik Deskriptif untuk Distribusi Spasial

Statistik Sentrografik

Konsep Utama, Spasial Spesial

Jarak (Distance)

Kedekatan / Ketetanggan (Adjacency/ neighborhood)

Interaksi (Interaction)

A

• Besarnya pemisahan spasial

• Jarak Euclidean (garis lurus) hanya perkiraan

• Nominal / biner (0,1) setara dengan jarak

• Tingkat Kedekatan : 1st, 2nd, 3rd ketetanggaan (nearest neighbor)

• Kekuatan hubungan antar entitas

• Fungsi terbalik dari jarak

Ketetanggan Spasial berdasarkan Kedekatan

Dasar:

Berbagi Batas atau Point (Sharing a boundary)

HexagonalTak Beraturan(Irregular)

Raster persegi

Kedekatan 1st and 2nd order

hexagonrook queen

1st

order

2nd

order

Deskripsi & Analisis

Deskripsi

GIS banyak digunakan o/ Pemerintah & Swasta untuk menggambarkan (describe) the real world

Contoh: Mengelola pipa PDAM &

saluran air

Mengelola sumberdaya lahan

GIS pada akhirnya didesain untuk Membangun Database

Spasial u/ menggambarkan realita dan pengelolaannya

Deskripsi & Analisis

Analisis

Mencoba untuk memahami proses yang menyebabkan/ membuat pola di dunia nyata

Memahami proses: Membantu dalam

pekerjaan

Membuat keputusan yang tepat

Membantu memahami fenomena

Merupaan peran Ilmu pengetahuan

Apakah lokasi dari industri Software berbeda dari industri telekomunikasi...?

Kasus ini, dapat menggunakan “centrographic statistics” u/ menyelesaikan pertanyaan tsb

Analisis Spasial bertujuan: Identifikasi dan

menggambarkan pola

Pola titik secara jelas Berkelompok (clustered)

(Titik2 dalam beberapa “Grup”)

• Identifikasi dan memahami proses

Aksessibilitas Transportasi

Aglomerasi ekonomi * dari berbagi ide, akses ke tenaga kerja terampil, akses ke layanan bisnis.

*penghematan biaya untuk perusahaan2 pada lokasi yang sama

Proses, Pola & AnalisisProses menjalankan sistem menghasilkan

Pola

Analisis Spasial bertujuan: Identifikasi dan menggambarkan Pola

Identifikasi dan memahami proses

CreateProses Pola/Patterns

(or cause)

Proses, Pola & AnalisisTerkadang, kita tidak dapat mengamati

(melihat) proses, jadi kita harus menyimpulkan (menebak ...?) proses dengan mengamati pola

CreateProses Pola

(or “cause”)

MendugaNo

Yes

Tingkatan /Level Analisis Spasial (Berdasarkan Tingkat Kecanggihan)

1.Deskripsi Data Spasial

2.Analisis Data Spasial Eksplorasi (ESDA)

3.Analisis Statistik Spasial and Uji Hipotesis

4.Permodelan Spasial dan Prediksi

More difficult,but more useful!(more powerful)

Analisis Spasial Level 1

1.Deskripsi Data Spasial Focus is on describing the

world,

and representing it in a digital

format

- computer map

- computer database

Uses classic GIS capabilities

- buffering, map layer overlay

- spatial queries & measurement

Analisis Spasial Level 2

2. Exploratory Spatial Data Analysis (ESDA): Mencari pola dan penjelasan (yang mungkin)

GeoVisualization melalui perhitungan dan tampilan Centrographic statistics

Calculation of CentrographicStatistics

Analisis Spasial Level 3

3.Analisis Statistik Spasial dan Uji Hipotesis data “diharapkan” atau “tidak diharapkan” bergantung

pada model statistik,

biasanya dari proses acak (probabilitas)

Uji Hipotesis:

- Pola Titik (point patterns)

- Termasuk data Poligon (polygon data)

Uji apakah industri software & industri telekomunukasi memiliki pola:

cluster (berpola) atau “acak” (todak berpola)

0-1.96

2.5%

1.96

2.5%

4.Permodelan Spasial: Prediksi Membangun model2 (proses) u/

Memprediksi hasil spasial (pola spasial)

Notice how the density of points (number per square km) decreases as we move away from the highway.

We can construct regression models to predict location patterns.

