Hands-on_Ex08
Erika Aldisa
9/28/2020 (updated: 2020-10-12)
Geographical Segmentation with Spatially Constrained Clustering Techniques
IS415 Geospatial Analytics and Application
Instructor: Dr. Kam Tin Seong.
Assoc. Professor of Information Systems (Practice)
1. Overview
When last week we learnt about localised geospatial statistics analysis to perform spatial clustering (LISA cluster map, Local Moran’s I, Geary’s C values). This localised analysis is only based on a single geographically referenced data.
However, in this hands-on exercise, we will learn how to delineate homogeneous region by using geographically referenced multivariate data, using more than 1 variables to perform spatial clustering on a big area (region).
In geobusiness and spatial policy, it is a common practice to delineate the market or planning area into homogeneous regions by using multivariate data. In this hands-on exercise, we are interested to delineate Shan State, Myanmar into homogeneous regions by using multiple Information and Communication technology (ICT) variables, namely: Radio, Television, Land line phone, Mobile phone, Computer, and Internet at home.
The 2 major analysis methods are:
Hierarchical cluster analysis
Spatially constrained cluster analysis
1.1 Dataset
Myanmar_township_boundaries shapefile contaaining the township boundary information, spatial data in polygon features
Shan-ICT.csv containing the ICT-related variables data which is extracted from The 2014 Myanmar Population and Housing Census Myanmar at the township level
Shan-ICT.csv: This is an extract of The 2014 Myanmar Population and Housing Census Myanmar at the township level.
Both data sets can be download from Myanmar Information Management Unit (MIMU)
2. Load/Install necessary R packages
We will be using these R packages:
sf, rgdal - for handling spatial data
spdep - for spatial statistical analysis
ClustGeo - for geospatial analysis (ClustGeo is a method of spatially constrained clustering)
tmap - for choropleth mapping
tidyverse - for tidying attribute/variable data (tidyr, readr, ggplot2 & dplyr)
ggpubr - for creating ‘ggplot2’-based publication ready plots, more info can be found here
heatmaply, corrplot - for creating interactive cluster heat maps using ‘plotly’ and correlation matrix with confidence interval, more info can be found here and here
cluster - for extended cluster analysis methods, such as:
Agnes (agglomerative nesting - hierarchical clustering)
Clara (clustering large applications into k clusters)
Diana (divisive analysis clustering)
Fanny (fuzzy analysis clustering into k clusters), more info can be found here
packages = c('sf', 'rgdal', 'spdep', 'ClustGeo', 'tmap', 'tidyverse', 'cluster', 'heatmaply', 'ggpubr', 'corrplot' , 'psych')
for (p in packages){
if(!require(p, character.only = T)){
install.packages(p)
}
library(p, character.only = T)
}3. Importing Data into R
We import the shapefile using st_read() function of sf package.
Then, we import the csv file using read_csv() function of readr package.
3.1 Importing geospatial data (shapefile)
- Imported as simple feature data.frame
shan_sf <- st_read(dsn = "data/geospatial", layer = "myanmar_township_boundaries") %>%
filter(ST %in% c("Shan (East)", "Shan (North)", "Shan (South)"))## Reading layer `myanmar_township_boundaries' from data source `D:\SMU Year 3 Sem 1\IS415 Geospatial Analytics and Application\In_class_exercise\In_class_exercise08\data\geospatial' using driver `ESRI Shapefile'
## Simple feature collection with 330 features and 14 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: 92.17275 ymin: 9.671252 xmax: 101.1699 ymax: 28.54554
## geographic CRS: WGS 84shan_sf## Simple feature collection with 55 features and 14 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: 96.15107 ymin: 19.29932 xmax: 101.1699 ymax: 24.15907
## geographic CRS: WGS 84
## First 10 features:
## OBJECTID ST ST_PCODE DT DT_PCODE TS TS_PCODE
## 1 163 Shan (North) MMR015 Mongmit MMR015D008 Mongmit MMR015017
## 2 203 Shan (South) MMR014 Taunggyi MMR014D001 Pindaya MMR014006
## 3 240 Shan (South) MMR014 Taunggyi MMR014D001 Ywangan MMR014007
## 4 106 Shan (South) MMR014 Taunggyi MMR014D001 Pinlaung MMR014009
## 5 72 Shan (North) MMR015 Mongmit MMR015D008 Mabein MMR015018
## 6 40 Shan (South) MMR014 Taunggyi MMR014D001 Kalaw MMR014005
## 7 194 Shan (South) MMR014 Taunggyi MMR014D001 Pekon MMR014010
## 8 159 Shan (South) MMR014 Taunggyi MMR014D001 Lawksawk MMR014008
## 9 61 Shan (North) MMR015 Kyaukme MMR015D003 Nawnghkio MMR015013
## 10 124 Shan (North) MMR015 Kyaukme MMR015D003 Kyaukme MMR015012
## ST_2 LABEL2 SELF_ADMIN ST_RG T_NAME_WIN
## 1 Shan State (North) Mongmit\n61072 <NA> State rdk;rdwf
## 2 Shan State (South) Pindaya\n77769 Danu State yif;w,
## 3 Shan State (South) Ywangan\n76933 Danu State &GmiH
## 4 Shan State (South) Pinlaung\n162537 Pa-O State yifavmif;
## 5 Shan State (North) Mabein\n35718 <NA> State rbdrf;
## 6 Shan State (South) Kalaw\n163138 <NA> State uavm
## 7 Shan State (South) Pekon\n94226 <NA> State z,fcHk
## 8 Shan State (South) Lawksawk <NA> State &yfapmuf
## 9 Shan State (North) Nawnghkio\n128357 <NA> State aemifcsdK
## 10 Shan State (North) Kyaukme\n172874 <NA> State ausmufrJ
## T_NAME_M3
## 1 <U+1019><U+102D><U+102F><U+1038><U+1019><U+102D><U+1010><U+103A>
## 2 <U+1015><U+1004><U+103A><U+1038><U+1010><U+101A>
## 3 <U+101B><U+103D><U+102C><U+1004><U+1036>
## 4 <U+1015><U+1004><U+103A><U+101C><U+1031><U+102C><U+1004><U+103A><U+1038>
## 5 <U+1019><U+1018><U+102D><U+1019><U+103A><U+1038>
## 6 <U+1000><U+101C><U+1031><U+102C>
## 7 <U+1016><U+101A><U+103A><U+1001><U+102F><U+1036>
## 8 <U+101B><U+1015><U+103A><U+1005><U+1031><U+102C><U+1000><U+103A>
## 9 <U+1014><U+1031><U+102C><U+1004><U+103A><U+1001><U+103B><U+102D><U+102F>
## 10 <U+1000><U+103B><U+1031><U+102C><U+1000><U+103A><U+1019><U+1032>
## AREA geometry
## 1 2703.611 MULTIPOLYGON (((96.96001 23...
## 2 629.025 MULTIPOLYGON (((96.7731 21....
## 3 2984.377 MULTIPOLYGON (((96.78483 21...
## 4 3396.963 MULTIPOLYGON (((96.49518 20...
## 5 5034.413 MULTIPOLYGON (((96.66306 24...
## 6 1456.624 MULTIPOLYGON (((96.49518 20...
## 7 2073.513 MULTIPOLYGON (((97.14738 19...
## 8 5145.659 MULTIPOLYGON (((96.94981 22...
## 9 3271.537 MULTIPOLYGON (((96.75648 22...
## 10 3920.869 MULTIPOLYGON (((96.95498 22...We can see that the simple feature data.frame is already conformed to Hardy Wickham’s tidy framework.
glimpse(shan_sf)## Rows: 55
## Columns: 15
## $ OBJECTID <dbl> 163, 203, 240, 106, 72, 40, 194, 159, 61, 124, 71, 155, ...
## $ ST <chr> "Shan (North)", "Shan (South)", "Shan (South)", "Shan (S...
## $ ST_PCODE <chr> "MMR015", "MMR014", "MMR014", "MMR014", "MMR015", "MMR01...
## $ DT <chr> "Mongmit", "Taunggyi", "Taunggyi", "Taunggyi", "Mongmit"...
## $ DT_PCODE <chr> "MMR015D008", "MMR014D001", "MMR014D001", "MMR014D001", ...
## $ TS <chr> "Mongmit", "Pindaya", "Ywangan", "Pinlaung", "Mabein", "...
## $ TS_PCODE <chr> "MMR015017", "MMR014006", "MMR014007", "MMR014009", "MMR...
## $ ST_2 <chr> "Shan State (North)", "Shan State (South)", "Shan State ...
## $ LABEL2 <chr> "Mongmit\n61072", "Pindaya\n77769", "Ywangan\n76933", "P...
## $ SELF_ADMIN <chr> NA, "Danu", "Danu", "Pa-O", NA, NA, NA, NA, NA, NA, NA, ...
## $ ST_RG <chr> "State", "State", "State", "State", "State", "State", "S...
## $ T_NAME_WIN <chr> "rdk;rdwf", "yif;w,", "&GmiH", "yifavmif;", "rbdrf;", "u...
## $ T_NAME_M3 <chr> "<U+1019><U+102D><U+102F><U+1038><U+1019><U+102D><U+1010>\u103a", "<U+1015><U+1004>\u103a<U+1038><U+1010><U+101A>", "<U+101B>\u103d<U+102C><U+1004><U+1036>", "<U+1015><U+1004>\u103a<U+101C>...
