Introduction to Pattern Recognition: A Matlab Approach

3.6 Laplacian Eigenmap 101

Exercise 3.5.1

In this exercise, we see how the original space is transformed using kernel PCA. To ensure visualization of the

results, we consider a 2-dimensional problem, which will be mapped to the 2-dime nsional space spanned by

the first two principal components that result from the kernel PCA. More specifically, go through the following

steps:

Step 1. Generate a data set X, which contains 200 2-dimensional vectors. N

1

=100 vectors stem from class

1, which is modeled by the uniform distributio n in [−0.5, 0.5]

2

; N

2

=100 vectors stem from class −1 and

lie around the circle with radius 1 and centered at the origin. The N

2