LBSC 796 /INFM 718R: Homework 2 Answers Part 1: Boolean Retrieval 1. Term frequency matrix Term Doc 1 Doc 2 Doc 3 Doc 4cornell 1 0 0 0 for 0 1 0 0 implementation 1 0 1 0 information 0 1 1 1 introduction 0 0 0 1 manual 0 1 0 0 modern 0 0 0 1 of 1 0 1 0 retrieval 0 1 1 1 smart 1 1 1 0 system 1 1 1 0 the 2 1 1 0 to 0 0 0 1 user's 0 1 0 0 2. New matrix Term Doc 1 Doc 2 Doc 3 Doc 4cornell 1 0 0 0 for 0 1 0 0 implementation 1 0 1 0 information 0 1 1 1 introduction 0 0 0 1 manual 0 1 0 0 modern 0 0 0 1 of 1 0 1 0 retrieval 0 1 1 1 smart 1 1 1 0 system 1 1 1 0 the 1 1 1 0 to 0 0 0 1 user's 0 1 0 03. Docs having "information" and "retrieval" Term Doc 1 Doc 2 Doc 3 Doc 4 information 0 1 1 1 retrieval 0 1 1 1 Information AND retrieval 0 1 1 1 Answer: Doc 2, Doc 3, and Doc 4. 4. A. (smart AND implementation) OR (introduction AND retrieval) step 1: (smart AND implementation) Term Doc 1 Doc 2 Doc 3 Doc 4 smart 1 1 1 0 implementation 1 0 1 0 smart AND implementation 1 0 1 0 step 2: (introduction AND retrieval) Term Doc 1 Doc 2 Doc 3 Doc 4 introduction 0 0 0 1 retrieval 0 1 1 1 introduction AND retrieval 0 0 0 1 step 3: (smart AND implementation) OR (introduction AND retrieval) Term Doc 1 Doc 2 Doc 3 Doc 4 smart AND implementation 1 0 1 0 introduction AND retrieval 0 0 0 1 (smart AND implementation) OR (introduction AND retrieval) 1 0 1 1 Answer: Doc 1, Doc 3 and Doc 4.B. (Cornell OR SMART) AND (Implementation) step 1: (Cornell OR SMART) Term Doc 1 Doc 2 Doc 3 Doc 4 cornell 1 0 0 0 smart 1 1 1 0 cornell OR smart 1 1 1 0 step 2: (Cornell OR SMART) AND (Implementation) Term Doc 1 Doc 2 Doc 3 Doc 4 cornell OR smart 1 1 1 0 implementation 1 0 1 0 (cornell OR smart) AND (implementation) 1 0 1 0 Answer: Doc1 and Doc3. C. (information NOT retrieval) Term Doc 1 Doc 2 Doc 3 Doc 4 information 0 1 1 1 retrieval 0 1 1 1 information NOT retrieval 0 0 0 0 Answer: None. 5. Perform the same computation for the query: (information XOR system) Term Doc 1 Doc 2 Doc 3 Doc 4 information 0 1 1 1 system 1 1 1 0 information XOR system 1 0 0 1 Answer: Doc 1 and Doc 4.Part 2: Vector Space Retrieval 1. Build the w matrix TF IDF Wij 1 2 3 1 2 3 t1 5 log(3/1)=0.477 2.385 t2 4 1 3 log(3/3)=0.000 t3 5 4 log(3/2)=0.176 0.880 0.704 t4 6 3 3 log(3/3)=0.000 t5 1 log(3/1)=0.477 0.477 t6 3 7 log(3/2)=0.176 0.528 1.232 t7 6 1 log(3/2)=0.176 1.056 0.176 t8 2 log(3/1)=0.477 0.954 2. Build the w' matrix Wij W’ij 1 2 3 1 2 3 t1 2.385 0.858t2 t3 0.880 0.704 0.628 0.253t4 Æ t5 0.477 0.412 t6 0.528 1.232 0.377 0.443t7 1.056 0.176 0.911 0.063t8 0.954 0.681 length 1.402 1.159 2.7813. Compute rank order using vector space method for UNWEIGHTED query t2 t7 W’ij query 1 2 3 t1 0.858 t2 1 t3 0.628 0.253 t4 t5 0.412 t6 0.377 0.443 t7 1 0.911 0.063 t8 0.681 Similarity score 0 0.911 0.063 Rank order: Doc 2, Doc 3, Doc 1 4. Compute rank order for WEIGHTED query t2(7) t7 W’ij query 1 2 3 t1 0.858 t2 7 t3 0.628 0.253 t4 t5 0.412 t6 0.377 0.443 t7 1 0.911 0.063 t8 0.681 Similarity score 0 0.911 0.063 Rank order: Doc 2, Doc 3, Doc 1 5. Doc 4 in the class example is missing here; the change has an overall impact on the IDF values, which leads to differences in Wij, W’ij, and hence document similarity