Homework 11
1. Download the dataset faces.zip from Blackboard. It contains 2429 faces of
size 19 × 19 pixels each, and background.zip , containing background samples
somehow resembling faces. If there are any unreadable images, discard them.
a) Perform Principal Component Analysis on the faces. Discard the two largest
eigenvalue and plot the graph of the remaining eigenvalues sorted in decreasing
order. (1 point)
b) Plot a graph of the coordinates of the faces projected to the 2D plane generated
by the eigenvectors corresponding to the largest and second largest eigenvalues.
(1 point)
c) On the same graph, display the coordinates of the projections from b) using one
color (black) and the projections of the background patches on the same two
eigenvectors using another color (e.g. red or light gray). Be sure to subtract the
mean of the faces and project to the eigenvectors of the faces. (1 point)
d) Compute the distances of the faces and the background points to the plane from
b). On the same graph, plot the computed distances (on the y-axis) vs the coordinates of the projections on the eigenvector of the largest eigenvalue (on the xaxis) for the faces and background patches using two different colors. (2 points)
e) Repeat point d) displaying the computed distances (on y) vs the coordinates of
the projections on the eigenvector of the second largest eigenvalue(on x). (2
points)
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