Assignment
1. Consider the covariance matrix in a two-dimensional case given by
Show that the squared Mahalanobis distance is a weighted version of
squared Euclidean distance in this case.
2. Consider d-dimensional binary patterns, where each pattern is a d-bit
binary string. Show that for two such patterns X and Y, the Manhattan
distance and squared Euclidean distance between X and Y are the same.
3. Show that the KL-distance does not satisfy symmetry.
4. Let S(A,B) be the cosine of the angle between vectors A and B. Let
D(A,B) = 1 - S(A,B) is the distance between A and B. Is D a metric?
5. Consider two binary strings X(x1, x2, ..., xd) and Y(y1, y2, ..., yd).
Hamming distance between X and Y is defined as
where mismatch(xi,
yi) = 1, when xi = yi and 0 otherwise. Is
Hamming distance a metric?
6. Obtain the edit distance between strings ‘TRAIN’ and ‘CRANE’.
7. Show that the Mutual Neighbourhood Distance (MND) is not a metric.
8. Consider vectors X and Y where X = (50, 2, 29, 62, 140) and Y = (55,
15, 50, 70, 170). Obtain the k-Median distance where k = 3.