Q1.A)
function D = getDegreeMatrix(W)
% Calculates the Degree Matrix for a given adjacency matrix
D = zeros(size(W, 1), size(W, 2));
for i=1:length(W)
D(i,i) = sum(W(i,:))
end
% Fill in D here
End
Q1.B)
function L = getNormalizedLaplacian(W, D)
% Calculates the Normalized Laplacian for an adjacency matrix W
% and degree matrix D
W = full(W);
D(D==0) = eps; % avoid dividing by zero
L = zeros(size(W, 1), size(W, 2));
% Calculate L here
L = D - W;
L = inv(D) * L
end
Q1c
Use the runExperimentsQ1.m _le to plot all the data points, colored by
their cluster label from the Spectral Clustering method. Include your plots in your handin. Qualitatively,
what is the difference between the decision surfaces of the two methods? Where does this difference come
from?
The decision surface for spectral clustering is a non linear whereas for kmeans its linear.
This is basically because Kmeans uses a centroid based approach such that the clusters are formed by the
perpendicular bisector of the line joining the centroids.
Spectral Clustering clusters the data set into non linear clusters. Spectral Clustering performs
dimensionality reduction(Feature transformation) before clustering the data into fewer dimensions.