Analisis Spasial Level 4

Distance from highway

Density of points

Density of points = f (distance from highway)

However, for spatial data, we need special:Spatial regression models

The first example of Spatial Analysis

John Snow’s maps of cholera in 1850s London

Was it ESDA or hypothesis testing?

Did he discover the association between water and cholera after drawing the map: ESDA

Did he draw the map in order to prove the association: using a map for hypothesis testing

Maps are good—but more is needed!

A. Is this clustered? B. Is this clustered?

Source: R & Y, p. 5

We must test rigorously using spatial analysis methods.

Not just look and guess

Why is this important?

? Is it clustered?

We must measure and test --not just look and guess! Because that is science!

Because that is how earth management decisions must be made!

Statistik Deskriptif untuk Distribusi Spasial

Review Statistik Descriptif Standar Statistik Sentrografik untuk Data Spasial

Mean Center, Centroid, Standard Distance Deviation, Standard Distance Ellipse, Density Kernel Estimation, Mapping

1. Statistik Deskriptif Concerned with obtaining summary measures to describe

a set of data

Calculate a few numbers to represent all the data

we begin by looking at one variable (“univariate”)Later , we will look at two variables (bivariate)

Three types: Measures of Central Tendency

Measures of Dispersion or Variability

Frequency distributions

Analisis Statistik Standar :A Quick Review

Statistik Deskriptif StandarCentral Tendency

Central Tendency: single summary measure for one variable:

1.mean (Rata2)

2.median (Nilai Tengah)

- 50% larger and 50% smaller

- rank order data and select middle number

3. mode (most frequently occurring)

Formula for mean

These may be obtained in ArcGIS by:- opening a table, right clicking on column heading, and selecting Statistics- going to ArcToolbox>Analysis>Statistics>Summary Statistics

Kalkulasi mean and median

Mean 296.15 / 34 = 8.71

Median(7.69 + 7.8)/2 = 7.75(there are 2 “middle

values”)

Note: data for Taiwan is included

ADMIN_NAME Illiteracy-Prcnt Rank orderBeijing 3.11 1Liaoning 3.48 2Tianjin 3.52 3Taiwan 3.9 4Shanghai 3.97 5Guangdong 4.02 6Heilongjiang 4.16 7Shanxi 4.42 8Jilin 4.44 9Xinjiang 4.64 10Hebei 4.83 11Guangxi 5.61 12Hunan 5.87 13Jiangxi 6.49 14Hong Kong 6.5 15Henan 7.36 16Hubei 7.69 17Chongqing 7.8 18Shandong 7.96 19Jiangsu 8.05 20Nei Mongol 8.14 21Shaanxi 8.19 22Hainan 8.65 23Macao 8.7 24Zhejiang 9.36 25Ningxia 10.09 26Sichuan 10.24 27Fujian 10.38 28Yunnan 13.29 29Anhui 14.49 30Guizhou 14.58 31Qinghai 16.68 32Gansu 17.77 33Xizang 37.77 34

Sum 296.15

Statistik Deskriptif StandarVariability or Dispersion Variance

rata-rata dari skor penyimpangan kuadrat atau ukuran keberagaman data,

Semakin besar angka varians maka semakin beragamlah data yang kita miliki

Standard Deviation (square root of variance) ukuran dispersi yang paling banyak dipakai

These may be obtained in ArcGIS by:- opening a table, right clicking on column heading, and selecting Statistics- going to ArcToolbox>Analysis>Statistics>Summary Statistics

Formula for variance (populasi)

2)(1

2å=

-

N

XXn

ii ]/)[(

1

2å=å

=-

N

NXXn

ii

Definition Formula Computation Formula

KalkulasiVariance dan

Standard Deviation

Variance from Definition Formula

1361.370/34 = 40.04

Variance from Computation Formula[3940.924 – (296.15 * 296.15)/34]/34

=40.04

Standard Deviation = 40.04

=6.33

Note: data for Taiwan is included

ADMIN_NAME

Illiteracy-Prcnt

(X - Xmean)(X-Xmean)

