library(mapdeck)## Warning: package 'mapdeck' was built under R version 3.6.2library(factoextra)## Loading required package: ggplot2## Welcome! Related Books: `Practical Guide To Cluster Analysis in R` at https://goo.gl/13EFCZlibrary(plotly)##
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library(dplyr)##
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#The goal of the job is to get the probability of being a victim of a crime on each suburb of Buenos Aires city for a specific time zone.
#The data is available from the Buenos Aires government web
crimes_2016 <- read.csv(file = "/Users/user/Desktop/Data Scientis R Python SQL/Datasets/Delitos/delitos_2016.csv")
crimes_2017 <- read.csv(file = "/Users/user/Desktop/Data Scientis R Python SQL/Datasets/Delitos/delitos_2017.csv")
crimes_2018 <- read.csv(file = "/Users/user/Desktop/Data Scientis R Python SQL/Datasets/Delitos/delitos_2018.csv")
crimes_2019 <- read.csv(file = "/Users/user/Desktop/Data Scientis R Python SQL/Datasets/Delitos/delitos_2019.csv")
crimes_2020 <- read.csv(file = "/Users/user/Desktop/Data Scientis R Python SQL/Datasets/Delitos/delitos_2020.csv")
crimes_2021 <- read.csv(file = "/Users/user/Desktop/Data Scientis R Python SQL/Datasets/Delitos/delitos_2021.csv", header = T, sep = ";")#There are some columns unnecessary for the analysis that will be removed from the datasets.
crimes_2016_df <- crimes_2016[,c(-1,-2,-5,-7)]
crimes_2017_df <- crimes_2017[,c(-1,-2,-5,-7)]
crimes_2018_df <- crimes_2018[,c(-1,-2,-5,-7)]
crimes_2019_df <- crimes_2019[,c(-1,-2,-5,-7)]
crimes_2020_df <- crimes_2020[,c(-1,-2,-3,-4,-5,-8,-9,-11)]
crimes_2021_df <- crimes_2021[,c(-1,-2,-3,-4,-5,-8,-9,-11)]
colnames(crimes_2020_df) = c("franja_horaria","tipo_delito","barrio","lat","long","cantidad_registrada")
colnames(crimes_2021_df) = c("franja_horaria","tipo_delito","barrio","lat","long","cantidad_registrada")#The datasets will be merged into one
crimes_2016_df <- crimes_2016_df[,c("franja_horaria","tipo_delito","barrio","lat","long","cantidad_registrada")]
crimes_2017_df <- crimes_2017_df[,c("franja_horaria","tipo_delito","barrio","lat","long","cantidad_registrada")]
crimes_2018_df <- crimes_2018_df[,c("franja_horaria","tipo_delito","barrio","lat","long","cantidad_registrada")]
crimes_2019_df <- crimes_2019_df[,c("franja_horaria","tipo_delito","barrio","lat","long","cantidad_registrada")]
crimes <- rbind(crimes_2016_df,crimes_2017_df,crimes_2018_df,crimes_2019_df,crimes_2020_df,crimes_2021_df)
#Column names are translated
colnames(crimes) <-c("time_zone","crime_type","suburb","lat","long","number")#The dataset has 7 columns and 648656 registers
summary(crimes)## time_zone crime_type suburb
## 20 : 41735 Homicidio : 1424 Palermo : 51904
## 19 : 40951 Hurto (sin violencia):242060 Balvanera : 44464
## 18 : 39915 Lesiones : 52414 Flores : 33398
## 21 : 36949 Robo (con violencia) :352758 Recoleta : 30185
## 17 : 35347 Caballito : 29799
## 12 : 33954 San Nicolás: 27739
## (Other):419805 (Other) :431167
## lat long number
## Length:648656 Length:648656 Min. : 1.00
## Class :character Class :character 1st Qu.: 1.00
## Mode :character Mode :character Median : 1.00
## Mean : 1.01
## 3rd Qu.: 1.00
## Max. :16.00
## NA's :259972##The columns are:
#time_zone: Time zone where the crimen was commited displayed in hours. (1 to 24 hs)
#crime_type: Crime type
#suburb: Suburb of Buenos Aires city
#lat: Latitude
#long: Longitude
#number: Number of victims affected by the crime#Preprocessing data
#The "latitude" and "longitude" columns will be changed to the correct datatype
crimes$lat <- as.double(crimes$lat)## Warning: NAs introduced by coercioncrimes$long <- as.double(crimes$long)## Warning: NAs introduced by coercion#There are some grammatical errors that will be fixed using gsub function.
