Materials for L07 on clustering

R/L07_Clustering_SMD.Rmd

+---
+title: "Clustering with smart meter data"
+output: html_notebook
+editor_options: 
+  chunk_output_type: inline
+---
+
+```{r load and format data}
+# load and prepare the data ----
+SMD_Readings=read.csv2("../data/SMD_BIA_Data.csv")
+
+# we use the data for a single week
+time_stamps <- as.numeric(as.character(unique(SMD_Readings$Timestamp)))
+single_week <- as.character(time_stamps[time_stamps>25000  & time_stamps<25700])
+length(single_week)
+
+# select the measurements for one single week
+SMD_Readings <- SMD_Readings[SMD_Readings$Timestamp %in% single_week, ]
+
+# the reshape package helps us to transform the data innto a more condensed table form
+#install.packages("reshape2")
+library("reshape2")
+
+Formatted_Readings <- dcast(SMD_Readings, ID ~ Timestamp, value.var = "Consumption")
+head(Formatted_Readings)
+
+# remmove the IDs from the matrix
+IDs <- Formatted_Readings[,1]
+Formatted_Readings[,1] <- NULL
+```
+
+```{r first k-Means clustering}
+# simple k-means clustering ----
+set.seed(1)
+Cluster1 <- kmeans(Formatted_Readings, centers=3)
+```
+
+
+```{r function to plot the results}
+# Creating cluster visualization ----
+plotcl <- function(SMD_Readings, clusters,lim=c(0,2), ...){
+  plot(colMeans(SMD_Readings[,1:48]), type="n", ylim=lim, ...)
+  for(i in unique(clusters)){
+    lines(colMeans(SMD_Readings[clusters==i,1:48]),col=i, lwd=3)
+  }
+}
+
+plotclWeek <- function(SMD_Readings, clusters,lim=c(0,2), ...){
+  plot(colMeans(SMD_Readings[,]),type="n", ylim=lim, ...)
+  for(i in unique(clusters)){
+    lines(colMeans(SMD_Readings[clusters==i,]),col=i, lwd=3)
+  }
+}
+
+plotcl(Formatted_Readings, Cluster1$cluster, ylab="Consumption (kWh)")
+plotclWeek(Formatted_Readings, Cluster1$cluster, ylab="Consumption (kWh)")
+```
+
+```{r second k-Meand clustering}
+# Improve the clustering ----
+#Normalize the values and then run the k-means again
+set.seed(2)
+Data_Norm <- Formatted_Readings/rowMeans(Formatted_Readings)
+Cluster2 <- kmeans(Data_Norm, centers=3)
+plotcl(Formatted_Readings, Cluster2$cluster, ylab="Consumption (kWh)", main="Max-normaized consumption", lim=c(0,1.2))
+
+#Transform the values to a more normally distributed form and run the k-means agaein
+Datas <- sqrt(Formatted_Readings)
+Datasn <- Datas/rowMeans(Datas)
+set.seed(4)
+Cluster3 <- kmeans(Datasn, centers=3)
+plotcl(Formatted_Readings, Cluster3$cluster, ylab="Consumption (kWh)", main="Sqrt and Max-normaized consumption", lim=c(0,1.2))
+
+```
+
+```{r obtain the optimal number of clusters}
+set.seed(2)
+Clusters <- list()
+Clusters[[1]] <- kmeans(Datasn, centers=2)
+Clusters[[2]] <- kmeans(Datasn, centers=3)
+Clusters[[3]] <- kmeans(Datasn, centers=4)
+Clusters[[4]] <- kmeans(Datasn, centers=5)
+Clusters[[5]] <- kmeans(Datasn, centers=6)
+Clusters[[6]] <- kmeans(Datasn, centers=7)
+Clusters[[7]] <- kmeans(Datasn, centers=8)
+Clusters[[8]] <- kmeans(Datasn, centers=9)
+
+#the total sum of squares
+tot.withinss <- sapply(Clusters, function(v){return(v$tot.withinss)})
+plot(2:9, tot.withinss, xlab="Num. of clusters", ylab="Total sum of squares", type="b")
+
+#the min / max sum of squares in the clusters
+min.withinss <- sapply(Clusters, function(v){return(min(v$withinss))})
+max.withinss <- sapply(Clusters, function(v){return(max(v$withinss))})
+plot(2:9, max.withinss, xlab="Num. of clusters", 
+     ylab="Within clusters sum of squares", type="b", ylim=c(min(min.withinss), max(max.withinss)))
+lines(2:9, min.withinss, type="b", col=2)
+legend("topright", c("Max. WSS", "Min. WSS"), col=c(1,2), lty=1)
+
+numOneElemClusters <- sapply(Clusters, function(v){return(sum(v$size==1))})
+barplot(numOneElemClusters, names.arg = 2:9, main="Single-element clusters", 
+        xlab="Total number of k-Means clusters")
+```
+
+
+```{r hierarchical clustering}
+library(cluster)
+
+#create distance matrix
+C <- 1-cor(t(Formatted_Readings))
+
+Dendrogram <- agnes(C,diss=T,method="complete")
+plot(Dendrogram, which.plot=2) #plot the dendrogram
+
+Cluster4 <- cutree(Dendogram, k=3)
+plotcl(Formatted_Readings, Cluster4, main="Hierarchical clustering results", ylab="Consumption (kWh)", lim=c(0,1.3))
+
+```
+