squared

Anhui 14.49 5.780 33.40500009

Beijing 3.11 -5.600 31.3632942

Fujian 10.38 1.670 2.787917734

Gansu 17.77 9.060 82.07827067

Guangdong 4.02 -4.690 21.99885891

Guangxi 5.61 -3.100 9.611823616

Guizhou 14.58 5.870 34.45344715

Hainan 8.65 -0.060 0.003635381

Hebei 4.83 -3.880 15.05668244

Heilongjiang 4.16 -4.550 20.70517656

Henan 7.36 -1.350 1.823294204

Hubei 7.69 -1.020 1.041000087

Hunan 5.87 -2.840 8.067270675

Nei Mongol 8.14 -0.570 0.325235381

Jiangsu 8.05 -0.660 0.435988322

Jiangxi 6.49 -2.220 4.929705969

Jilin 4.44 -4.270 18.23541185

Liaoning 3.48 -5.230 27.35597656

Ningxia 10.09 1.380 1.903588322

Qinghai 16.68 7.970 63.51621185

Shaanxi 8.19 -0.520 0.270705969

Shandong 7.96 -0.750 0.562941263

Shanghai 3.97 -4.740 22.47038832

Shanxi 4.42 -4.290 18.40662362

Sichuan 10.24 1.530 2.340000087

Taiwan 3.9 -4.810 23.1389295

Tianjin 3.52 -5.190 26.93915303

Xizang 37.77 29.060 844.466506

Xinjiang 4.64 -4.070 16.5672942

Yunnan 13.29 4.580 20.97370597

Zhejiang 9.36 0.650 0.422117734

Chongqing 7.8 -0.910 0.828635381

Hong Kong 6.5 -2.210 4.885400087

Macao 8.7 -0.010 0.000105969

Sum 296.15 0.000 1361.370297

Mean 8.710294118 Variance 40.04030285StanDev 6.3277

Classic Descriptive Statistics: UnivariateFrequency distributions

In ArcGIS, you may obtain frequency counts on a categorical variable via: --ArcToolbox>Analysis>Statistics>Frequency

under 15

years

15 to 29

years

30 to 44

years

45 to 59

years

60 to 74

years

75 and older

0

10000

20000

30000

40000

50000

60000

70000

Series1

Often represented by the area under a frequency curve

US population, by age group: 50 million people age 45-59 (data for 2000)

Source:http://www.census.gov/compendia/statab/US Bureau of the Census: Statistical Abstract of the US

under 15 years

15 to 29 years

30 to 44 years

45 to 59 years

60 to 74 years

75 and older

0

10000

20000

30000

40000

50000

60000

70000

Series1

This area represents 100% of the data

100%

Caution—these values are incorrect!

Why?

Incorrect to calculate mean for percentages Each percentage has a different base population

Should calculate weighted mean

wi =population of each

province

Very common error in GIS because we use aggregated data frequently

n

ii

n

iii

w

xw

1

1X

Correct Values! Unweighted mean = 8.7

Weighted mean = 7.75

Weighted mean is smaller. Why?

The largest provinces Highest rates in

have lower illiteracy small provinces

ADMIN_NAME Illiteracy-Prcnt Pop2008

Guangdong 4.02 95,440,000

Henan 7.36 94,290,000

Shandong 7.96 94,172,300

ADMIN_NAME Illiteracy-Prcnt Pop2008

Ningxia 10.09 6,176,900

Qinghai 16.68 5,543,000

Xizang (Tibet) 37.77 2,870,000

Calculation of weighted mean

ADMIN_NAME Illiteracy-Prcnt Pop2008 x*wAnhui 14.49 61,350,000 888961500Beijing 3.11 22,000,000 68420000Fujian 10.38 36,040,000 374095200Gansu 17.77 26,281,200 467016924Guangdong 4.02 95,440,000 383668800Guangxi 5.61 48,160,000 270177600Guizhou 14.58 37,927,300 552980034Hainan 8.65 8,540,000 73871000Hebei 4.83 69,888,200 337560006Heilongjiang 4.16 38,253,900 159136224Henan 7.36 94,290,000 693974400Hubei 7.69 57,110,000 439175900Hunan 5.87 63,800,000 374506000Nei Mongol 8.14 24,137,300 196477622Jiangsu 8.05 76,773,000 618022650Jiangxi 6.49 44,000,000 285560000Jilin 4.44 27,340,000 121389600Liaoning 3.48 43,147,000 150151560Ningxia 10.09 6,176,900 62324921Qinghai 16.68 5,543,000 92457240Shaanxi 8.19 37,620,000 308107800Shandong 7.96 94,172,300 749611508Shanghai 3.97 19,210,000 76263700Shanxi 4.42 34,106,100 150748962Sichuan 10.24 81,380,000 833331200Taiwan 3.9 23,140,000 90246000Tianjin 3.52 11,760,000 41395200Xizang 37.77 2,870,000 108399900Xinjiang 4.64 21,308,000 98869120Yunnan 13.29 45,430,000 603764700Zhejiang 9.36 51,200,000 479232000Chongqing 7.8 31,442,300 245249940Hong Kong 6.5 7,003,700 45524050

