library(data.table)
library(ggplot2)

Demographics <- fread("demographics.csv")

#Cluster states on demographic
StatePredictors <- Demographics[,-(1:2),with=FALSE]
length(names(Demographics))
CityPredictorsIncome <- Demographics[,c((28-10):26)]
CityPredictorsPopulation <- Demographics[,c(4:16)]
#Normalise to proportions in  each age group
CityPredictorsPopulation <- CityPredictorsPopulation/Demographics$population
PCAPopulation <- prcomp(CityPredictorsPopulation,center = T)
PCAIncome <- prcomp(CityPredictorsIncome,center = T,scale. = T)

#Proportion of variance explained by components
plot(PCAPopulation$sdev/sum(PCAPopulation$sdev))
PCAPopulation$rotation[,1] #First component has >45  year olds
PCAPopulation$rotation[,2] #Second component has <45
plot(PCAPopulation$x[,1],PCAPopulation$x[,2])
PCAKMeansClust <- kmeans(PCAPopulation$x[,1:2],4)
plot(PCAPopulation$x[,1],PCAPopulation$x[,2])
points(PCAKMeansClust$centers,col="red")