ICS 273A
Spring 2009
Homework 6
1) Kernel PCA & Kernel Clustering
a) Perform a PCA on the Iris data. Make sure you first center the data. Extract the first
two eigenvalues and eigenvectors.
b) Project the data down to a two dimensional subspace and produce a scatter plot of the
data. Make sure you plot each of the three classes differently (using color or different
markers). Can you see the three Iris flower clusters?
 
 K

c) Define the following kernel: K ( x , y )  c exp   wk || x k  y k || 2  where “w”
 k 1

represents weights on the attributes. Compute the kernel matrix (or Gram matrix) for the
Iris dataset. You can choose all weights to be equal. Do not use the class labels as
features. Make sure you center the data in kernel space first.
d) Project the Iris data down to a two dimensional subspace using the features computed
from kernel-PCA. Can you see any differences between PCA and kernel-PCA?
e) Perform a spectral clustering of the Iris data (using 3 clusters). Report the error by
comparing to the true class labels.
f) Redo the kernel-PCA after adding the class labels as attributes. What happens if you
increase the weights in the kernel on the class-labels relative to the other attributes?
Explain what you observe.