Description
Purpose
This lab investigates orthonormal transformations and distance-based classification.
Class Data
We will consider four cases. The first three are Gaussian, with the following given means and covariances:
1. µA =
”
0
0
#
ΣA =
”
1 0
0 1 #
µB =
”
3
0
#
ΣB =
”
1 0
0 1 #
2. µA =
”
−1
0
#
ΣA =
”
4 3
3 4 #
µB =
”
1
0
#
ΣB =
”
4 3
3 4 #
3. µA =
”
0
0
#
ΣA =
”
3 1
1 2 #
µB =
”
3
0
#
ΣB =
”
7 −3
−3 4 #
4. See LEARN for Matlab file case4.mat
In each case, each cluster has NA = NB = 200 data points. For MAP we assume the clusters to be equally
likely.
Generating Clusters
Use the Matlab function randn to assist in the generation of the 2D clusters for cases 1-3. The randn
function will produce normally (ie, Gaussian) distributed data with mean 0 and variance 1.0. To create the
correlated data as required, you will need to apply a transformation to the uncorrelated, equal-variance data.
1
Distance Classifiers
We will be considering six classifiers:
1. Minimum Euclidean Distance (MED), with the sample mean as the prototype.
2. Minimum Generalized-Euclidean Distance (GED, also called MICD in the 372 notes), using sample
means and covariances.
3. Nonparametric classifier NN using a Euclidean distance.
4. Nonparametric classifier 3-NN using a Euclidean distance.
5. Nonparametric classifier 5-NN using a Euclidean distance.
6. Although not distance-based, we will also show the MAP classifier as a reference, for the first three
cases, using exact means and covariances.
For each of the four cases plot the class samples, the MED and GED classification boundaries, and for cases
1-3 the the unit standard deviation contours and MAP classification boundary, all superimposed on the same
plot. (ie, four plots; one per case)
Also produce three plots, one for NN, one for 3-NN, and one for the 5-NN classifier, for case 3. On each
plot superimpose the optimal (MAP) classification boundary.
Note that you should not try to find the boundaries analytically. Approach the problem numerically: grid
the domain, classify each point, and then generate a contour plot (help contour in MATLAB).
Comment briefly on both sets of plots.
2
