kuliah 2_analisis spasial
Post on 02-Nov-2014
171 Views
Preview:
DESCRIPTION
TRANSCRIPT
2012
Analisis Spasial
Ove
rvie
w
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
Terima Kasih
top related