#Values without data will be imputed by NA
crimes$suburb <- as.factor(gsub("^$",NA, crimes$suburb))
crimes$time_zone <- as.factor(gsub("S/D",NA, crimes$time_zone))
crimes$time_zone <- as.factor(gsub("sd",NA, crimes$time_zone))
crimes$suburb <- as.factor(gsub("La Boca","Boca", crimes$suburb))
crimes$time_zone <- as.factor(gsub("SD",NA, crimes$time_zone))
#For each crime is assumed at least one victim. So, in column "number" NA values will be imputed by 1.
crimes[is.na(crimes$number),"number"] <- 1
#Atypical values in "Lat" and "Long" columns will be removed
crimes <- crimes[crimes$lat>-35 & crimes$long>-59,]
#There are some registers with NA values in each columns that will be removed
crimes <- crimes[rowSums(is.na(crimes)) != ncol(crimes), ]
#Registers without time zone will be removed
crimes <- crimes[!is.na(crimes$time_zone),]#Functions
#The function "proportion" will return the proportions of a numeric column grouping by categorical column
proportion <- function(df,categoric_column,numeric_column,column_name){
prop <- data.frame()
for (i in unique(df[,categoric_column])){
b <- data.frame(column_name =df[df[,categoric_column]==i,numeric_column]/sum(df[df[,categoric_column]==i,numeric_column]))
colnames(b) <- column_name
prop <- rbind(prop,b)
}
return(prop)
}
#The function "sample_function" will return a random sample of index
sample_function <- function(dataframe, proportion){
n = round(nrow(dataframe)*proportion,0)
indice = sample(1:n,n, replace = F)
return(indice)
}#Making of the final dataset:
#It is assumed that there are some areas more dangerous than others in each suburb
#So each suburb will be grouping into three zones. For example, the suburb "Palermo" will be divided in "Palermo Zone 1", "Palermo Zone 2" and "Palermo Zone 3"
crimes_zone <- data.frame()
for (i in unique(crimes$suburb)){
for (j in 1:3){
data <- subset(crimes, suburb == i)
filt_long <- scale(subset(crimes, suburb == i, select = "long"),
center = T,
scale = F)
filt_lat <- scale(subset(crimes, suburb == i, select = "lat"),
center = T,
scale = F)
if (j==1){
data_filt <- data.frame(data[filt_long > 0 & filt_lat > 0,],
Zone = paste(i," Zone ",j))}
else if (j==2){
data_filt <- data.frame(data[filt_long < 0 & filt_lat > 0,],
Zone = paste(i," Zone ",j))}
else {
data_filt <- data.frame(data_filt <- data[filt_lat < 0,],
Zone = paste(i," Zone ",j))}
crimes_zone <- rbind(crimes_zone,data_filt)
}
}
#Next step is to group by zone and timezone
crimes_group <- data.frame(
aggregate(number~Zone+time_zone,crimes_zone, FUN = sum),
lat = aggregate(lat~Zone+time_zone,crimes_zone, FUN = mean)[,"lat"],
long = aggregate(long~Zone+time_zone,crimes_zone, FUN = mean)[,"long"])
#The suburb column will be added into the final dataset
crimes_group$suburb <- gsub(" Zone 3","",gsub(" Zone 2","",gsub(" Zone 1", "", crimes_group$Zone)))
#The portion of victims grouping by suburb will be added into the final dataset
crimes_group[,"prop_suburb"] <- proportion(crimes_group,"suburb","number","prop_suburb")
#The portion of victims grouping by time zone will be added into the final dataset
crimes_group[,"prop_time_zone"] <- proportion(crimes_group,"time_zone","number","prop_time_zone")
#Transform the number of victims as proportion
crimes_group$prop_number <- prop.table(crimes_group$number)
#Suburb column in no longer needed
crimes_group$suburb <- NULL
#Final dataset:
head(crimes_group)## Zone time_zone number lat long
