Difference between revisions of "Normalized discounted cumulative gain"
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| − | The discounted cumulative gain (DCG) accumulated at a particular rank position <math>p</math> is defined as: | + | The discounted cumulative gain (DCG) measures the quality of the results in a ranked list, where items in that list are graded in some way. Typically the ranked list in question is the query results of an IR system, and the grading is a relevance judgment for each result. DCG accumulated at a particular rank position <math>p</math> is defined as: |
<math> \mathrm{DCG_{p}} = rel_{1} + \sum_{i=2}^{p} \frac{rel_{i}}{\log_{2}i} </math> | <math> \mathrm{DCG_{p}} = rel_{1} + \sum_{i=2}^{p} \frac{rel_{i}}{\log_{2}i} </math> | ||
| − | Normalized DCG (nDCG) is a way to calculate this measure across | + | Normalized DCG (nDCG) is a way to calculate this measure across many independent queries, the result lists for which might all be of different length. nDCG is computed as: |
<math> \mathrm{nDCG_{p}} = \frac{DCG_{p}}{IDCG{p}} </math> | <math> \mathrm{nDCG_{p}} = \frac{DCG_{p}}{IDCG{p}} </math> | ||
| − | The nDCG values for all queries can be averaged to obtain a measure of the average performance of a search engine's ranking algorithm. | + | The nDCG values for all queries can be averaged to obtain a measure of the average performance of a search engine's ranking algorithm over many queries. |
Latest revision as of 14:54, 29 March 2011
The discounted cumulative gain (DCG) measures the quality of the results in a ranked list, where items in that list are graded in some way. Typically the ranked list in question is the query results of an IR system, and the grading is a relevance judgment for each result. DCG accumulated at a particular rank position is defined as:
Normalized DCG (nDCG) is a way to calculate this measure across many independent queries, the result lists for which might all be of different length. nDCG is computed as:
The nDCG values for all queries can be averaged to obtain a measure of the average performance of a search engine's ranking algorithm over many queries.
