Question

5. Consider the following table of relevant items in ranked order where zero means it was on the hit list but not relevant. NV = not viewed which means it was on hit ist and relevant or not if it has value of zero but not looked at by the user. It also has all the relevant documents from the database in the first 10 hits.

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10

Query 1 0 0 (NV) 3 0 2 2 5 0 0 4

Query 2 4 0 3 (NV) 0 2 0 4 0 1 2

a. Calculate the interpolated precision recall graph showing both queries

b. Calculate the MAP value

c. For Query1 and Query 2 Calculate the Bpref.

d. For Query 1 calculate the DCG and Normalized DCG at 10 items.

Use the formula: DCG = rel1 + ?????????2i/log2 (i)

Log(2) = 1

Log(3) = 1.58

Log(4) = 2

Log(5) = 2.32

Log(6) = 2.58

Log(7) = 2.80

Log(8) = 3

Log(9) = 3.17

Log(10) = 3.32

Answer 1

a.

For query 1

For query 2

b.

c.

Where,

R = Relevant documents

N= Non-Relevant documents

n= non relevant documents before a relevant document position

nr= relevant document at a position

d.