Vector Model
This question requires you to use the following data. Assume a repository of 10 documents over eight key terms. Table 2.1 gives the document-term table that shows the raw frequencies with which the eight key terms appear 1 in each of the 10 documents, as well as the TF values for a query document.
Exercise 1. Using the information from Table 2.1, which documents would be returned by the following queries:
a) Term2 AND Term7
b) Term4 OR Term2
c) (Term2 OR Term7) AND (NOT Term7)
Table 2.1: A2: Document-Term and Query-Term Table
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Term 1
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Term 2
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Term 3
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Term 4
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Term 5
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Term 6
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Term 7
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Term 8
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Doc 1
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4
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8
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9
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0
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10
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8
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0
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9
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Doc 2
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1
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5
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0
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0
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12
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0
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1
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3
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Doc 3
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0
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3
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0
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0
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0
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4
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2
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0
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Doc 4
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1
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0
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4
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3
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9
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0
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0
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0
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Doc 5
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0
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4
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0
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0
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0
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5
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1
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0
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Doc 6
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1
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2
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2
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0
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3
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1
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0
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1
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Doc7
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0
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5
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3
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4
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0
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0
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4
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2
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Doc 8
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0
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7
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0
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3
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0
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0
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3
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3
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Doc 9
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0
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5
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0
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0
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0
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4
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1
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2
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Doc 10
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0
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3
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4
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0
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0
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2
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4
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0
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Query
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2
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3
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1
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2
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2
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0
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1
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0
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Is it possible to rank the documents returned in (a) to (c)? If it is possible, then supply the rankings in each case. If it is not possible, then state why.
Exercise 2. Answer the following questions.
a) Using the information from Table 2.1, calculate the ranking score for each of the ten documents based on each of the following query-document similarity measures:
dot product using TF weight for both documents and query vectors cosine coefficient using TF weight for both documents and query vectors.
b) Compare the rankings that you obtained using the two similarity measures. If there are differences between the rankings, then discuss why you think these differences occurred.
Exercise 3. Answer the following questions.
a) Using the information in Table 2.1, calculate the idf (inverse document frequency) weight vector. Make sure you show how your calculation was performed.
b) Construct a table similar Table 2.1, but, instead of raw term frequencies, show the tf-idf weights.
c) Using tf weights for the query vector, and tf-idf weights for the document vectors, and the cosine coefficient as a similarity measure, compute the ranking scores using the cosine coefficient. Show how your calculations were performed for the first document only.
d) How does this ranking compare with ranking obtained using the cosine similarity measure in Exercise 20? If there are differences between the rankings, then discuss why you think these differences occurred.
Exercise 4. Answer the following questions.
a) This time, using tf-idf weights for both the query and document vectors, and the cosine coefficient as a similarity measure, compute the ranking scores using the cosine coefficient. Show how your calculations were performed for the first document only.
b) How does this ranking compare with ranking obtained in Exercise 21? If there are differences between the rankings, then discuss why you think these differences occurred.
Exercise 5. This time, use tf weights for the query vector, tf-idf weights for the document vectors, and the Dice coefficient rather than the Cosine coefficient as the similarity measure.
a) Compute the ranking scores for all documents. Show how your calculations were performed for the first document only.
b) How does the ranking compare with ranking obtained in Exercise 21? If there are differences between the rankings, then discuss why you think these differences occurred.
2.2. IR Evaluation
Exercise 6. The following data displays retrieval results for two different algorithms (Algorithm 1 and Algorithm 2) in response to two distinct queries (Query 1 and Query 2). An expert has manually labelled each of the documents as being either relevant or not relevant to the queries.
Algorithm 1 Returns the following results:
Query 1 : d4 , d15 , d1 , d3 , d8 , d76 , d2 , d33 , d30 , d5 , d11 , d29 , d66 , d10
Query 2 : d9 , d91 , d2 , d87 , d13 , d52 , d92 , d16 , d17 , d22 , d20 , d71 , d48 , d60 , d56
Algorithm 2 Returns the following results:
Query 1 : d8 , d29 , d6 , d5 , d15 , d17 , d20 , d65 , d2 , d33 , d44 , d41 , d7 , d77 , d13 , d14 , d90 , d80 , d70 , d4
Query 2 : d3 , d87 , d2 , d28 , d15 , d14 , d12 , d10 , d41 , d11 , d85 , d89 , d1 , d49 , d52 , d76 , d55 , d9 , d91 , d99 , d30 , d17 , d13 , d26 , d94 , d18 , d86 , d72 , d48 , d8 , d93 , d42 , d79 , d43 , d88 , d7 , d98 , d51 , d50 , d6
Relevance The known one is as follows:
Query 1 : d2 , d4 , d7 , d15 , d29
Query 2 : d1 , d2 , d3 , d7 , d8 , d9 , d11 , d12 , d13 , d15 , d16 , d20
a) For Algorithm 1, plot the precision versus recall curves for Query 1 and Query 2, interpolated to the 11 standard recall levels. Also plot the average precision versus recall curve for Algorithm 1 (all three curves should be on a single chart).
b) For Algorithm 2, plot the precision versus recall curves for Query 1 and Query 2, interpolated to the 11 standard recall levels. Also plot the average precision versus recall curve for Algorithm 2 (all three curves should be on a single chart, but a separate chart from that used in part (a)).
c) Plot the averages for Algorithm 1 and Algorithm 2 on a separate chart, and compare the algorithms in terms of precision and recall. Do you think one of the algorithms is superior? Why?