Macao 8.7 542,400 4718880

Sum 296.15 1347382600 10445390141

Unweighted mean 296.15 / 34 = 8.71

Weighted mean10,445,390,141 /

1,347,382,600

= 7.75 Note: we should also calculate a weighted standard deviation

Statistik SentrografikStatistik Deskriptif untuk Distribusi

spasialMean Center

CentroidStandard Distance Deviation

Standard Distance EllipseDensity Kernel Estimation

Statistik SentrografikMeasures of Centrality Measures of Dispersion

Mean Center -- Standard Distance

Centroid -- Standard Deviational Ellipse

Weighted mean center

Center of Minimum Distance

Two dimensional (spatial) equivalents of standard descriptive statistics for a single-variable (univariate).

Used for point data May be used for polygons by first obtaining the centroid

of each polygon

Best used to compare two distributions with each other 1990 with 2000

males with females

Mean CenterSimply the mean of the X and the

mean of the Y coordinates for a set of points

Sum of differences between the mean X and all other Xs is zero (same for Y)

Minimizes sum of squared distances between itself and all points

Distant points have large effect:Values for Xinjiang will have larger effect

2min iCd

Provides a single point summary measure for the location of a set of points

The equivalent for polygons of the mean center for a point distribution

The center of gravity or balancing point of a polygon

if polygon is composed of straight line segments between nodes, centroid given by “average X, average Y” of nodes

(there is an example later)

Calculation sometimes approximated as center of bounding box Not good

By calculating the centroids for a set of polygons can apply Centrographic Statistics to polygons

Centroid

Centroids for Provinces of China

Centroids for Provinces of China

Warning: Centroid may not be inside its polygon

For Gansu Province, China, centroid is within neighboring province of Qinghai

• Problem arises with crescent- shaped polygons

Weighted Mean CenterProduced by weighting each X and Y

coordinate by another variable (Wi)

Centroids derived from polygons can be weighted by any characteristic of the polygon For example, the population of a province

n

ii

n

iii

w

yw

1

1Y

n

ii

n

iii

w

xw

1

1X

ID X Y1 2 32 4 73 7 74 7 35 6 2

sum 26 22Centroid/MC 5.2 4.4

n

YY

n

XX

n

i

i

n

i

i 11 ,

0 105

010

5

2,3

7,7

7,3

6,2

4,7

Calculating the centroid of a polygon or the mean center of a set of points.

(same example data as for area of polygon)

i X Y weight wX wY

1 2 3 3,000 6,000 9,0002 4 7 500 2,000 3,5003 7 7 400 2,800 2,8004 7 3 100 700 3005 6 2 300 1,800 600

sum 26 22 4,300 13,300 16,200w MC 3.09 3.77

Calculating the weighted mean center. Note how it is pulled toward the high weight point.

i

n

i

ii

i

n

i

ii

w

YwY

w

XwX 11 ,

0 105

010

5

2,3

7,7

7,3

6,2

4,7

Center of Minimum Distance or Median Center

Also called point of minimum aggregate travel

That point (MD) which minimizessum of distances between itself and all other points (i)

No direct solution. Can only be derived by approximation

Not a determinate solution. Multiple points may meet this criteria—see next bullet.

Same as Median center: Intersection of two orthogonal lines

(at right angles to each other), such that each line has half of the points to its left and half to its right

Because the orientation of the axis for thelines is arbitrary, multiple points may meet this criteria.

iMDdmin

Source: Neft, 1966

Median Center:Intersection of a north/south and an east/west line drawn so half of population lives above and half below the e/w line, and half lives to the left and half to the right of the n/s line

Mean Center:Balancing point of a weightless map, if equal weights placed on it at the residence of every person on census day.

Source: US Statistical Abstract 2003

Median and Mean Centers for US Population

Standard Distance Deviation Represents the standard deviation of the

distance of each point from the mean center

Is the two dimensional equivalent of standard deviation for a single variable

Given by:

which by Pythagorasreduces to:

---essentially the average distance of points from the center

Provides a single unit measure of the spread or dispersion of a distribution.