## $ AREA <dbl> 2703.611, 629.025, 2984.377, 3396.963, 5034.413, 1456.62...
## $ geometry <MULTIPOLYGON [°]> MULTIPOLYGON (((96.96001 23..., MULTIPOLYGO...3.2 Importing aspatial data (csv)
- Imported as tibble data.frame
ict <- read_csv("data/aspatial/Shan-ICT.csv")##
## -- Column specification -------------------------------------------------------------------------
## cols(
## `District Pcode` = col_character(),
## `District Name` = col_character(),
## `Township Pcode` = col_character(),
## `Township Name` = col_character(),
## `Total households` = col_double(),
## Radio = col_double(),
## Television = col_double(),
## `Land line phone` = col_double(),
## `Mobile phone` = col_double(),
## Computer = col_double(),
## `Internet at home` = col_double()
## )summary(ict)## District Pcode District Name Township Pcode Township Name
## Length:55 Length:55 Length:55 Length:55
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## Total households Radio Television Land line phone
## Min. : 3318 Min. : 115 Min. : 728 Min. : 20.0
## 1st Qu.: 8711 1st Qu.: 1260 1st Qu.: 3744 1st Qu.: 266.5
## Median :13685 Median : 2497 Median : 6117 Median : 695.0
## Mean :18369 Mean : 4487 Mean :10183 Mean : 929.9
## 3rd Qu.:23471 3rd Qu.: 6192 3rd Qu.:13906 3rd Qu.:1082.5
## Max. :82604 Max. :30176 Max. :62388 Max. :6736.0
## Mobile phone Computer Internet at home
## Min. : 150 Min. : 20.0 Min. : 8.0
## 1st Qu.: 2037 1st Qu.: 121.0 1st Qu.: 88.0
## Median : 3559 Median : 244.0 Median : 316.0
## Mean : 6470 Mean : 575.5 Mean : 760.2
## 3rd Qu.: 7177 3rd Qu.: 507.0 3rd Qu.: 630.5
## Max. :48461 Max. :6705.0 Max. :9746.04. Derive new variables using dplyr package
In general, the townships with relatively higher total number of households will also have higher number of households owning radio, TV, internet, etc.
Since the unit of measurement of the variables depend on the total number of households, we will derive the penetration rate of each ICT variable.
ict_derived <- ict %>%
mutate(`RADIO_PR` = `Radio`/`Total households` * 1000) %>%
mutate(`TV_PR` = `Television`/`Total households` * 1000) %>%
mutate(`LLPHONE_PR` = `Land line phone`/`Total households` * 1000) %>%
mutate(`MPHONE_PR` = `Mobile phone`/`Total households` * 1000) %>%
mutate(`COMPUTER_PR` = `Computer`/`Total households` * 1000) %>%
mutate(`INTERNET_PR` = `Internet at home`/`Total households` * 1000) %>%
rename(`DT_PCODE` = `District Pcode`, `DT` = `District Name`, `TS_PCODE` = `Township Pcode`, `TS` = `Township Name`, `TT_HOUSEHOLDS` = `Total households`, `RADIO` = `Radio`, `TV` = `Television`, `LLPHONE` = `Land line phone`, `MPHONE` = `Mobile phone`, `COMPUTER` = `Computer`, `INTERNET` = `Internet at home`)Let’s check the summary again
summary(ict_derived)## DT_PCODE DT TS_PCODE TS
## Length:55 Length:55 Length:55 Length:55
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
## TT_HOUSEHOLDS RADIO TV LLPHONE
## Min. : 3318 Min. : 115 Min. : 728 Min. : 20.0
## 1st Qu.: 8711 1st Qu.: 1260 1st Qu.: 3744 1st Qu.: 266.5
## Median :13685 Median : 2497 Median : 6117 Median : 695.0
## Mean :18369 Mean : 4487 Mean :10183 Mean : 929.9
## 3rd Qu.:23471 3rd Qu.: 6192 3rd Qu.:13906 3rd Qu.:1082.5
## Max. :82604 Max. :30176 Max. :62388 Max. :6736.0
## MPHONE COMPUTER INTERNET RADIO_PR
## Min. : 150 Min. : 20.0 Min. : 8.0 Min. : 21.05
## 1st Qu.: 2037 1st Qu.: 121.0 1st Qu.: 88.0 1st Qu.:138.95
## Median : 3559 Median : 244.0 Median : 316.0 Median :210.95
## Mean : 6470 Mean : 575.5 Mean : 760.2 Mean :215.68
## 3rd Qu.: 7177 3rd Qu.: 507.0 3rd Qu.: 630.5 3rd Qu.:268.07
## Max. :48461 Max. :6705.0 Max. :9746.0 Max. :484.52
## TV_PR LLPHONE_PR MPHONE_PR COMPUTER_PR
## Min. :116.0 Min. : 2.78 Min. : 36.42 Min. : 3.278
## 1st Qu.:450.2 1st Qu.: 22.84 1st Qu.:190.14 1st Qu.:11.832
## Median :517.2 Median : 37.59 Median :305.27 Median :18.970
## Mean :509.5 Mean : 51.09 Mean :314.05 Mean :24.393
## 3rd Qu.:606.4 3rd Qu.: 69.72 3rd Qu.:428.43 3rd Qu.:29.897
## Max. :842.5 Max. :181.49 Max. :735.43 Max. :92.402
## INTERNET_PR
## Min. : 1.041
## 1st Qu.: 8.617
## Median : 22.829
## Mean : 30.644
## 3rd Qu.: 41.281
## Max. :117.9855. Exploratory Data Analysis (EDA)
5.1 EDA w/ statistical graphs
We can plot the distribution of the variables such as plotting histogram which can tell us the overall distribution of the data values, whether it is normally distributed or skewed.
ggplot(data = ict_derived, aes(x= `RADIO`))+
geom_histogram(bins = 20, color = "black", fill = "light blue")
We can also plot boxplot to detect outliers.
ggplot(data = ict_derived, aes(x=`RADIO`))+
geom_boxplot(color= "black", fill="light blue")
We can see that both the histogram and boxplot are skewed to the left, so let’s plot the newly derived variable (penetration rate) and see if they are more normally distributed.
ggplot(data = ict_derived, aes(x= `RADIO_PR`))+
geom_histogram(bins = 20, color = "black", fill = "light blue")
ggplot(data = ict_derived, aes(x=`RADIO_PR`))+
geom_boxplot(color= "black", fill="light blue")
The penetration rate of radio is more normally distributed compared to the no. of households owning radio.
Now, we will reveal the distribution of the penetration rate of all ICT variables in the ict_derived data.frame. Firstly, we will create the individual histograms then use gggarrange() function of ggpubr package to group the histograms together.
radio <- ggplot(data=ict_derived,
aes(x= `RADIO_PR`)) +
geom_histogram(bins=20,
color="black",
fill="light blue")
tv <- ggplot(data=ict_derived,
aes(x= `TV_PR`)) +
geom_histogram(bins=20,
color="black",
fill="light blue")
llphone <- ggplot(data=ict_derived,
aes(x= `LLPHONE_PR`)) +
geom_histogram(bins=20,
color="black",
fill="light blue")
mphone <- ggplot(data=ict_derived,
aes(x= `MPHONE_PR`)) +
geom_histogram(bins=20,
color="black",
fill="light blue")
computer <- ggplot(data=ict_derived,
aes(x= `COMPUTER_PR`)) +
geom_histogram(bins=20,
color="black",
fill="light blue")
internet <- ggplot(data=ict_derived,
aes(x= `INTERNET_PR`)) +
geom_histogram(bins=20,
color="black",
fill="light blue")ggarrange(radio, tv, llphone, mphone, computer, internet, ncol = 3, nrow = 2)
5.2 EDA w/ choropleth maps
Before we can create the choropleth maps, we have to combine the geospatial data object (shan_sf) and aspatial data frame object (ict_derived), which will be done using left_join() mfunction of dplyr package. The shan_sf will be used as base and ict_derived will be used as the join table.
shan_sf <- left_join(shan_sf, ict_derived, by = c("TS_PCODE" = "TS_PCODE"))It is important to note that there is no new output data been created. Instead, the data fields from ict_derived data frame are now updated into the data frame of shan_sf.
Let’s have a quick look at the distribution of Radio penetration rate (RADIO_PR) of Shan State at township level using qtm() function for quick thematic mapping.
qtm(shan_sf, "RADIO_PR")
In order to reveal that the distribution shown by RADIO_PR is proportionate to the underlying total number of households at the township level, we will plot one map for total number of households and beside it a map for no. of households owning radio.
TT_HOUSEHOLDS.map <- tm_shape(shan_sf) +
tm_fill(col = "TT_HOUSEHOLDS",
n = 5,
style = "jenks",
title = "Total households") +
tm_borders(alpha = 0.5)
RADIO.map <- tm_shape(shan_sf) +
tm_fill(col = "RADIO",
n = 5,
style = "jenks",
title = "Households with Radio") +
tm_borders(alpha = 0.5)
tmap_arrange(TT_HOUSEHOLDS.map, RADIO.map, asp = NA, ncol = 2)
We can see that the choropleth maps above clearly show that townships with larger number of households also show relatively higher number of radio ownership.
tm_shape(shan_sf) +
tm_polygons(c("TT_HOUSEHOLDS", "RADIO_PR"), style = "jenks") +
tm_facets(sync = TRUE, ncol = 2) +
tm_legend(legend.position = c("right", "bottom")) +
tm_layout(outer.margins = 0, asp = 0)
Can you identify the difference?
We can see that there are townships which have higher radio penetration rate compared to other townships which have higher total number of households.
5.3 EDA w/ correlation analysis
Before we perform cluster analysis, it’s important to detect the input variables that are highly correlated.
We will use corrplot.mixed() function of corrplot package to visualize & analyse the correlation of the input variables / geographically referenced multivariate data.
cluster_vars.cor = cor(ict_derived[,12:17])
corrplot.mixed(cluster_vars.cor,
lower = "ellipse",
upper = "number",
tl.pos = "lt",
diag = "l",
tl.col = "black")
From the correlation plot above, we can see that COMPUTER_PR and INTERNET_PR are highly correlated. Hence, we should only use one of them in the cluster analysis instead of both.
