REL = { d1, d5, d10, d88, d150, d200, d210, d250, d300, d400, d405, d472, 
               d500, d501, d545, d600, d635, d700, d720, d800}

Two different retrieval systems S1 and S2 are used to retrieve ranked lists of documents from this collection using the above query. The top 10 retrieved documents for these two systems are given below (each list is in decreasing order of relevance).

RET(S1, Q) = d1,d200,d150,d4,d10,d400,d88,d600,d500,d520
RET(S2, Q) = d400,d33,d150,d117,d999,d101,d501,d800,d15,d88

This information is provided in the following CSV files for your convenience:

hw1-relevant.csv - test documents relevant to query Q and their relevance weight (or gain). The gain is only used for part c below.

hw1-retrieved.csv - Top 10 document retrieved by S1 and S2, respectively, ranked in decreasing order of relevance.

[Note: for this problem you do not need to write a program (though you can if you wish). At minimum, you should consider using a spreadsheet program (such as Microsoft Excel) to facilitate performing the computations and visualization. You should submit your spreadsheet or program, and the answers to the following questions clearly identified.

1. Compute the Precision and the Recall graphs for each system as a function of the number of documents returned (for 1 document returned, 2 documents returned, etc.). First, compile your calculations in a table which shows the Precision and Recall for S1 and S2 as a function of the number of documents returned (from 1 to 10). Then, create separate graphs for Precision and Recall, in each case comparing the two systems. For each graph, use the number of retrieved docs (from 1 to 10) as the x-axis and the value of the metric (precision or recall) as the y-axis.
2. A single metric that can be used to combine precision and recall is the F Measure (see Section 8.3 of the IR Book). Using the F measure with B=0.5 (equation 8.5), create a graph similar to the above comparing the two systems.
3. Next, using the graded relevance weights (gain) provided for the relevant documents,  compute the Discounted Cumulative Gain (DCG) and the Normalized DSG (NDCG) values for the retrieved documents for both S1 and S2. Depict the results in a graph similar to previous parts comparing NDCG for S1 and S2.
    

1. Show the full contents of the dictionary in lexicographic order of tokens along with document frequencies and total frequencies in an easily readable format (see this example of what a partial output might look like). In your submission, clearly show the execution of your program and the output generated.
2. Show the output of your program when searching the postings for these individual tokens: "index", "cluster", "query", "search", "engine", and "retrieve" (in each case the output should show the "hit list" of documents containing the token along with the token's occurrence count in each document. In your submission, clearly show the execution of your program and the output generated.
3. Based on the results obtained in part b show the set of documents resulting from the following Boolean queries (you need not implement a query mechanism; you only need to give the end result for each query):
   1. index AND query
   2. index OR query
   3. index AND (NOT query)
   4. (search AND query) OR (search AND retrieve)
   5. (index OR cluster) AND (engine OR search)
      
      

• proportion
• proportional
• promotion
• emotional

In each case provide the intermediate outputs of your program specified above as well as the final similarity score.