Please post your solutions to the Feb 23 In-Class Exercise to this thread.

Best,

Chris

[u, v] = [0, 1]
D = 1
Score = 0
J = 0

U = -inf < inf:
	d < docid(u) #False
	score = 1 / (1 - 0 + 1) = 0.5
	[u, v] = [5, 6]
	d < docid(u) #False
	score = 0.5 + 1 / (6 -5 + 1) = 1
	[u, v] = [3, 5]
	d < docid(u) #True
		j = 1
		Result[1].docid = 1
		Result[1].score = 1
		d = 2
		score = 0
	score = 0 + 1 / (5 - 3 + 1) = 0.3
	[u, v] = [7, 8]
	d < docid(u) #False 
	score = 0.3 + 1 / (8 - 7 + 1) = 0.8
	[u, v] = [inf, inf]

D < inf #True 
	j = 2
	Result[2].docid = 2
	Result[2].score = 0.8

#answer: 
Result = [
    {
        docid = 1
        score = 1
    },
    {
        docid = 1
        score = 0.8
    }
]

d1 = “All the king's horses and all the king's men"

d2 = "Which is correct: all of the people, all the people, or all people?"

rankProximity(“all”, “the”, 2)

For document 1:

[u,v] = [0,1], [1,5], [5,6]

For document 2:

[u,v] = [3,5], [5,7], [7,8], [8,11]

j = 0, d = 1, score = 0

1st score = 0 + 0.5 = 0.5

2nd score = 0.5 + 0.2 = 0.7

3rd score = 0.7 + 0.5 = 1.2

result[1].docid = 1

result[1].score = 1.2

j = 1, d = 2, score = 0

1st score = 0 + 0.33 = 0.33

2nd score = 0.33 + 0.33 = 0.66

3rd score = 0.66 + 0.5 = 1.166

4th score = 1.166 + 0.25 = 1.416

result[2].docid = 2

result[2].score = 1.416

result = [{score = 1.416, doc_id=2},{score = 1.2, doc_id= 1}]

The return result is doc 2, doc 1 with 1.42, 1.2 scores respectively. The detailed step-by-step analysis is shown below in images.

d1="All the king's horses and all the king's men"
d2 = "Which is correct: all of the people, all the people, or all people?"

rankProximity processing:

'''Initially:'''
u = -infinity
nextCover("all", "the", -infinity) would give us [0:0,0:1]
Thus, [u, v] = [0, 1]
d = 0
score = 0
j = 0

'''Iterating through while loop:'''

1.
docid(u) = 0, d = 0
score += 1/(1-0+1) = 1/2
nextCover("all", "the", 0) would give us [0:1,0:5]
Thus, [u, v] = [1, 5]

2.
docid(u) = 0, d = 0
score += 1/(5-1+1) = 1/2 + 1/5 = 7/10
nextCover("all", "the", 1) would give us [0:5,0:6]
Thus, [u, v] = [3, 5]

3.
docid(u) = 0, d = 0
score += 1/(6-5+1) = 7/10 + 1/2 = 6/5 = 1.2
nextCover("all", "the", 5) would give us [1:3,1:5]
Thus, [u, v] = [3, 5]

4.
docid(u) = 1, d = 0
From if condition (d<docid(u)):
   j = 1
   Result[1].docid = 0
   Result[1].score = 1.16
   d = 1
   score = 0
score += 1/(5-3+1) = 1/3
nextCover("all", "the", 3) would give us [1:5,1:7]
Thus, [u, v] = [5, 7]

5.
docid(u) = 1, d = 1
score += 1/(7-5+1) = 1/3 + 1/3 = 2/3
nextCover("all", "the", 7) would give us [1:7,1:8]
Thus, [u, v] = [7, 8]

6.
docid(u) = 1, d = 1
score += 1/(8-7+1) = 2/3 + 1/2 = 7/6
nextCover("all", "the", 7) would give us [1:8,1:11]
Thus, [u, v] = [8, 11]

7.
docid(u) = 1, d = 1
score += 1/(11-8+1) = 7/6 + 1/4 = 17/12
nextCover("all", "the", 8) would give us [infinity, infinity]
Thus, [u, v] = [infinity, infinity]

Exiting the while loop and checking the if condition (d<infinity),
j = 2
Result[2].docid = 1
Result[2].score = 17/12 = 1.46

Sorting Result by score and returning top 2 documents:
1. {docid: 1, score: 1.46}
2. {docid: 0, score: 1.2}

''rankProximity(“all”, “the”, 2)

Doc1: [u,v] = [0,1], [1,5], [5,6]

Doc2: [u,v] = [3,5], [5,7], [7,8], [8,11]

j = 0 d = 1 score = 0

Score = score + 1/ (v-u + 1)

Score 1 = 0 + 1 / (1 - 0 + 1) = 0.5 ,

Score 2 = 0.5 + 1 / (5 - 1 + 1) = 0.7,

Score 3 = 0.7 +1 / ( 6 - 5 + 1) = 1.2

result[1].docid = 1 , result[1].score = 1.2

j = 1 d = 2 score = 0

Score 1 = 0 + 1 / (5 - 3 + 1) = 0.3,

Score 2 = 0.3 + 1 / (7 - 5 + 1) = 0.6,

Score 3 = 0.6 + 1 / (8 - 7 + 1) = 1.1,

Score 4 = 1.1+ 1 / (11 - 8 + 1) = 1.35

result[2].docid = 2 , result[2].score = 1.35

After sorting result by score: result = score = 1.35, doc_id =2] , [score = 1.2, doc_id = 1''

rankProximity(t[1],.., t[n], k) // t[] term vector = all, the // k = 2

{

   u := - infty;
   [u,v] := nextCover(t[1],.., t[n], u); // for d1 for the first round [0,1]
   d := docid(u);
   score := 0;
   j := 0;
   while( u < infty) do
       if(d < docid(u) ) then
       // if docid changes record info about last docid
           j := j + 1; // j = 1
           Result[j].docid := d;
           Result[j].score := score;
           d := docid(u);
           score := 0;
       score := score + 1/(v - u + 1); // 0+1/(1-0+1 ) = 0.5 
       [u, v] := nextCover(t[1],.., t[n], u); // next cover [1,5]
//… j = 2
//0+1/(5-1+1) = 0.2
//next cover [5,6]
//j= 3
//0.3 +1/(6-5+1) = 0.5
//end of document 

//now second document
//[3,5]
//j =1
//0+1/(5-3+1)=0.33
//next cover [5,7]
//j=2
//0+1/(7-5+1)=0.33
//next cover [7,8]
//j=3
//0+1/(8-7+1)=0.5
//next cover[8,11]
//j=4
//0+1/(11-8+1)= 0.25
//end of document 

   if(d < infty) then
       // record last score if not recorded
       j := j + 1; //1
       Result[j].docid := d;//docid = 1
       Result[j].score := score; //score: 1.2

// second result : docid = 2, score = 1.41

   sort Result[1..j] by score;
   return Result[1..k];

Results: 1. Docid:1, score: 1.2

       2. Docid:2 score 1.41