6. Hierarchy Cluster Analysis
6.1 Extract clustering variables
Remember that since computer ownership vs internet ownership are highly correlated, we should just choose one so we choose computer variable here.
Without using st_set_geometry() function, the resulting class of cluster_vars is simple feature (sf) data.frame. Using st_set_geometry() function, the resulting class of cluster_vars is just data.frame (not containing dimension, geometry type, bounding box and geographic CRS).
cluster_vars <- shan_sf %>%
st_set_geometry(NULL) %>%
select("TS.x", "RADIO_PR", "TV_PR", "LLPHONE_PR", "MPHONE_PR", "COMPUTER_PR")
head(cluster_vars, 10)## TS.x RADIO_PR TV_PR LLPHONE_PR MPHONE_PR COMPUTER_PR
## 1 Mongmit 286.1852 554.1313 35.30618 260.6944 12.15939
## 2 Pindaya 417.4647 505.1300 19.83584 162.3917 12.88190
## 3 Ywangan 484.5215 260.5734 11.93591 120.2856 4.41465
## 4 Pinlaung 231.6499 541.7189 28.54454 249.4903 13.76255
## 5 Mabein 449.4903 708.6423 72.75255 392.6089 16.45042
## 6 Kalaw 280.7624 611.6204 42.06478 408.7951 29.63160
## 7 Pekon 318.6118 535.8494 39.83270 214.8476 18.97032
## 8 Lawksawk 387.1017 630.0035 31.51366 320.5686 21.76677
## 9 Nawnghkio 349.3359 547.9456 38.44960 323.0201 15.76465
## 10 Kyaukme 210.9548 601.1773 39.58267 372.4930 30.94709Next, we will change the rows by township name instead of row number.
row.names(cluster_vars) <- cluster_vars$TS.x
head(cluster_vars, 10)## TS.x RADIO_PR TV_PR LLPHONE_PR MPHONE_PR COMPUTER_PR
## Mongmit Mongmit 286.1852 554.1313 35.30618 260.6944 12.15939
## Pindaya Pindaya 417.4647 505.1300 19.83584 162.3917 12.88190
## Ywangan Ywangan 484.5215 260.5734 11.93591 120.2856 4.41465
## Pinlaung Pinlaung 231.6499 541.7189 28.54454 249.4903 13.76255
## Mabein Mabein 449.4903 708.6423 72.75255 392.6089 16.45042
## Kalaw Kalaw 280.7624 611.6204 42.06478 408.7951 29.63160
## Pekon Pekon 318.6118 535.8494 39.83270 214.8476 18.97032
## Lawksawk Lawksawk 387.1017 630.0035 31.51366 320.5686 21.76677
## Nawnghkio Nawnghkio 349.3359 547.9456 38.44960 323.0201 15.76465
## Kyaukme Kyaukme 210.9548 601.1773 39.58267 372.4930 30.94709Next, we will delete the TS.x column/variable since the identifier row is already TS.x township name.
shan_ict <- select(cluster_vars, c(2:6))
head(shan_ict, 10)## RADIO_PR TV_PR LLPHONE_PR MPHONE_PR COMPUTER_PR
## Mongmit 286.1852 554.1313 35.30618 260.6944 12.15939
## Pindaya 417.4647 505.1300 19.83584 162.3917 12.88190
## Ywangan 484.5215 260.5734 11.93591 120.2856 4.41465
## Pinlaung 231.6499 541.7189 28.54454 249.4903 13.76255
## Mabein 449.4903 708.6423 72.75255 392.6089 16.45042
## Kalaw 280.7624 611.6204 42.06478 408.7951 29.63160
## Pekon 318.6118 535.8494 39.83270 214.8476 18.97032
## Lawksawk 387.1017 630.0035 31.51366 320.5686 21.76677
## Nawnghkio 349.3359 547.9456 38.44960 323.0201 15.76465
## Kyaukme 210.9548 601.1773 39.58267 372.4930 30.947096.2 Data standardisation
In general, multiple variables will be used in cluster analysis so it’s not unusual that their values range are different. In order to avoid cluster analysis result to be biased to the clustering variables with large values, it’s useful to standardise the input variables before performing cluster analysis.
6.2.1 Min-Max standardisation
We will use normalize() function of heatmaply package to standardise the input variables using Min-Max method. Then, summary() function is used to display the summary statistics of the standardised clustering variables.
shan_ict.std <- normalize(shan_ict)
summary(shan_ict.std)## RADIO_PR TV_PR LLPHONE_PR MPHONE_PR
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.2544 1st Qu.:0.4600 1st Qu.:0.1123 1st Qu.:0.2199
## Median :0.4097 Median :0.5523 Median :0.1948 Median :0.3846
## Mean :0.4199 Mean :0.5416 Mean :0.2703 Mean :0.3972
## 3rd Qu.:0.5330 3rd Qu.:0.6750 3rd Qu.:0.3746 3rd Qu.:0.5608
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## COMPUTER_PR
## Min. :0.00000
## 1st Qu.:0.09598
## Median :0.17607
## Mean :0.23692
## 3rd Qu.:0.29868
## Max. :1.00000Now, the values range of the Min-Max standardised clustering variables are from 0 to 1.
6.2.2 Z-score standardisation
We will use the scale() function of Base R package to perform Z-score standardisation.
shan_ict.z <- scale(shan_ict)
describe(shan_ict.z)## vars n mean sd median trimmed mad min max range skew kurtosis
## RADIO_PR 1 55 0 1 -0.04 -0.06 0.94 -1.85 2.55 4.40 0.48 -0.27
## TV_PR 2 55 0 1 0.05 0.04 0.78 -2.47 2.09 4.56 -0.38 -0.23
## LLPHONE_PR 3 55 0 1 -0.33 -0.15 0.68 -1.19 3.20 4.39 1.37 1.49
## MPHONE_PR 4 55 0 1 -0.05 -0.06 1.01 -1.58 2.40 3.98 0.48 -0.34
## COMPUTER_PR 5 55 0 1 -0.26 -0.18 0.64 -1.03 3.31 4.34 1.80 2.96
## se
## RADIO_PR 0.13
## TV_PR 0.13
## LLPHONE_PR 0.13
## MPHONE_PR 0.13
## COMPUTER_PR 0.13Notice that the mean and standard deviation of the Z-score standardised clustering variables range from 0 to 1.
describe() function psych package is used here instead of the usual summary() because the describe() provides standard deviation values.
WARNING: Z-score standardisation method should only be used if we assume all input variables come from some normal distribution
6.2.3 Visualizing the standardised clustering variables
Not only do we review the summary statistics but it’s also good to visualize the distribution of the standardised clustering variables.
r <- ggplot(data = ict_derived, aes(x=`RADIO_PR`)) +
geom_histogram(bins = 20, color = "black", fill = "light blue") +
ggtitle("Radio penetration rate")
shan_ict_s_df <- as.data.frame(shan_ict.std)
s <- ggplot(data = shan_ict_s_df, aes(x=`RADIO_PR`)) +
geom_histogram(bins = 20, color = "black", fill = "light blue") +
ggtitle("Min-Max Standardisation")
shan_ict_z_df <- as.data.frame(shan_ict.z)
z <- ggplot(data = shan_ict_z_df, aes(x=`RADIO_PR`)) +
geom_histogram(bins = 20, color = "black", fill = "light blue") +
ggtitle("Z-score Standardisation")
ggarrange(r, s, z,
ncol = 3,
nrow = 1)
We can see that the overall distribution of the clustering variables will change after the data standardisation step. Hence, it’s not recommended to perform data standardisation to a variable if the value range or that variable is not very large.
6.3 Computing proximity matrix
In R, many packages provide functions to calculate distance matrix. We will compute the proximity matrix using dist() function of Base R package.
dist() function supports six distance proximity calculations, namely euclidean, maximum, manhattan, canberra, binary & minkowski. The default is euclidean proximity matrix.
This will result in a dist object called proxmat.
