Big Data – Assignment 2

1)On the space of nonnegative integers, which of the following functions are distance measures? If so, prove it;
if not, prove that it fails to satisfy one or more of the axioms.
(a) max(x,y) = the larger of x and y.
(b) diff(x,y) = |x−y| (the absolute magnitude of the difference between x and y).
(c) sum(x,y) = x+y 2) Prove that if i and j are any positive integers, and i<j, then the Li-norm between any two points is greater
than the Lj-norm between those same two points.3)Find the edit distances (using only insertions and deletions) between the following pairs of strings.
(a) abcdef and bdaefc.
(b) abccdabc and acbdcab.
(a) abcdef and baedfc4)Perform a hierarchical clustering of the one-dimensional set of points 1,4,9,16,25,36,49,64,81,
assuming clusters are represented by their centroid (average), and at each step the clusters with the closest
centroids are merged.5)Considering DGIM approach, there are several ways that the bit-stream below could be partitioned into
buckets. Find all of them.
1001101001101101011011011011001