1. K-Means Lab

2. Start with 1D Data
# input data: # 1) use wget to copy the dataset to the vm # 2) use GUI import from Text (base) to import state_income.csv #Sort data tmp = sort(state_income$V2) #Visualize data plot(tmp) # create 4 clusters kmeans=kmeans(tmp,4,15) #Visualize the cluster centers points(kmeans$centers, col = 1:4, pch=20)

3. Higher Dimensional Data
# input data: # 1) use wget to copy to vm # 2) use GUI import from Text (base) to import iris.csv # Lets start with 2 dimensions: visualize data plot(iris[,1:2]) # create 4 clusters kmeans=kmeans(iris[,1:2],4,15) #Visualize the cluster centers points(kmeans$centers, col = 1:4, pch=20)

4. # examine kmeans object kmeans # note: clustering statistics
cluster sizes
cluster means
clustering vector
within cluster sum of squares

5. Plot Results
# Visualize clusters plot(iris[,1:2], col=kmeans$cluster) # Visualize the cluster centers points(kmeans$centers, col = 1:4, pch=20)

6. Best K? # Is 4 the best number of clusters?
# explore different number of clusters
withinSumSqrs = numeric(20)
for (k in 1:20) withinSumSqrs[k] = sum(kmeans(iris[,1:2],centers=k)$withinss)
#Visualize within cluster sum of square
plot(1:20, withinSumSqrs, type="b", xlab="# Clusters", ylab="Within sum of square")

7. Best K? Elbow Method Look for the “elbow”
We want a small k that has a low WSS value
What does a low WSS value indicate?

8. Higher Dimensional Data
# Lets consider 3 dimensions: visualize data plot(iris[,1:3]) # create 4 clusters kmeans=kmeans(iris[,1:3],4,15) # Visualize the clusters plot(iris[,1:3], col=kmeans$cluster)

9. Higher Dimensional Data
# Examine a single 2D projection plot(iris[,1:2], col=kmeans$cluster) #Visualize the cluster centers points(kmeans$centers, col = 1:4, pch=20) # Examine another single 2D projection plot(iris[,1:3], col=kmeans$cluster) points(kmeans$centers[,c(1,3)], col = 1:4, pch=20)

10. Best K? # Is 4 the best number of clusters?
# explore different number of clusters
withinSumSqrs = numeric(20)
for (k in 1:20) withinSumSqrs[k] = sum(kmeans(iris[,1:3],centers=k)$withinss)
#Visualize within cluster sum of square
plot(1:20, withinSumSqrs, type="b", xlab="# Clusters", ylab="Within sum of square")

11. Higher Dimensional Data
# Finally consider 4 dimensions: visualize data
plot(iris[,1:4])
# create 4 clusters
kmeans=kmeans(iris[,1:4],4,15)
# Visualize the clusters
plot(iris[,1:4], col=kmeans$cluster)

12. Normalization? # notice that the columns are not the same scale
> summary(iris[,1:4])
Sepal.Length Sepal.Width Petal.Length Petal.Width
Min. : Min. : Min. : Min. :0.100
1st Qu.: st Qu.: st Qu.: st Qu.:0.300
Median : Median : Median : Median :1.300
Mean : Mean : Mean : Mean :1.199
3rd Qu.: rd Qu.: rd Qu.: rd Qu.:1.800
Max. : Max. : Max. : Max. :2.500
#Which will have more influence: petal width or petal length?

13. Normalization? # apply this function to one column
# Let’s shift and scale the data to be in the range [0,1]
#  each dimension should be able to exert equal influence
# function to “shift” a vector
# subtract the min value so that it ranges from 0 to ??
myShift = function(x) { x - min(x, na.rm=TRUE)}
# apply this function to one column
myShift(iris[,3])
# apply this function to multiple columns
as.data.frame(lapply(iris[,1:4], myShift))
#verify with summary statistics
summary(as.data.frame(lapply(iris[,1:4], myShift)))

14. Normalization? # Still need to scale data
# function to “scale” a vector
myScale = function(x) { max(x,na.rm=TRUE) - min(x,na.rm=TRUE)}
# apply this function to one column
myScale(iris[,3])
# apply this function to multiple columns
as.data.frame(lapply(iris[,1:4], myScale))

15. Normalization? # apply this function to a column
# Put it all together
# myShift= function(x) { x - min(x, na.rm=TRUE)}
# myScale = function(x) { max(x,na.rm=TRUE) - min(x,na.rm=TRUE)}
myNorm = function(x) { myShift(x)/myScale(x) }
# apply this function to a column
myNorm(iris[,3])
# apply this function to multiple columns
tmp = as.data.frame(lapply(iris[,1:4], myNorm))
#verify with summary statistics
summary(as.data.frame(lapply(iris[,1:4], myNorm)))

16. Higher Dimensional Data
# visualize “normalized” data
plot(tmp[,1:4])
# try from 1 to 20 clusters
for (k in 1:20) withinSumSqrs[k] = sum(kmeans(tmp[,1:4],centers=k)$withinss)
#Visualize within cluster sum of square
plot(1:20, withinSumSqrs, type="b", xlab="# Clusters", ylab="Within sum of square")