Question $1(30$ points$)$: Consider the following shingle$-$document matrix.

a$)$ Compute the signature matrix using $4$ different permutations of your choice

b$)$ Compute all pairwise column similarities for both the $Co\frac{l}{C}ol$ and $Si\frac{g}{S}ig$

c$)$ Compute the minhash signature for each column if we use the following three hash

functions: $[$Hint: Substitute the element index in the hash function to generate the

permutation$]$

$[$Example of modulus function:

$45$mod$6$

$45=6**7+(3)$

$45$ when divided by $6,$ leaves a remainder $3.$ So $45$ mod $6=3.]$

i$)h1(x)=x+1$mod$6$;

ii$)h2(x)=x+4$mod$6$;

iii$)h3(x)=2x+5$mod$6$