proxmat <- dist(shan_ict, method = "euclidean")
proxmat## Mongmit Pindaya Ywangan Pinlaung Mabein Kalaw
## Pindaya 171.86828
## Ywangan 381.88259 257.31610
## Pinlaung 57.46286 208.63519 400.05492
## Mabein 263.37099 313.45776 529.14689 312.66966
## Kalaw 160.05997 302.51785 499.53297 181.96406 198.14085
## Pekon 59.61977 117.91580 336.50410 94.61225 282.26877 211.91531
## Lawksawk 140.11550 204.32952 432.16535 192.57320 130.36525 140.01101
## Nawnghkio 89.07103 180.64047 377.87702 139.27495 204.63154 127.74787
## Kyaukme 144.02475 311.01487 505.89191 139.67966 264.88283 79.42225
## Muse 563.01629 704.11252 899.44137 571.58335 453.27410 412.46033
## Laihka 141.87227 298.61288 491.83321 101.10150 345.00222 197.34633
## Mongnai 115.86190 258.49346 422.71934 64.52387 358.86053 200.34668
## Mawkmai 434.92968 437.99577 397.03752 398.11227 693.24602 562.59200
## Kutkai 97.61092 212.81775 360.11861 78.07733 340.55064 204.93018
## Mongton 192.67961 283.35574 361.23257 163.42143 425.16902 267.87522
## Mongyai 256.72744 287.41816 333.12853 220.56339 516.40426 386.74701
## Mongkaing 503.61965 481.71125 364.98429 476.29056 747.17454 625.24500
## Lashio 251.29457 398.98167 602.17475 262.51735 231.28227 106.69059
## Mongpan 193.32063 335.72896 483.68125 192.78316 301.52942 114.69105
## Matman 401.25041 354.39039 255.22031 382.40610 637.53975 537.63884
## Tachileik 529.63213 635.51774 807.44220 555.01039 365.32538 373.64459
## Narphan 406.15714 474.50209 452.95769 371.26895 630.34312 463.53759
## Mongkhet 349.45980 391.74783 408.97731 305.86058 610.30557 465.52013
## Hsipaw 118.18050 245.98884 388.63147 76.55260 366.42787 212.36711
## Monghsat 214.20854 314.71506 432.98028 160.44703 470.48135 317.96188
## Mongmao 242.54541 402.21719 542.85957 217.58854 384.91867 195.18913
## Nansang 104.91839 275.44246 472.77637 85.49572 287.92364 124.30500
## Laukkaing 568.27732 726.85355 908.82520 563.81750 520.67373 427.77791
## Pangsang 272.67383 428.24958 556.82263 244.47146 418.54016 224.03998
## Namtu 179.62251 225.40822 444.66868 170.04533 366.16094 307.27427
## Monghpyak 177.76325 221.30579 367.44835 222.20020 212.69450 167.08436
## Konkyan 403.39082 500.86933 528.12533 365.44693 613.51206 444.75859
## Mongping 265.12574 310.64850 337.94020 229.75261 518.16310 375.64739
## Hopong 136.93111 223.06050 352.85844 98.14855 398.00917 264.16294
## Nyaungshwe 99.38590 216.52463 407.11649 138.12050 210.21337 95.66782
## Hsihseng 131.49728 172.00796 342.91035 111.61846 381.20187 287.11074
## Mongla 384.30076 549.42389 728.16301 372.59678 406.09124 260.26411
## Hseni 189.37188 337.98982 534.44679 204.47572 213.61240 38.52842
## Kunlong 224.12169 355.47066 531.63089 194.76257 396.61508 273.01375
## Hopang 281.05362 443.26362 596.19312 265.96924 368.55167 185.14704
## Namhkan 386.02794 543.81859 714.43173 382.78835 379.56035 246.39577
## Kengtung 246.45691 385.68322 573.23173 263.48638 219.47071 88.29335
## Langkho 164.26299 323.28133 507.78892 168.44228 253.84371 67.19580
## Monghsu 109.15790 198.35391 340.42789 80.86834 367.19820 237.34578
## Taunggyi 399.84278 503.75471 697.98323 429.54386 226.24011 252.26066
## Pangwaun 381.51246 512.13162 580.13146 356.37963 523.44632 338.35194
## Kyethi 202.92551 175.54012 287.29358 189.47065 442.07679 360.17247
## Loilen 145.48666 293.61143 469.51621 91.56527 375.06406 217.19877
## Manton 430.64070 402.42888 306.16379 405.83081 674.01120 560.16577
## Mongyang 309.51302 475.93982 630.71590 286.03834 411.88352 233.56349
## Kunhing 173.50424 318.23811 449.67218 141.58836 375.82140 197.63683
## Mongyawng 214.21738 332.92193 570.56521 235.55497 193.49994 173.43078
## Tangyan 195.92520 208.43740 324.77002 169.50567 448.59948 348.06617
## Namhsan 237.78494 228.41073 286.16305 214.33352 488.33873 385.88676
## Pekon Lawksawk Nawnghkio Kyaukme Muse Laihka
## Pindaya
## Ywangan
## Pinlaung
## Mabein
## Kalaw
## Pekon
## Lawksawk 157.51129
## Nawnghkio 113.15370 90.82891
## Kyaukme 202.12206 186.29066 157.04230
## Muse 614.56144 510.13288 533.68806 434.75768
## Laihka 182.23667 246.74469 211.88187 128.24979 526.65211
## Mongnai 151.60031 241.71260 182.21245 142.45669 571.97975 100.53457
## Mawkmai 416.00669 567.52693 495.15047 512.02846 926.93007 429.96554
## Kutkai 114.98048 224.64646 147.44053 170.93318 592.90743 144.67198
## Mongton 208.14888 311.07742 225.81118 229.28509 634.71074 212.07320
## Mongyai 242.52301 391.26989 319.57938 339.27780 763.91399 264.13364
## Mongkaing 480.23965 625.18712 546.69447 586.05094 995.66496 522.96309
## Lashio 303.80011 220.75270 230.55346 129.95255 313.15288 238.64533
## Mongpan 243.30037 228.54223 172.84425 110.37831 447.49969 210.76951
## Matman 368.25761 515.39711 444.05061 505.52285 929.11283 443.25453
## Tachileik 573.39528 441.82621 470.45533 429.15493 221.19950 549.08985
## Narphan 416.84901 523.69580 435.59661 420.30003 770.40234 392.32592
## Mongkhet 342.08722 487.41102 414.10280 409.03553 816.44931 324.97428
## Hsipaw 145.37542 249.35081 176.09570 163.95741 591.03355 128.42987
## Monghsat 225.64279 352.31496 289.83220 253.25370 663.76026 158.93517
## Mongmao 293.70625 314.64777 257.76465 146.09228 451.82530 185.99082
## Nansang 160.37607 188.78869 151.13185 60.32773 489.35308 78.78999
## Laukkaing 624.82399 548.83928 552.65554 428.74978 149.26996 507.39700
## Pangsang 321.81214 345.91486 287.10769 175.35273 460.24292 214.19291
## Namtu 165.02707 260.95300 257.52713 270.87277 659.16927 185.86794
## Monghpyak 190.93173 142.31691 93.03711 217.64419 539.43485 293.22640
## Konkyan 421.48797 520.31264 439.34272 393.79911 704.86973 351.75354
## Mongping 259.68288 396.47081 316.14719 330.28984 744.44948 272.82761
## Hopong 138.86577 274.91604 204.88286 218.84211 648.68011 157.48857
## Nyaungshwe 139.31874 104.17830 43.26545 126.50414 505.88581 201.71653
## Hsihseng 105.30573 257.11202 209.88026 250.27059 677.66886 175.89761
## Mongla 441.20998 393.18472 381.40808 241.58966 256.80556 315.93218
## Hseni 243.98001 171.50398 164.05304 81.20593 381.30567 204.49010
## Kunlong 249.36301 318.30406 285.04608 215.63037 547.24297 122.68682
## Hopang 336.38582 321.16462 279.84188 154.91633 377.44407 230.78652
## Namhkan 442.77120 379.41126 367.33575 247.81990 238.67060 342.43665
## Kengtung 297.67761 209.38215 208.29647 136.23356 330.08211 258.23950
## Langkho 219.21623 190.30257 156.51662 51.67279 413.64173 160.94435
## Monghsu 113.84636 242.04063 170.09168 200.77712 633.21624 163.28926
## Taunggyi 440.66133 304.96838 344.79200 312.60547 250.81471 425.36916
## Pangwaun 423.81347 453.02765 381.67478 308.31407 541.97887 351.78203
## Kyethi 162.43575 317.74604 267.21607 328.14177 757.16745 255.83275
## Loilen 181.94596 265.29318 219.26405 146.92675 560.43400 59.69478
## Manton 403.82131 551.13000 475.77296 522.86003 941.49778 458.30232
## Mongyang 363.58788 363.37684 323.32123 188.59489 389.59919 229.71502
## Kunhing 213.46379 278.68953 206.15773 145.00266 533.00162 142.03682
## Mongyawng 248.43910 179.07229 220.61209 181.55295 422.37358 211.99976
## Tangyan 167.79937 323.14701 269.07880 306.78359 736.93741 224.29176
## Namhsan 207.16559 362.84062 299.74967 347.85944 778.52971 273.79672
## Mongnai Mawkmai Kutkai Mongton Mongyai Mongkaing
## Pindaya
## Ywangan
## Pinlaung
## Mabein
## Kalaw
## Pekon
## Lawksawk
## Nawnghkio
## Kyaukme
## Muse
## Laihka
## Mongnai
## Mawkmai 374.50873
## Kutkai 91.15307 364.95519
## Mongton 131.67061 313.35220 107.06341
## Mongyai 203.23607 178.70499 188.94166 159.79790
## Mongkaing 456.00842 133.29995 428.96133 365.50032 262.84016
## Lashio 270.86983 638.60773 289.82513 347.11584 466.36472 708.65819
## Mongpan 178.09554 509.99632 185.18173 200.31803 346.39710 563.56780
## Matman 376.33870 147.83545 340.86349 303.04574 186.95158 135.51424
## Tachileik 563.95232 919.38755 568.99109 608.76740 750.29555 967.14087
## Narphan 329.31700 273.75350 314.27683 215.97925 248.82845 285.65085
## Mongkhet 275.76855 115.58388 273.91673 223.22828 104.98924 222.60577
## Hsipaw 