Cluster Analysis

1
Cluster Analysis

• Classifying the Exoplanets

2
Cluster Analysis

• Simple idea, difficult execution
• Used for indexing large amounts of data in
  databases. (very hot skill to have 70/hour)
• The best form of cluster analysis is ordination,
  because ordination is not a form of cluster
  analysis. Morgan Byron
• No formal def. of a cluster
• Results are descriptive and subjective.

3
R Commands

• library("scatterplot3d")
• scatterplot3d(log(planetsmass),
  log(planetsperiod), log(planetseccen), type
  "h", angle 55, scale.y 0.7, pch 16,
  y.ticklabs seq(0, 10, by 2), y.margin.add
  0.1)
• Taking the log of the each data point
• Setting the angle and the physical scale so it
  looks like a box
• Pch is the symbol used for the data point
• Seq() function sets the numeric scales
• Y.margin.add adds a bit to the vertical margins

4
Interpretation

• No real insight after our first view of the data,
  but it looks neat.

5
R Commands

• rge lt- apply(planets, 2, max) - apply(planets, 2,
  min)
• Stores the range of the data
• 2 indicates the column margin of the data matrix
• planet.dat lt- sweep(planets, 2, rge, FUN "/")
• Divides each element in the matrix by the range
  of the column margin
• n lt- nrow(planet.dat)
• wss lt- rep(0, 10)
• Creates a 10 dimensional vector of all 0s
• wss1 lt- (n-1)sum(apply(planet.dat, 2, var))
• This is the sum of squares of all the points if
  we partition the data in 1 group.
• for (i in 210) wssi lt- sum(kmeans(planet.dat,
  centers i)withinss)
• Using the kmeans method, as the number of
  partitions increases, calculates the sum of
  squares of the members of each group.

6
The K-Means Method

• This method uses different ways of minimizing a
  numerical value - often a notion of distance- by
  partitioning the data.
• The method used in this analysis is minimizing
  the sums of squares of data within a group, and
  finding a number of groups that has the lowest SS
• This method can be impractical with the number of
  partitions increasing very quickly as the number
  of groups and data points increases.

7
The Elbow

• In choosing a good number of partitions, the
  elbow or the sharpest angle in the graph is an
  easy approach.
• The steepest angles look to be at 3 and 5 number
  of groups.

8
Number of planets in the groups

• planet_kmeans3 lt- kmeans(planet.dat, centers
  3)
• We chose to try 3 groups
• table(planet_kmeans3cluster)
• 1 2 3
• 14 53 34
• ccent lt- function(cl)
• f lt- function(i) colMeans(planetscl i, )
• Finds the mean for each cluster
• x lt- sapply(sort(unique(cl)), f)
• Sorts
• colnames(x) lt- sort(unique(cl))
• return(x)

9
The results

• gt ccent(planet_kmeans3cluster)
• Cluster 1 2 3
• mass 10.56786 1.6710566 2.9276471
• period 1693.17201 427.7105892 616.0760882
• eccen 0.36650 0.1219491 0.4953529
• Number 14 53 34

10
Model-Based Clustering in brief

• The subjective decision or assumption is the
  number of clusters.
• After that, it becomes a problem of maximizing
  the likelihood that a partition is the best.

11
Mclust function

• Mclust find an appropriate model AND the optimal
  number of groups.
• Not Free?!! Need a liscence agreement from
  University of Washington.
• R Commands
• Library(mclust)
• Planet_mclust lt- Mclust(planet.dat)
• Plot(planet_mclust, planet.dat)
• Print(planet_mclust)
• The best model is of diagonal clusters of
  varying volume and shape with 3 groups

12
Homework

• Spend 30 minutes attempting exercise 15.1 and
  send me what you get done.
• Stick it to the Man!
• Then practice your air guitar
• zweihanderdawg_at_gmail.com