Assignment
1. Let us consider a two-dimensional data set of 10 vectors given by
X1 = (1, 1) X2 = (2, 1) X3 = (1, 2)
X4 = (2, 2) X5 = (6, 1) X6 = (7, 1)
X7 = (6, 2) X8 = (6, 7) X9 = (7, 7)
X10 = (7, 6)
Let us say that any two points belong to the same cluster if the Eu-
clidean distance between them is less than a threshold of 5 units. Form
the Clusters.
2. Consider the following data set of 4 patterns. Use Hamming distance
to cluster the rows and then columns. How is the result superior to the
original data? Pattern f1 f2 f3 f4
1 1 0 0 1
2 0 1 1 0
3 0 1 1 0
4 1 0 0 1
3. Consider the two-dimensional dataset given below.
A = (0.5, 0.5);B = (2, 1.5);C = (2, 0.5);D = (5, 1);
E = (5.75, 1); F = (5, 3);G = (5.5, 3);H = (2, 3).
Obtain 3 clusters using the single-link algorithm.
4. Obtain three clusters of the data given in problem 3 using the K-Means
algorithm.
5. Consider the 7 two-dimensional patterns. The patterns are located at
A = (1, 1),B = (1, 2),C = (2, 2),D = (6, 2),E = (7, 2), F = (6, 6),G =
(7, 6).
Use the K-Means algorithm with A, B, and C as the initial seed points.
Is the resulting partition satisfactory?
6. Can we get a better partition than the one obtained in problem 5?
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