Question

Assume that an IR, system returns a ranked list of 10 total documents for a given query. Assume that according to a gold-standard labelling there are 5 relevant documents for this query, and that the only relevant documents in the ranked list are in the 2nd, 3rd, 4th and 8th positions in the ranked results. Calculate and clearly show the interpolated precision value for each of the following standard recall levels: (0.0, 0.1 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) for this individual query.

Answer 1

Answer:

Precision = 0.625

Recall = 0.5

Step-by-step explanation:

Data:

Let: total documents = 10

      relevant documents = 5

if 2 documents are removed, the total number of documents remaining will be

documents remaining = total - 2 documents

                                     = 10 - 2

                                     = 8 documents

therefore, the precision will be = $\frac{relevant documents}{remainder after 2 docs are removed} \\= \frac{5}{8} \\= 0.625$

Recall = $\frac{5}{10}\\ = 0.5$

Answer 2

Answer:

Step-by-step explanation:

Answer:

Precision-Recall values corresponding to relevant documents positions

Doc. No    Recall         Precision

2nd          1/5 = 0.2      1/2 = 0.5

3rd           2/5 = 0.4     2/3 = 0.67

4th           3/5 = 0.6     3/4 = 0.75

8th           4/5 = 0.8     4/8 = 0.5

Going by the above results, the interpolation of Precision and Recall will be:

Interpolated Precision-Recall values

Recall    Precision

0.0.           0.75

0.1             0.75

0.2             0.75

0.3              0.75

0.4              0.75

0.5               0.75

0.6               0.75

0.7                 0.5

0.8                 0.5

0.9                   0

1.0                     0