We can also calculate a weighted standard distance analogous to the weighted mean center.

N

YYXXn

i

n

icici

1 1

22 )()(

N

dn

iiC 1

2

N

XXn

ii

1

2)(

Formulae for standarddeviation of single variable

n

ii

n

i

n

iciicii

w

YYwXXw

1

1 1

22 )()(

Or, with weights

Standard Distance Deviation Example

i X Y (X - Xc)2 (Y - Yc)2

1 2 3 10.2 2.02 4 7 1.4 6.83 7 7 3.2 6.84 7 3 3.2 2.05 6 2 0.6 5.8

sum 26 22 18.8 23.2Centroid 5.2 4.4

sum 42.00divide N 8.40sq rt 2.90

N

YYXXsdd

n

i

n

icici

1 1

22 )()(

0 105

010

5

2,3

7,7

7,3

6,2

4,7

i X Y (X - Xc)2 (Y - Yc)2

1 2 3 10.2 2.02 4 7 1.4 6.83 7 7 3.2 6.84 7 3 3.2 2.05 6 2 0.6 5.8

sum 26 22 18.8 23.2Centroid 5.2 4.4

sum of sums 42divide N 8.4sq rt 2.90

Circle with radii=SDD=2.9

Standard Deviational Ellipse: concept

Standard distance deviation / Jarak deviasi standar : ukuran tunggal yang baik dari penyebaran titik-titik di sekitar pusat berarti, tetapi tidak menangkap adanya bias arah tidak menangkap bentuk distribusi

The standard deviation ellipse gives dispersion in two dimensions

Defined by 3 parameters Angle of rotation

Dispersion (spread) along major axis

Dispersion (spread) along minor axis

The major axis defines the direction of maximum spreadof the distribution

The minor axis is perpendicular to itand defines the minimum spread

Standard Deviational Ellipse: calculation

Basic concept is to: Temukan sumbu melalui dispersi maksimum

(dengan demikian berasal sudut rotasi)

Hitung standar deviasi dari titik-titik di sepanjang sumbu (dengan demikian menurunkan panjang (radius) dari sumbu utama)

Hitung standar deviasi titik di sepanjang sumbu tegak lurus terhadap sumbu utama (dengan demikian menurunkan panjang (radius) dari sumbu minor)

Briggs Henan University

2010

44

Tampaknya tidak ada perbedaan besar antara lokasi perangkat lunak dan industri telekomunikasi di North Texas

Mean Center & Standard Deviational Ellipse:

example

Implementation in ArcGIS

To calculate centroid for a set of polygons, with ArcGIS:ArcToolbox>Data Management Tools>Features>Feature to Point (requires ArcInfo)

To calculate using GeoDA: Tools>Shape>Polygons to Centroids

45

In ArcToolbox

Centroid for a set of points

Median Center for a set of points

Standard distance

Standard deviation ellipse

Density Kernel Estimation biasanya digunakan untuk "meningkatkan visual" pola

titik

Is an example of “exploratory spatial data analysis” (ESDA)

Kernel=10,000 Kernel=5,000

low low

high high

• SIMPLE Kernel option (see example above) – “Ketetanggan" atau kernel didefinisikan sekitar setiap sel grid yang terdiri dari

semua sel grid dengan pusat dalam kernel tertentu (pencarian) radius – Jumlah titik yang berada dalam ketetanggaan adalah total titik – Total poin dibagi dengan luas ketetanggan untuk memberikan nilai sel grid

• Density KERNEL option – permukaan lancar melengkung yang dipasang di setiap titik– Nilai permukaan tertinggi pada lokasi titik, dan berkurang dengan peningkatan jarak dari

titik, mencapai nol pada jarak kernel dari titik. – Volume bawah permukaan sama dengan 1 (atau nilai populasi jika variabel populasi

digunakan)– Menggunakan fungsi kernel kuadrat– Kepadatan di setiap sel grid output dihitung dengan menambahkan nilai-nilai dari semua

permukaan kernel mana mereka overlay pusat sel grid

• If specify a “population field” software calculates as if there are that number of points at that location.

• The search radius:• the size of the neighborhood or

kernel which is successively defined around every cell (simple kernel) or each point (density kernel)

• Output cell size:• Size of each raster cell

• Search radius and output cell size are based on measurement units of the data (here it is feet)• It is good to “round” them (e.g.

to 10,000 and 1,000)

Implementation in ArcGIS

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