Tutorial exercises Clustering ? K-means, Nearest Neighbor and

Corrigé. Exercice 1 (03 points) : a/ Expliquez le principe d'une classification KMeans. (1.5 points). Exercice 2 (07 points) : Le tableau suivant contient des 

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Tutorial exercises
Clustering - K-means, Nearest Neighbor and Hierarchical.

Exercise 1.
K-means clustering

Use the k-means algorithm and Euclidean distance to cluster the following 8 examples into 3 clusters:
A1=(2,10), A2=(2,5), A3=(8,4), A4=(5,8), A5=(7,5), A6=(6,4), A7=(1,2), A8=(4,9).
The distance matrix based on the Euclidean distance is given below:

Suppose that the initial seeds (centers of each cluster) are A1, A4 and A7. Run the k-means algorithm for
1 epoch only. At the end of this epoch show:
a) The new clusters (i.e. the examples belonging to each cluster)
b) The centers of the new clusters
c) Draw a 10 by 10 space with all the 8 points and show the clusters after the first epoch and the new
d) How many more iterations are needed to converge? Draw the result for each epoch.

d(a,b) denotes the Eucledian distance between a and b. It is obtained directly from the distance matrix or
calculated as follows: d(a,b)=sqrt((xb