## 1 Parque Avellaneda Zone 1 0 158 -34.64349 -58.47105
## 2 Parque Avellaneda Zone 2 0 145 -34.64352 -58.48404
## 3 Parque Avellaneda Zone 3 0 275 -34.65383 -58.47556
## 4 Palermo Zone 1 0 365 -34.57501 -58.41387
## 5 Palermo Zone 2 0 465 -34.57356 -58.43393
## 6 Palermo Zone 3 0 1395 -34.58866 -58.42350
## prop_suburb prop_time_zone prop_number
## 1 0.01764574 0.005606018 0.0002861127
## 2 0.01619388 0.005144763 0.0002625718
## 3 0.03071253 0.009757309 0.0004979809
## 4 0.00580746 0.012950610 0.0006609565
## 5 0.00692428 0.016498723 0.0008420405
## 6 0.01183828 0.049496168 0.0025261214#Clustering: Under the assumption that suburbs don’t have a high rate of full-time crime, each zone/hour will be clustered into three groups: 1, 2 or 3, where group number 1 will have a high rate of crime, the second one a medium rate and the third one a low rate
#Using the kmeans function, 3 centers will be taken
set.seed(1)
k3 <- kmeans(scale(crimes_group[,c("lat","long","prop_suburb","prop_time_zone","prop_number")], center = T, scale = T)
,nstart = 25,
centers = 3)
clusters <- fviz_cluster(k3, data = scale(data.frame(crimes_group[,c("lat","long","prop_suburb","prop_time_zone","prop_number")]), center = T, scale = T))[[1]]["cluster"]
#Cluster column is added to the final dataset
crimes_group_clust <- cbind(crimes_group,clusters)
#The clustering shows that the cluster 1 groups 371 zones and 207980 number of crimes, resutlting in the highest ratio of 561 numbers of victims per zone. Cluster 2 represent a medium risk of crime with a ratio of 147 crimes per zone; and the cluster 3 the lower risk with 80 crimes per zone.
clusters_info <- data.frame(table(clusters),aggregate(number~cluster,crimes_group_clust,FUN =sum)[2])
clusters_info$ratio <- round((clusters_info$number/clusters_info$Freq))
clusters_info## clusters Freq number ratio
## 1 1 371 207980 561
## 2 2 1351 199204 147
## 3 3 1804 145046 80#Next map shows the locations of the zones clustered in the "Cluster 3". Those zones represents the highest number of crimes in Buenos Aires.
#By double clic on map to zoome in
map <- mapdeck(token = "pk.eyJ1IjoidGFmdTUiLCJhIjoiY2s5Mm10aXNlMGE1NTNnbWsyc3hlcmJsMiJ9.t-XtysS1KobBYLBrig_VEQ", style = mapdeck_style("dark"), location = c(-58.48307 , -34.54591), zoom =100)
map <- add_pointcloud(map,
data =subset(crimes_group_clust, clusters ==1, select = c("lat","long")) ,
lon ="long" ,
lat = "lat",
layer_id = "clusters",
focus_layer = T,
digits = 100,
fill_colour = "red")## Registered S3 method overwritten by 'jsonify':
## method from
## print.json jsonlite map#Propability: By using Bayes’ Theorem it is possible to calculate the probability of crimes for each zone given an specific timezone
#The Bayes data frame will display the probability of crime for each zone at each timezone. One column per timezone will be added
bayes_prob <- data.frame(Zone = as.character(rev(unique(crimes_group$Zone))))
x <- data.frame()
for(h in as.character(0:23)){
for (e in unique(crimes_group$Zone)){
prob_h <- sum(subset(crimes_group,
time_zone==h,
select ="number")) /sum(subset(crimes_group,
select ="number"))
prob_e <- sum(subset(crimes_group,
Zone == e,
select ="number"))/sum(subset(crimes_group,
select ="number"))
prob_h_given_e <-if(nrow(subset(crimes_group,
time_zone == h & Zone == e,
select ="number"))==0){
0} else{
sum(subset(crimes_group,
time_zone == h & Zone == e,
select ="number")) / sum(subset(crimes_group,
Zone == e,
select ="number"))}
prob_e_given_h <- prob_h_given_e*prob_e/prob_h
x <- rbind(prob_e_given_h,x)
}
names(x) <- gsub(" ","",paste("prob_at_",h,"_hs"))
bayes_prob <- cbind(bayes_prob,x)
x <- data.frame()
}
head(bayes_prob)## Zone prob_at_0_hs prob_at_1_hs prob_at_2_hs
