Project 2: Multidimensional Methods: Due March 14th

The undergraduates may choose any subject, the graduates may not choose the first one, they may also come and see me to choose a project related to their research work.

Linear Discriminant Analysis in Matlab

1. Write a matlab m file with functions that enable a full linear discriminant analysis as we saw lda in Splus.
2. A predict function that says which class a test observation would be assigned to using a chosen number of discriminant variables.
3. A cross validation facility enabling the computation of the estimated cross validated percentage of well-classified observations.

Bootstrap of a Principal Component Analysis

Choice of either Splus or matlab for this project.

1. Write a pca program.
2. Write a bootstrap program that generates new resamples.
3. Execute the pca program many times, each time, lining up the components so they are comparable.
4. Project all the reconstructions on a same plane.
5. Construct convex hulls around these points.

Interface Xgobi with matlab

Write a matlab front end for calling xgobi on a matlab matrix. This requires using !cmex the compiler for matlab and also getting matrices from matlab into a compatible structure for xgobi to deal with

Projection Pursuit algorithm

With either Splus or matlab, write a projectiuon pursuit program that finds the best two dimensional plane to project to optimize several possible indices:
-Friedman and Tukey's
-Entropy
-optionally-a user defined one

By using the resident optimization, or by programming your own.

Program a Multidimensional Method of your choice

Up to you, preferably with quality graphics etc....