Clustering: Face recognition [3 P]

In this homework example you should cluster images derived from the Olivetti face database with the cluster algorithms 'k-means' and 'k-medoids'. You can download the dataset and its description from the course homepage.³

• Normalize the pixels in each 50 by 50 image (each column of the design matrix) to have mean 0 and variance 0.1.

• Apply k-means and k-medoids to the dataset. For k-means use the MATLAB function kmeans. For k-medoids you have to write your own MATLAB function. For both algorithms use the squared Euclidean distance. Analyze the dependence of the average squared error on the number of clusters.

• Analyze for $k\in\{2,5,10,30\}$ the cluster centers and outliers (points with the largest squared errors) for both algorithms. Explain the differences in the results.