## 1 Villa Del Parque Zone 3 0.0003902924 0.0007842454 0.0010101010
## 2 Villa Del Parque Zone 2 0.0001064434 0.0006099686 0.0007856341
## 3 Villa Del Parque Zone 1 0.0001419245 0.0004356919 0.0006734007
## 4 Puerto Madero Zone 3 0.0008515470 0.0008713838 0.0001122334
## 5 Puerto Madero Zone 2 0.0004967357 0.0009585221 0.0006734007
## 6 Puerto Madero Zone 1 0.0001419245 0.0002614151 0.0001122334
## prob_at_3_hs prob_at_4_hs prob_at_5_hs prob_at_6_hs prob_at_7_hs
## 1 0.0003883495 0.0001296008 0.0005010020 0.0004850445 0.0012759171
## 2 0.0002588997 0.0003888025 0.0002004008 0.0005658852 0.0005741627
## 3 0.0007766990 0.0006480041 0.0008016032 0.0004850445 0.0003827751
## 4 0.0005177994 0.0005184033 0.0005010020 0.0013742926 0.0007017544
## 5 0.0006472492 0.0002592017 0.0003006012 0.0002425222 0.0005103668
## 6 0.0001294498 0.0005184033 0.0006012024 0.0001616815 0.0003189793
## prob_at_8_hs prob_at_9_hs prob_at_10_hs prob_at_11_hs prob_at_12_hs
## 1 0.0011819749 0.0014663450 0.0010674181 0.0011401546 0.0011531204
## 2 0.0006894853 0.0006149189 0.0005977542 0.0004222795 0.0004892026
## 3 0.0004432406 0.0006149189 0.0005123607 0.0001266838 0.0004892026
## 4 0.0004924895 0.0008041247 0.0005123607 0.0006756471 0.0007338039
## 5 0.0006402364 0.0002838087 0.0003415738 0.0005067354 0.0004542596
## 6 0.0003447427 0.0001892058 0.0001707869 0.0001689118 0.0001397722
## prob_at_13_hs prob_at_14_hs prob_at_15_hs prob_at_16_hs prob_at_17_hs
## 1 0.0006946476 0.0005189593 0.0005349882 0.0005924171 0.0007637897
## 2 0.0002559228 0.0005535566 0.0003923247 0.0004878729 0.0006973732
## 3 0.0002193624 0.0004843620 0.0002853271 0.0002787845 0.0001992495
## 4 0.0006215268 0.0011071132 0.0011769741 0.0010454419 0.0009962475
## 5 0.0004387248 0.0005189593 0.0003566588 0.0005227209 0.0003984990
## 6 0.0002924832 0.0002421810 0.0002853271 0.0003484806 0.0002656660
## prob_at_18_hs prob_at_19_hs prob_at_20_hs prob_at_21_hs prob_at_22_hs
## 1 0.0005242159 0.0005103343 5.486667e-04 0.0008235976 0.0008367617
## 2 0.0002038617 0.0003118709 1.920334e-04 0.0002135253 0.0002091904
## 3 0.0002329848 0.0003118709 1.920334e-04 0.0001830217 0.0002091904
## 4 0.0011649241 0.0010490204 6.309668e-04 0.0005185614 0.0003835158
## 5 0.0004950928 0.0005103343 3.840667e-04 0.0003355398 0.0003486507
## 6 0.0002912310 0.0001134076 5.486667e-05 0.0001830217 0.0001045952
## prob_at_23_hs
## 1 4.910714e-04
## 2 2.678571e-04
## 3 4.464286e-05
## 4 5.357143e-04
## 5 6.250000e-04
## 6 1.785714e-04#Once the Bayes dataframe is made it’s possible to plot the probabilities of crime for a specific zone in each timezone. A random zone will be taken for this example.
index_zone <- sample(1:147,1)
data_zone <- data.frame(t(bayes_prob[index_zone,-1])[,])
zone_name <- gsub(" ","_",bayes_prob[index_zone,1])
colnames(data_zone) <- zone_name
data_zone[,"time_zone"] <- factor(0:23, labels=rownames(data_zone))
rownames(data_zone) <- NULL
plotly <- plot_ly(data = data_zone,
x = ~time_zone,
y =~data_zone[,1],
type = "scatter",
mode = "lines+markers",
line = list(width = 4))
plotly <- layout(plotly,
title = gsub("__"," ",colnames(data_zone)[1]),
xaxis = list(title = "Time Zone",
showgrid = F,
tickfont = list(family = 'Arial',
size = 12,
color = 'dark')),
yaxis = list(title = "Probability",
showgrid = F,
tickfront = list(family = 'dark',
size = 12)))
plotly#In the same way might be interesting to see the probabilities for a specific timezone in each zone. In this section the sum of all probabilities is 1
index_time <- sample(2:24,1)
data_time <- bayes_prob[,c(1,index_time)]
data_time <- data_time[order(data_time$Zone),]
plotly <- plot_ly(data = data_time,
x = ~Zone,
y =~data_time[,2],
type = "scatter",
mode = "lines+markers",
line = list(width = 4))
plotly <- layout(plotly,
title = str_to_title(gsub("_"," ",colnames(data_time)[2])),
xaxis = list(title = "Zone",
showgrid = F,
tickfont = list(family = 'Arial',
size = 12,
color = 'dark')),
yaxis = list(title = "Probability",
showgrid = F,
tickfront = list(family = 'dark',
size = 12)))
plotly#By using plotly function the top 20 highest probability of crime will be represented in a graphic with the corresponding zone. All zones were clustered as Cluster 1 which represents the highest rate of crime.