52.68195 351.34601 51.46282 90.69766 177.33790 423.77868
## Monghsat 125.25968 275.09705 154.32012 150.98053 127.35225 375.60376
## Mongmao 188.29603 485.52853 204.69232 206.57001 335.61300 552.31959
## Nansang 92.79567 462.41938 130.04549 199.58124 288.55962 542.16609
## Laukkaing 551.56800 882.51110 580.38112 604.66190 732.68347 954.11795
## Pangsang 204.25746 484.14757 228.33583 210.77938 343.30638 548.40662
## Namtu 209.35473 427.95451 225.28268 308.71751 278.02761 525.04057
## Monghpyak 253.26470 536.71695 206.61627 258.04282 370.01575 568.21089
## Konkyan 328.82831 339.01411 310.60810 248.25265 287.87384 380.92091
## Mongping 202.99615 194.31049 182.75266 119.86993 65.38727 257.18572
## Hopong 91.53795 302.84362 73.45899 106.21031 124.62791 379.37916
## Nyaungshwe 169.63695 502.99026 152.15482 219.72196 327.13541 557.32112
## Hsihseng 142.36728 329.29477 128.21054 194.64317 162.27126 411.59788
## Mongla 354.10985 686.88950 388.40984 411.06668 535.28615 761.48327
## Hseni 216.81639 582.53670 229.37894 286.75945 408.23212 648.04408
## Kunlong 202.92529 446.53763 204.54010 270.02165 299.36066 539.91284
## Hopang 243.00945 561.24281 263.31986 273.50305 408.73288 626.17673
## Namhkan 370.05669 706.47792 392.48568 414.53594 550.62819 771.39688
## Kengtung 272.28711 632.54638 279.19573 329.38387 460.39706 692.74693
## Langkho 174.67678 531.08019 180.51419 236.70878 358.95672 597.42714
## Monghsu 84.11238 332.07962 62.60859 107.04894 154.86049 400.71816
## Taunggyi 448.55282 810.74692 450.33382 508.40925 635.94105 866.21117
## Pangwaun 312.13429 500.68857 321.80465 257.50434 394.07696 536.95736
## Kyethi 210.50453 278.85535 184.23422 222.52947 137.79420 352.06533
## Loilen 58.41263 388.73386 131.56529 176.16001 224.79239 482.18190
## Manton 391.54062 109.08779 361.82684 310.20581 195.59882 81.75337
## Mongyang 260.39387 558.83162 285.33223 295.60023 414.31237 631.91325
## Kunhing 110.55197 398.43973 108.84990 114.03609 238.99570 465.03971
## Mongyawng 275.77546 620.04321 281.03383 375.22688 445.78964 700.98284
## Tangyan 180.37471 262.66006 166.61820 198.88460 109.08506 348.56123
## Namhsan 218.10003 215.19289 191.32762 196.76188 77.35900 288.66231
## Lashio Mongpan Matman Tachileik Narphan Mongkhet
## Pindaya
## Ywangan
## Pinlaung
## Mabein
## Kalaw
## Pekon
## Lawksawk
## Nawnghkio
## Kyaukme
## Muse
## Laihka
## Mongnai
## Mawkmai
## Kutkai
## Mongton
## Mongyai
## Mongkaing
## Lashio
## Mongpan 172.33279
## Matman 628.11049 494.81014
## Tachileik 311.95286 411.03849 890.12935
## Narphan 525.63854 371.13393 312.05193 760.29566
## Mongkhet 534.44463 412.17123 203.02855 820.50164 217.28718
## Hsipaw 290.86435 179.52054 344.45451 576.18780 295.40170 253.80950
## Monghsat 377.86793 283.30992 313.59911 677.09508 278.21548 167.98445
## Mongmao 214.23677 131.59966 501.59903 472.95568 331.42618 375.35820
## Nansang 184.47950 144.77393 458.06573 486.77266 398.13308 360.99219
## Laukkaing 334.65738 435.58047 903.72094 325.06329 708.82887 769.06406
## Pangsang 236.72516 140.23910 506.29940 481.31907 316.30314 375.58139
## Namtu 365.88437 352.91394 416.65397 659.56458 494.36143 355.99713
## Monghpyak 262.09281 187.85699 470.46845 444.04411 448.40651 462.63265
## Konkyan 485.51312 365.87588 392.40306 730.92980 158.82353 254.24424
## Mongping 454.52548 318.47482 201.65224 727.08969 188.64567 113.80917
## Hopong 345.31042 239.43845 291.84351 632.45718 294.40441 212.99485
## Nyaungshwe 201.58191 137.29734 460.91883 445.81335 427.94086 417.08639
## Hsihseng 369.00833 295.87811 304.02806 658.87060 377.52977 256.70338
## Mongla 179.95877 253.20001 708.17595 347.33155 531.46949 574.40292
## Hseni 79.41836 120.66550 564.64051 354.90063 474.12297 481.88406
## Kunlong 295.23103 288.03320 468.27436 595.70536 413.07823 341.68641
## Hopang 170.63913 135.62913 573.55355 403.82035 397.85908 451.51070
## Namhkan 173.27153 240.34131 715.42102 295.91660 536.85519 596.19944
## Kengtung 59.85893 142.21554 613.01033 295.90429 505.40025 531.35998
## Langkho 115.18145 94.98486 518.86151 402.33622 420.65204 428.08061
## Monghsu 325.71557 216.25326 308.13805 605.02113 311.92379 247.73318
## Taunggyi 195.14541 319.81385 778.45810 150.84117 684.20905 712.80752
## Pangwaun 362.45608 232.52209 523.43600 540.60474 264.64997 407.02947
## Kyethi 447.10266 358.89620 233.83079 728.87329 374.90376 233.25039
## Loilen 268.92310 207.25000 406.56282 573.75476 354.79137 284.76895
## Manton 646.66493 507.96808 59.52318 910.23039 280.26395 181.33894
## Mongyang 209.33700 194.93467 585.61776 448.79027 401.39475 445.40621
## Kunhing 255.10832 137.85278 403.66587 532.26397 281.62645 292.49814
## Mongyawng 172.70139 275.15989 601.80824 432.10118 572.76394 522.91815
## Tangyan 429.84475 340.39128 242.78233 719.84066 348.84991 201.49393
## Namhsan 472.04024 364.77086 180.09747 754.03913 316.54695 170.90848
## Hsipaw Monghsat Mongmao Nansang Laukkaing Pangsang
## Pindaya
## Ywangan
## Pinlaung
## Mabein
## Kalaw
## Pekon
## Lawksawk
## Nawnghkio
## Kyaukme
## Muse
## Laihka
## Mongnai
## Mawkmai
## Kutkai
## Mongton
## Mongyai
## Mongkaing
## Lashio
## Mongpan
## Matman
## Tachileik
## Narphan
## Mongkhet
## Hsipaw
## Monghsat 121.78922
## Mongmao 185.99483 247.17708
## Nansang 120.24428 201.92690 164.99494
## Laukkaing 569.06099 626.44910 404.00848 480.60074
## Pangsang 205.04337 256.37933 57.60801 193.36162 408.04016
## Namtu 229.44658 231.78673 365.03882 217.61884 664.06286 392.97391
## Monghpyak 237.67919 356.84917 291.88846 227.52638 565.84279 315.11651
## Konkyan 296.74316 268.25060 281.87425 374.70456 635.92043 274.81900
## Mongping 168.92101 140.95392 305.57166 287.36626 708.13447 308.33123
## Hopong 62.86179 100.45714 244.16253 167.66291 628.48557 261.51075
## Nyaungshwe 169.92664 286.37238 230.45003 131.18943 520.24345 257.77823
## Hsihseng 136.54610 153.49551 311.98001 193.53779 670.74564 335.52974
## Mongla 373.47509 429.00536 216.24705 289.45119 202.55831 217.88123
## Hseni 231.48538 331.22632 184.67099 136.45492 391.74585 214.66375
## Kunlong 205.10051 202.31862 224.43391 183.01388 521.88657 258.49342
## Hopang 248.72536 317.64824 78.29342 196.47091 331.67199 92.57672
## Namhkan 382.79302 455.10875 223.32205 302.89487 196.46063 231.38484
## Kengtung 284.08582 383.72138 207.58055 193.67980 351.48520 229.85484
## Langkho 183.05109 279.52329 134.50170 99.39859 410.41270 167.65920
## Monghsu 58.55724 137.24737 242.43599 153.59962 619.01766 260.52971
## Taunggyi 462.31183 562.88102 387.33906 365.04897 345.98041 405.59730
## Pangwaun 298.12447 343.53898 187.40057 326.12960 470.63605 157.48757
## Kyethi 195.17677 190.50609 377.89657 273.02385 749.99415 396.89963
## Loilen 98.04789 118.65144 190.26490 94.23028 535.57527 207.94433
## Manton 359.60008 317.15603 503.79786 476.55544 907.38406 504.75214
## Mongyang 267.10497 312.64797 91.06281 218.49285 326.19219 108.37735
## Kunhing 90.77517 165.38834 103.91040 128.20940 500.41640 123.18870
## Mongyawng 294.70967 364.40429 296.40789 191.11990 454.80044 336.16703
## Tangyan 167.69794 144.59626 347.14183 249.70235 722.40954 364.76893
## Namhsan 194.47928 169.56962 371.71448 294.16284 760.45960 385.65526
## Namtu Monghpyak Konkyan Mongping Hopong Nyaungshwe
## Pindaya
## Ywangan
## Pinlaung
## Mabein
## Kalaw
## Pekon
## Lawksawk
## Nawnghkio
## Kyaukme
## Muse
## Laihka
## Mongnai
## Mawkmai
## Kutkai
## Mongton
## Mongyai
## Mongkaing
## Lashio
## Mongpan
## Matman
## Tachileik
## Narphan
## Mongkhet
## Hsipaw
## Monghsat
## Mongmao
## Nansang
## Laukkaing
## Pangsang
## Namtu
## Monghpyak 346.57799
## Konkyan 478.37690 463.39594
## Mongping 321.66441 354.76537 242.02901
## Hopong 206.82668 267.95563 304.49287 134.00139
## Nyaungshwe 271.41464 103.97300 432.35040 319.32583 209.32532
## Hsihseng 131.89940 285.37627 383.49700 199.64389 91.65458 225.80242
## Mongla 483.49434 408.03397 468.09747 512.61580 432.31105 347.60273
## Hseni 327.41448 200.26876 448.84563 395.58453 286.41193 130.86310
## Kunlong 233.60474 