[Big Data] Week 2: LSH (Basic)

Question 1

The edit distance is the minimum number of character insertions and character deletions required to turn one string into another. Compute the edit distance between each pair of the strings he, she, his, and hers. Then, identify which of the following is a true statement about the number of pairs at a certain edit distance.

 

Your Answer		Score	Explanation
There are 3 pairs at distance 1.
There is 1 pair at distance 4.	Correct	1.00
There are 4 pairs at distance 5.
There is 1 pair at distance 3.
Total		1.00 / 1.00

Question 2

Consider the following matrix:

 

	C1	C2	C3	C4
R1	0	1	1	0
R2	1	0	1	1
R3	0	1	0	1
R4	0	0	1	0
R5	1	0	1	0
R6	0	1	0	0

Perform a minhashing of the data, with the order of rows: R4, R6, R1, R3, R5, R2. Which of the following is the correct minhash value of the stated column? Note: we give the minhash value in terms of the original name of the row, rather than the order of the row in the permutation. These two schemes are equivalent, since we only care whether hash values for two columns are equal, not what their actual values are.

 

Your Answer		Score	Explanation
The minhash value for C1 is R6
The minhash value for C3 is R4	Correct	1.00
The minhash value for C1 is R2
The minhash value for C3 is R5
Total		1.00 / 1.00

Question 3

Here is a matrix representing the signatures of seven columns, C1 through C7.

 

C1	C2	C3	C4	C5	C6	C7
1	2	1	1	2	5	4
2	3	4	2	3	2	2
3	1	2	3	1	3	2
4	1	3	1	2	4	4
5	2	5	1	1	5	1
6	1	6	4	1	1	4

Suppose we use locality-sensitive hashing with three bands of two rows each. Assume there are enough buckets available that the hash function for each band can be the identity function (i.e., columns hash to the same bucket if and only if they are identical in the band). Find all the candidate pairs, and then identify one of them in the list below.

 

Your Answer		Score	Explanation
C2 and C3
C2 and C5	Correct	1.00
C4 and C5
C2 and C7
Total		1.00 / 1.00

Question 4

Find the set of 2-shingles for the "document":

 

ABRACADABRA

 

and also for the "document":

 

BRICABRAC

 

Answer the following questions:

 

1. How many 2-shingles does ABRACADABRA have?
2. How many 2-shingles does BRICABRAC have?
3. How many 2-shingles do they have in common?
4. What is the Jaccard similarity between the two documents"?

Then, find the true statement in the list below.

 

Your Answer		Score	Explanation
ABRACADABRA has 10 2-shingles.
ABRACADABRA has 9 2-shingles.
There are 5 shingles in common.	Correct	1.00
There are 4 shingles in common.
Total

 

Question 5

Suppose we want to assign points to whichever of the points (0,0) or (100,40) is nearer. Depending on whether we use the L1 or L2 norm, a point (x,y) could be clustered with a different one of these two points. For this problem, you should work out the conditions under which a point will be assigned to (0,0) when the L1 norm is used, but assigned to (100,40) when the L2 norm is used. Identify one of those points from the list below.

 

Your Answer		Score	Explanation
(53,15)	Correct	1.00
(58,13)
(52,13)
(54,8)
Total		1.00 / 1.00