t <- nrow(bayes_prob)
m<- data.frame()
for(i in 2:(ncol(bayes_prob))){
k <- as.data.frame(head(bayes_prob[order(bayes_prob[,i],decreasing = T),c(1,i)],t))
names(k) <- c("Zone","Probability")
m <- rbind(m,k)
}
s<- data.frame()
for (i in 0:23){
n <- as.matrix(rep(i,t))
s<- rbind(s,n)
}
m<- cbind(m,s)
colnames(m)<- c("Zone","Probability","time_zone")
m$time_zone <- as.character(m$time_zone)
data <- merge(unique(m),crimes_group_clust, by = c("Zone","time_zone"),,all.x = F)[,c("Zone","time_zone","cluster","Probability")]
data$zone_timezone <- as.factor(paste(data$Zone,":",data$time_zone, "hs"))
data_top20 <- data[order(data$Probability,decreasing = T),] %>% head(20)
data_top20$Zone <- NULL
plotly_time <- plot_ly(data_top20,
x = ~as.character(unique(data_top20$zone_timezone)),
y = ~Probability,
color = ~cluster,
name = ~"cluster",
text = ~paste("Cluster ",cluster),
textposition = "outside",
labels = ~cluster,
outsidetextfont = list(color = "#000000"),
type = 'bar',
mode = 'markers',
marker = list(size = ~zone_timezone,
opacity = 0.5))
plotly_time <- plotly_time %>% layout(title = "Zones With The Highest Probability Of Crime",
xaxis = list(title = "Zones",
showgrid = F,
showticklabels = F),
yaxis = list(title = "Probability of crime",
showgrid = F))
plotly_time## Warning: 'bar' objects don't have these attributes: 'labels', 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'meta', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'texttemplate', 'hovertext', 'hovertemplate', 'textposition', 'insidetextanchor', 'textangle', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'metasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'texttemplatesrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'data_low20 <- data[order(data$Probability,decreasing = F),] %>% head(20)
data_low20$Zone <- NULL
plotly_time <- plot_ly(data_low20,
x = ~as.character(unique(data_low20$zone_timezone)),
y = ~Probability,
color = ~cluster,
name = ~paste("Cluster ",cluster),
textposition = "outside",
labels = ~cluster,
outsidetextfont = list(color = "#000000"),
type = 'bar',
mode = 'markers',
marker = list(size = ~zone_timezone,
opacity = 0.5))
plotly_time <- plotly_time %>% layout(title = "Zones With The Lowest Probability Of Crime",
xaxis = list(title = "Zones",
showgrid = F,
showticklabels = F),
yaxis = list(title = "Probability of crime",
showgrid = F))
plotly_time## Warning: 'bar' objects don't have these attributes: 'labels', 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'meta', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'texttemplate', 'hovertext', 'hovertemplate', 'textposition', 'insidetextanchor', 'textangle', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'metasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'texttemplatesrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'
## Warning: 'bar' objects don't have these attributes: 'labels', 'mode'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'meta', 'selectedpoints', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'texttemplate', 'hovertext', 'hovertemplate', 'textposition', 'insidetextanchor', 'textangle', 'textfont', 'insidetextfont', 'outsidetextfont', 'constraintext', 'cliponaxis', 'orientation', 'base', 'offset', 'width', 'marker', 'offsetgroup', 'alignmentgroup', 'selected', 'unselected', 'r', 't', '_deprecated', 'error_x', 'error_y', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'metasrc', 'hoverinfosrc', 'xsrc', 'ysrc', 'textsrc', 'texttemplatesrc', 'hovertextsrc', 'hovertemplatesrc', 'textpositionsrc', 'basesrc', 'offsetsrc', 'widthsrc', 'rsrc', 'tsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'