357.44661 329.11433 309.05385 219.06817 285.13095
## Hopang 408.24516 304.26577 348.18522 379.27212 309.77356 247.19891
## Namhkan 506.32466 379.50202 481.59596 523.74815 444.13246 333.32428
## Kengtung 385.33554 221.47613 474.82621 442.80821 340.47382 177.75714
## Langkho 305.03473 200.27496 386.95022 343.96455 239.63685 128.26577
## Monghsu 209.64684 232.17823 331.72187 158.90478 43.40665 173.82799
## Taunggyi 518.72748 334.17439 650.56905 621.53039 513.76415 325.09619
## Pangwaun 517.03554 381.95144 263.97576 340.37881 346.00673 352.92324
## Kyethi 186.90932 328.16234 400.10989 187.43974 136.49038 288.06872
## Loilen 194.24075 296.99681 334.19820 231.99959 124.74445 206.40432
## Manton 448.58230 502.20840 366.66876 200.48082 310.58885 488.79874
## Mongyang 413.26052 358.17599 329.39338 387.80686 323.35704 294.29500
## Kunhing 296.43996 250.74435 253.74202 212.59619 145.15617 189.97131
## Mongyawng 262.24331 285.56475 522.38580 455.59190 326.59925 218.12104
## Tangyan 178.69483 335.26416 367.46064 161.67411 106.82328 284.14692
## Namhsan 240.95555 352.70492 352.20115 130.23777 132.70541 315.91750
## Hsihseng Mongla Hseni Kunlong Hopang Namhkan
## Pindaya
## Ywangan
## Pinlaung
## Mabein
## Kalaw
## Pekon
## Lawksawk
## Nawnghkio
## Kyaukme
## Muse
## Laihka
## Mongnai
## Mawkmai
## Kutkai
## Mongton
## Mongyai
## Mongkaing
## Lashio
## Mongpan
## Matman
## Tachileik
## Narphan
## Mongkhet
## Hsipaw
## Monghsat
## Mongmao
## Nansang
## Laukkaing
## Pangsang
## Namtu
## Monghpyak
## Konkyan
## Mongping
## Hopong
## Nyaungshwe
## Hsihseng
## Mongla 478.66210
## Hseni 312.74375 226.82048
## Kunlong 231.85967 346.46200 276.19175
## Hopang 370.01334 147.02444 162.80878 271.34451
## Namhkan 492.09476 77.21355 212.11323 375.73885 146.18632
## Kengtung 370.72441 202.45004 66.12817 317.14187 164.29921 175.63015
## Langkho 276.27441 229.01675 66.66133 224.52741 134.24847 224.40029
## Monghsu 97.82470 424.51868 262.28462 239.89665 301.84458 431.32637
## Taunggyi 528.14240 297.09863 238.19389 471.29032 329.95252 257.29147
## Pangwaun 433.06326 319.18643 330.70182 392.45403 206.98364 310.44067
## Kyethi 84.04049 556.02500 388.33498 298.55859 440.48114 567.86202
## Loilen 158.84853 338.67408 227.10984 166.53599 242.89326 364.90647
## Manton 334.87758 712.51416 584.63341 479.76855 577.52046 721.86149
## Mongyang 382.59743 146.66661 210.19929 247.22785 69.25859 167.72448
## Kunhing 220.15490 306.47566 206.47448 193.77551 172.96164 314.92119
## Mongyawng 309.51462 315.57550 173.86004 240.39800 290.51360 321.21112
## Tangyan 70.27241 526.80849 373.07575 268.07983 412.22167 542.64078
## Namhsan 125.74240 564.02740 411.96125 310.40560 440.51555 576.42717
## Kengtung Langkho Monghsu Taunggyi Pangwaun Kyethi
## Pindaya
## Ywangan
## Pinlaung
## Mabein
## Kalaw
## Pekon
## Lawksawk
## Nawnghkio
## Kyaukme
## Muse
## Laihka
## Mongnai
## Mawkmai
## Kutkai
## Mongton
## Mongyai
## Mongkaing
## Lashio
## Mongpan
## Matman
## Tachileik
## Narphan
## Mongkhet
## Hsipaw
## Monghsat
## Mongmao
## Nansang
## Laukkaing
## Pangsang
## Namtu
## Monghpyak
## Konkyan
## Mongping
## Hopong
## Nyaungshwe
## Hsihseng
## Mongla
## Hseni
## Kunlong
## Hopang
## Namhkan
## Kengtung
## Langkho 107.16213
## Monghsu 316.91914 221.84918
## Taunggyi 186.28225 288.27478 486.91951
## Pangwaun 337.48335 295.38434 343.38498 497.61245
## Kyethi 444.26274 350.91512 146.61572 599.57407 476.62610
## Loilen 282.22935 184.10672 131.55208 455.91617 331.69981 232.32965
## Manton 631.99123 535.95620 330.76503 803.08034 510.79265 272.03299
## Mongyang 217.08047 175.35413 323.95988 374.58247 225.25026 453.86726
## Kunhing 245.95083 146.38284 146.78891 429.98509 229.09986 278.95182
## Mongyawng 203.87199 186.11584 312.85089 287.73864 475.33116 387.71518
## Tangyan 429.95076 332.02048 127.42203 592.65262 447.05580 47.79331
## Namhsan 466.20497 368.20978 153.22576 631.49232 448.58030 68.67929
## Loilen Manton Mongyang Kunhing Mongyawng Tangyan
## Pindaya
## Ywangan
## Pinlaung
## Mabein
## Kalaw
## Pekon
## Lawksawk
## Nawnghkio
## Kyaukme
## Muse
## Laihka
## Mongnai
## Mawkmai
## Kutkai
## Mongton
## Mongyai
## Mongkaing
## Lashio
## Mongpan
## Matman
## Tachileik
## Narphan
## Mongkhet
## Hsipaw
## Monghsat
## Mongmao
## Nansang
## Laukkaing
## Pangsang
## Namtu
## Monghpyak
## Konkyan
## Mongping
## Hopong
## Nyaungshwe
## Hsihseng
## Mongla
## Hseni
## Kunlong
## Hopang
## Namhkan
## Kengtung
## Langkho
## Monghsu
## Taunggyi
## Pangwaun
## Kyethi
## Loilen
## Manton 419.06087
## Mongyang 246.76592 585.70558
## Kunhing 130.39336 410.49230 188.89405
## Mongyawng 261.75211 629.43339 304.21734 295.35984
## Tangyan 196.60826 271.82672 421.06366 249.74161 377.52279
## Namhsan 242.15271 210.48485 450.97869 270.79121 430.02019 63.676136.4 Computing hierarchical clustering
For this hands-on exercise, we will use hclust() function of R stats package.
hclust() function employed agglomeration method to compute the cluster. 8 clustering algorithms are supported, namely ward.D, ward.D2, single, complete, average (UPGMA), mcquitty (WPGMA), median (WPGMC) and centroid (UPGMC).
hclust_ward <- hclust(proxmat, method = "ward.D")Then, we can plot the cluster tree using plot() function of R graphics.
plot(hclust_ward, cex = 0.6)
6.5 Selecting the optimal clustering algorithm
A challenge in performing hierarchical clustering is to identify stronger clustering structures.
This challenge can be solved by using the agnes() function of cluster package. agnes() functions like hclust() function. However, with agnes() function, you can also get the agglomerative coefficient, which measures the amount of clustering structure found. (Values closer to 1 suggest strong clustering structure)
m <- c("average", "single", "complete", "ward")
names(m) <- c("average", "single", "complete", "ward")
ac <- function(x) {
agnes(shan_ict, method = x)$ac
}
map_dbl(m, ac)## average single complete ward
## 0.8131144 0.6628705 0.8950702 0.9427730We can see that ward’s method provides the strongest clustering structure among the four methods used. Hence, we will use ward’s method.
6.5.1 Interpreting the dendograms
In the dendogram above, each leaf corresponds to one observation. As we move up the dendogram tree, observations that are similar to each other are combined into branches, which are fused again at higher height.
The height of the dendogram tree, provided on the vertical axis, indicates the (dis)similarity between two observations. The higher the height of the fusion, the less similar the observations are. Note that, conclusions about the proximity of two observations can be drawn only based on the height where branches containing those two observations first are fused. We cannot use the proximity of two observations along the horizontal axis as a criteria of their similarity.
We can also create a dendogram with a border around the selected clusters using rect.hclust() function of R stats package. The argument border is used to specify the border colours for the rectangles.
plot(hclust_ward, cex = 0.6)
rect.hclust(hclust_ward, k=5, border = 2:5)
6.6 Visually-driven hierarchical clustering analysis
We will also learn how to perform visually-driven hierarchical clustering analysis by using heatmaply package to produce both static & interactive cluster heatmaps.
6.6.1 Transforming data frame into matrix
The data was loaded into a data frame, but it has to be a data matrix to make your heatmap.
shan_ict_mat <- data.matrix(shan_ict)6.6.2 Plotting interactive cluster heatmap
heatmaply(normalize(shan_ict_mat),
Colv = NA,
dist_method = "euclidean",
hclust_method = "ward.D",
seriate = "OLO",
colors = Blues,
k_row = 5,
margins = c(NA,200,60,NA),
fontsize_row = 4,
fontsize_col = 5,
main = "Geographic Segmentation of Shan State by ICT Indicators",
xlab = "ICT Indicators",
ylab = "Townships of Shan State")6.7 Mapping the clusters formed
With closed examination of the dendogram above, we have decided to retain 5 clusters.
