**STAT244 ASSIGNMENT 1 SPRING, 2011**

##
1 Power Method for Eigenvalues and Eigenvectors

Use the power method to iteratively find
the eigenvalues and eigenvectors of a real, symmetric 5×5
matrix of your choice. If you don't have an orthogonalization
routine, you can use the Gram-Schmidt program in the
file `~s244/samples/gs.c` . Also extract the eigenvalues and
eigenvectors using some standard routine (EISPACK, LAPACK, etc.) and
compare the results to those from using the power method, both
numerically and with regard to execution time.
##
2 Cluster Analysis using the Leader algorithm

Write a program to implement the leader algorithm. Your program
should try a variety of threshold values, and calculate the
within cluster sum of squares for each threshold used, as well
as listing the number of clusters found, and the members of
each cluster. Examine the relationship between the threshold
you use and the sum of squares to see if some "natural"
number of clusters emerges.
Then compare your results to the results of
a cluster analysis method of your choice using `R`, `sas`,
`matlab` or some other program. You can use the dataset
crime in the `~s244/samples` directory or class web page to test your program, or you
can use a data set of your choice. (The file
`~s244/samples/crime.des` describes the contents of the crime dataset).
For extra credit, use the clustering from the leader algorithm as
the starting point for a k-means algorithm. What kind of
improvement in within cluster sum of squares does the k-means
algorithm provide compared to the leader algorithm?

File translated from
T_{E}X
by
T_{T}H,
version 3.67.

On 18 Jan 2011, 10:07.