For this, we will use cutree() function of Base R to derive a 5-cluster model.
groups <- as.factor(cutree(hclust_ward, k=5))
groups## Mongmit Pindaya Ywangan Pinlaung Mabein Kalaw Pekon
## 1 1 2 1 3 3 1
## Lawksawk Nawnghkio Kyaukme Muse Laihka Mongnai Mawkmai
## 3 3 3 4 1 1 2
## Kutkai Mongton Mongyai Mongkaing Lashio Mongpan Matman
## 1 1 2 2 3 3 2
## Tachileik Narphan Mongkhet Hsipaw Monghsat Mongmao Nansang
## 4 2 2 1 2 5 1
## Laukkaing Pangsang Namtu Monghpyak Konkyan Mongping Hopong
## 4 5 1 3 2 2 1
## Nyaungshwe Hsihseng Mongla Hseni Kunlong Hopang Namhkan
## 3 1 4 3 1 5 4
## Kengtung Langkho Monghsu Taunggyi Pangwaun Kyethi Loilen
## 3 3 1 4 5 1 1
## Manton Mongyang Kunhing Mongyawng Tangyan Namhsan
## 2 5 1 3 1 1
## Levels: 1 2 3 4 5The output “groups” is a factor list object.
To visualize the clusters, the groups object need to be appended onto shan_sf simple feature data.frame.
To join/append:
the groups object to be converted to a matrix
cbind() function of Base R used to append groups matrix to shan_sf to produce sf object called “shan_sf_cluster”
rename() function of dplyr package used to rename as.matrix.groups field as CLUSTER
shan_sf_cluster <- cbind(shan_sf, as.matrix(groups)) %>%
rename(`CLUSTER` = `as.matrix.groups.`)
head(shan_sf_cluster)## Simple feature collection with 6 features and 31 fields
## geometry type: MULTIPOLYGON
## dimension: XY
## bbox: xmin: 96.15107 ymin: 19.74308 xmax: 97.3376 ymax: 24.15907
## geographic CRS: WGS 84
## OBJECTID ST ST_PCODE DT.x DT_PCODE.x TS.x TS_PCODE
## Mongmit 163 Shan (North) MMR015 Mongmit MMR015D008 Mongmit MMR015017
## Pindaya 203 Shan (South) MMR014 Taunggyi MMR014D001 Pindaya MMR014006
## Ywangan 240 Shan (South) MMR014 Taunggyi MMR014D001 Ywangan MMR014007
## Pinlaung 106 Shan (South) MMR014 Taunggyi MMR014D001 Pinlaung MMR014009
## Mabein 72 Shan (North) MMR015 Mongmit MMR015D008 Mabein MMR015018
## Kalaw 40 Shan (South) MMR014 Taunggyi MMR014D001 Kalaw MMR014005
## ST_2 LABEL2 SELF_ADMIN ST_RG T_NAME_WIN
## Mongmit Shan State (North) Mongmit\n61072 <NA> State rdk;rdwf
## Pindaya Shan State (South) Pindaya\n77769 Danu State yif;w,
## Ywangan Shan State (South) Ywangan\n76933 Danu State &GmiH
## Pinlaung Shan State (South) Pinlaung\n162537 Pa-O State yifavmif;
## Mabein Shan State (North) Mabein\n35718 <NA> State rbdrf;
## Kalaw Shan State (South) Kalaw\n163138 <NA> State uavm
## T_NAME_M3
## Mongmit <U+1019><U+102D><U+102F><U+1038><U+1019><U+102D><U+1010><U+103A>
## Pindaya <U+1015><U+1004><U+103A><U+1038><U+1010><U+101A>
## Ywangan <U+101B><U+103D><U+102C><U+1004><U+1036>
## Pinlaung <U+1015><U+1004><U+103A><U+101C><U+1031><U+102C><U+1004><U+103A><U+1038>
## Mabein <U+1019><U+1018><U+102D><U+1019><U+103A><U+1038>
## Kalaw <U+1000><U+101C><U+1031><U+102C>
## AREA DT_PCODE.y DT.y TS.y TT_HOUSEHOLDS RADIO TV
## Mongmit 2703.611 MMR015D003 Kyaukme Mongmit 13652 3907 7565
## Pindaya 629.025 MMR014D001 Taunggyi Pindaya 17544 7324 8862
## Ywangan 2984.377 MMR014D001 Taunggyi Ywangan 18348 8890 4781
## Pinlaung 3396.963 MMR014D001 Taunggyi Pinlaung 25504 5908 13816
## Mabein 5034.413 MMR015D003 Kyaukme Mabein 8632 3880 6117
## Kalaw 1456.624 MMR014D001 Taunggyi Kalaw 41341 11607 25285
## LLPHONE MPHONE COMPUTER INTERNET RADIO_PR TV_PR LLPHONE_PR
## Mongmit 482 3559 166 321 286.1852 554.1313 35.30618
## Pindaya 348 2849 226 136 417.4647 505.1300 19.83584
## Ywangan 219 2207 81 152 484.5215 260.5734 11.93591
## Pinlaung 728 6363 351 737 231.6499 541.7189 28.54454
## Mabein 628 3389 142 165 449.4903 708.6423 72.75255
## Kalaw 1739 16900 1225 1741 280.7624 611.6204 42.06478
## MPHONE_PR COMPUTER_PR INTERNET_PR CLUSTER
## Mongmit 260.6944 12.15939 23.513038 1
## Pindaya 162.3917 12.88190 7.751938 1
## Ywangan 120.2856 4.41465 8.284282 2
## Pinlaung 249.4903 13.76255 28.897428 1
## Mabein 392.6089 16.45042 19.114921 3
## Kalaw 408.7951 29.63160 42.113156 3
## geometry
## Mongmit MULTIPOLYGON (((96.96001 23...
## Pindaya MULTIPOLYGON (((96.7731 21....
## Ywangan MULTIPOLYGON (((96.78483 21...
## Pinlaung MULTIPOLYGON (((96.49518 20...
## Mabein MULTIPOLYGON (((96.66306 24...
## Kalaw MULTIPOLYGON (((96.49518 20...Next, we will visualize the clusters using qtm() function of tmap package to plot the choropleth map.
qtm(shan_sf_cluster, "CLUSTER")
The choropleth map above displays the clusters computed using hierarchical clustering function hclust() of Base R. It also reveals that the clusters are very fragmented.
Fragmentation is one of the major limitation when performing non-spatial clustering algorithm such as hierarchical clustering analysis method.
7. Spatially Constrained Clustering - SKATER method
There are two approach to Spatially Constrained Clustering, SKATER method & ClustGeo method.
7.1 Converting shan_sf into SpatialPolygonsDataFrame
SKATER function only support sp Spatial objects such as SpatialPolygonsDataFrame or SpatialPointsDataFrame. Hence, we need to convert shan_sf into sp object using as_Spatial() function of sf package.
shan_sp <- as_Spatial(shan_sf)7.2 Computing Neighbour list
Next, we will use poly2nb() function of spdep package to compute the neighbours list from the shan_sp sp object.
This function builds a neighbours list based on regions with contiguous boundaries, since we did not specify the queen argument, it will return a list of first order neighbours using Queen criteria.
shan.nb <- poly2nb(shan_sp)
summary(shan.nb)## Neighbour list object:
## Number of regions: 55
## Number of nonzero links: 264
## Percentage nonzero weights: 8.727273
## Average number of links: 4.8
## Link number distribution:
##
## 2 3 4 5 6 7 8 9
## 5 9 7 21 4 3 5 1
## 5 least connected regions:
## 3 5 7 9 47 with 2 links
## 1 most connected region:
## 8 with 9 linksFrom the summary, we can find out that:
There are 55 townships (55 rows)
Most connected township has 9 neighbours which is shown by the first row 9 with the next row showing 1 meaning only 1 township has 9 neighbours
Since we can plot the community area boundaries, we should plot this graph on top of the map. The first plot command gives Shan state boundaries. This is followed by the plot of the neighbor list object, with coordinates applied to the original SpatialPolygonDataFrame (Shan state township boundaries) to extract the centroids of the polygons. These are used as the nodes for the graph representation. We also set the color to blue and specify add=TRUE to plot the network on top of the boundaries.
plot(shan_sp, border=grey(.5))
plot(shan.nb, coordinates(shan_sp), col="blue", add=TRUE)
Note that if you plot the network first and then the boundaries, some of the areas will be clipped. This is because the plotting area is determined by the characteristics of the first plot. In this example, because the boundary map extends further than the graph, we plot it first.
7.3 Computing minimum spanning tree
7.3.1 Calculating edge costs
Next, we will use nbcosts() function of spdep package to compute the cost of each edge, the distance between nodes.
This function compute this distance using a data.frame with observations vector in each node.
lcosts <- nbcosts(shan.nb, shan_ict)
lcosts## [[1]]
## [1] 263.3710 144.0247 430.6407 237.7849
##
## [[2]]
## [1] 257.3161 302.5179 204.3295
##
## [[3]]
## [1] 257.3161 432.1653
##
## [[4]]
## [1] 181.96406 94.61225 138.12050
##
## [[5]]
## [1] 263.3710 674.0112
##
## [[6]]
## [1] 302.51785 181.96406 140.01101 95.66782 252.26066
##
## [[7]]
## [1] 94.61225 139.31874
##
## [[8]]
## [1] 204.32952 432.16535 140.01101 90.82891 186.29066 625.18712 249.35081
## [8] 274.91604 304.96838
##
## [[9]]
## [1] 90.82891 157.04230
##
## [[10]]
## [1] 144.0247 186.2907 157.0423 163.9574 347.8594
##
## [[11]]
## [1] 592.9074 704.8697 238.6706
##
## [[12]]
## [1] 522.96309 78.78999 157.48857 255.83275 59.69478
##
## [[13]]
## [1] 374.50873 131.67061 178.09554 92.79567 202.99615 174.67678 110.55197
##
## [[14]]
## [1] 374.5087 462.4194 329.2948 531.0802 388.7339
##
## [[15]]
## [1] 592.9074 580.3811 310.6081 229.3789 204.5401 392.4857 361.8268
##
## [[16]]
## [1] 131.6706 200.3180 150.9805 119.8699 236.7088
##
## [[17]]
## [1] 466.3647 177.3379 137.7942 109.0851
##
## [[18]]
## [1] 625.1871 522.9631 423.7787 379.3792 352.0653
##
## [[19]]
## [1] 466.36472 290.86435 365.88437 79.41836 170.63913 646.66493 429.84475
##
## [[20]]
## [1] 178.09554 200.31803 94.98486
##
## [[21]]
## [1] 203.0285 506.2994 201.6522 308.1380 585.6178 242.7823
##
## [[22]]
## [1] 677.0951 444.0441 432.1012
##
## [[23]]
## [1] 331.4262 316.3031 264.6500
##
## [[24]]
## [1] 203.0285 113.8092 574.4029 531.3600 445.4062
##
## [[25]]
## [1] 249.3508 163.9574 177.3379 423.7787 290.8643 229.4466 195.1768 194.4793
##
## [[26]]
## [1] 150.9805 677.0951 356.8492 140.9539 383.7214
##
## [[27]]
## [1] 331.42618 57.60801 78.29342 187.40057 347.14183
##
## [[28]]
## [1] 78.78999 92.79567 462.41938 273.02385 94.23028 128.20940
##
## [[29]]
## [1] 580.3811 635.9204 521.8866 331.6720
##
## [[30]]
## [1] 506.29940 316.30314 57.60801 108.37735 364.76893
##
## [[31]]
## [1] 365.8844 229.4466 448.5823 240.9555
##
## [[32]]
## [1] 444.0441 356.8492 408.0340 221.4761 285.5647
##
## [[33]]
## [1] 704.8697 310.6081 635.9204
##
## [[34]]
## [1] 202.9962 119.8699 201.6522 113.8092 140.9539 442.8082 158.9048 212.5962
##
## [[35]]
## [1] 274.91604 157.48857 379.37916 91.65458 513.76415 124.74445
##
## [[36]]
## [1] 138.12050 95.66782 139.31874 225.80242 325.09619
##
## [[37]]
## [1] 329.29477 91.65458 225.80242 528.14240 158.84853
##
## [[38]]
## [1] 574.4029 408.0340 202.4500 146.6666 315.5755
##
## [[39]]
## [1] 229.37894 79.41836 276.19175 162.80878 584.63341
##
## [[40]]
## [1] 204.5401 521.8866 276.1918 271.3445
##
## [[41]]
## [1] 170.63913 78.29342 331.67199 162.80878 271.34451 412.22167
##
## [[42]]
## [1] 238.6706 392.4857 721.8615
##
## [[43]]
## [1] 531.3600 383.7214 221.4761 442.8082 202.4500
##
## [[44]]
## [1] 174.67678 531.08019 236.70878 94.98486
##
## [[45]]
## [1] 308.1380 158.9048 146.6157 146.7889 127.4220
##
## [[46]]
## [1] 252.2607 304.9684 513.7642 325.0962 528.1424
##
## [[47]]
## [1] 264.6500 187.4006
##
## [[48]]
## [1] 255.83275 137.79420 352.06533 195.17677 273.02385 146.61572 278.95182
## [8] 47.79331
##
## [[49]]
## [1] 59.69478 388.73386 94.23028 124.74445 158.84853
##
## [[50]]
## [1] 430.6407 674.0112 361.8268 646.6649 448.5823 584.6334 721.8615 210.4849
##
## [[51]]
## [1] 585.6178 445.4062 108.3773 146.6666
##
## [[52]]
## [1] 110.5520 128.2094 212.5962 146.7889 278.9518
##
## [[53]]
## [1] 432.1012 285.5647 315.5755
##
## [[54]]
## [1] 109.08506 429.84475 242.78233 347.14183 364.76893 412.22167 127.42203
## [8] 47.79331
##
## [[55]]
## [1] 237.7849 347.8594 194.4793 240.9555 210.4849
##
## attr(,"call")
## nbcosts(nb = shan.nb, data = shan_ict)
## attr(,"class")
## [1] "nbdist"lcosts is a nbdist object which for each observation, gives the pairwise dissimilarity between its values on the five variables & values for the neighbouring observation.
Basically, lcosts is the notion of a generalised weight for a spatial weights matrix.
Next, we will incorporate these spatial weights/costs into a weights object in the same way as we did in the calculation of inverse distance weights.
In other words, we convert the neighbour list to a list weights object by specifying the just computed lcosts as the weights.
We will use nb2listw() function of spdep package to achieve this and we specify the style as B to make sure the cost values are not row-standardised.
shan.w <- nb2listw(shan.nb, lcosts, style = "B")
summary(shan.w)## Characteristics of weights list object:
## Neighbour list object:
## Number of regions: 55
## Number of nonzero links: 264
## Percentage nonzero weights: 8.727273
## Average number of links: 4.8
## Link number distribution:
##
## 2 3 4 5 6 7 8 9
## 5 9 7 21 4 3 5 1
## 5 least connected regions:
## 3 5 7 9 47 with 2 links
## 1 most connected region:
## 8 with 9 links
##
## Weights style: B
## Weights constants summary:
## n nn S0 S1 S2
## B 55 3025 76267.65 58260785 5220160047.3.2 Computing minimum spanning tree
The minimum spanning tree (MST) is computed by mean of the mstree() function of spdep package.
shan.mst <- mstree(shan.w)After computing MST, we can check shan.mst’s class and dimension by using class() function.
class(shan.mst)## [1] "mst" "matrix"dim(shan.mst)## [1] 54 3We can see that shan.mst is a mst object & note that the dimension is 54 and not 55 because the MST consists of n-1 edges (links) in order to traverse all the nodes.
head(shan.mst)## [,1] [,2] [,3]
## [1,] 26 34 140.95392
## [2,] 34 24 113.80917
## [3,] 34 16 119.86993
## [4,] 16 13 131.67061
## [5,] 13 28 92.79567
## [6,] 28 12 78.78999The plot method for MST object include a way to show the observation numbers of the nodes in addition to the egde. As before, we will plot this together with the township boundaries. We can see how the initial neighbour list is simplified to just one edge connecting each of the nodes, while passing through all the nodes.
plot(shan_sp, border=gray(.5))
plot.mst(shan.mst, coordinates(shan_sp), col = "blue", cex.lab = 0.7, cex.circles = 0.005, add = TRUE)
7.4 Computing SKATER spatially constrained clusters
We will use skater() function of spdep package to compute the spatially constrained clusters.
clust5 <- skater(shan.mst[,1:2], shan_ict, method = "euclidean", 4)The skater() function takes 3 mandatory arguments:
the first two columns of the MST matrix
data matrix
number of cuts (set to one less than number of clusters)
The result will give “clust5”, an object of class skater.
str(clust5)## List of 8
## $ groups : num [1:55] 3 3 3 3 3 3 3 3 3 3 ...
## $ edges.groups:List of 5
## ..$ :List of 3
## .. ..$ node: num [1:22] 13 48 45 55 52 37 34 16 25 54 ...
## .. ..$ edge: num [1:21, 1:3] 48 55 45 37 34 34 52 25 16 13 ...
## .. ..$ ssw : num 3423
## ..$ :List of 3
## .. ..$ node: num [1:18] 47 27 53 38 42 15 41 51 43 32 ...
## .. ..$ edge: num [1:17, 1:3] 53 15 42 38 41 51 15 27 15 43 ...
## .. ..$ ssw : num 3759
## ..$ :List of 3
## .. ..$ node: num [1:12] 10 9 6 2 8 1 4 36 46 3 ...
## .. ..$ edge: num [1:11, 1:3] 2 6 8 1 36 4 6 10 10 8 ...
## .. ..$ ssw : num 1846
## ..$ :List of 3
## .. ..$ node: num [1:2] 44 20
## .. ..$ edge: num [1, 1:3] 44 20 95
## .. ..$ ssw : num 95
## ..$ :List of 3
## .. ..$ node: num 23
## .. ..$ edge: num[0 , 1:3]
## .. ..$ ssw : num 0
## $ not.prune : NULL
## $ candidates : int [1:5] 1 2 3 4 5
## $ ssto : num 12613
## $ ssw : num [1:5] 12613 10977 9962 9540 9123
## $ crit : num [1:2] 1 Inf
## $ vec.crit : num [1:55] 1 1 1 1 1 1 1 1 1 1 ...
## - attr(*, "class")= chr "skater"The most interesting component of this skater list structure is the groups vector containing the labels of the cluster to which each observation belongs to.
This is followed by a detailed summary for each of the clusters in the edges.groups list. Sum of squares measures are given as ssto for the total and ssw to show the effect of each of the cuts on the overall criterion.
Now, let’s check the cluster assignment by calling the groups variable of the clust5 skater object.
ccs5 <- clust5$groups
ccs5## [1] 3 3 3 3 3 3 3 3 3 3 2 1 1 1 2 1 1 1 2 4 1 2 5 1 1 1 2 1 2 2 1 2 2 1 1 3 1 2
## [39] 2 2 2 2 2 4 1 3 2 1 1 1 2 1 2 1 1We can find out how many observations are in each cluster by using table() function.
table(ccs5)## ccs5
## 1 2 3 4 5
## 22 18 12 2 1Lastly, we will plot the pruned tree that shows the 5 clusters on top of the township boundary layer.
plot(shan_sp, border=gray(.5))
plot(clust5, coordinates(shan_sp), cex.lab=.7, groups.colors=c("red","green","purple","blue","black"), cex.circles=0.005, add=TRUE)
7.5 Visualizing the clusters in choropleth map
We will use qtm() function to plot the newly derived clusters using SKATER method.
groups_mat <- as.matrix(clust5$groups)
shan_sf_spatialcluster <- cbind(shan_sf_cluster, as.factor(groups_mat)) %>%
rename(`SP_CLUSTER` = `as.factor.groups_mat.`)
qtm(shan_sf_spatialcluster, "SP_CLUSTER")