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# Comparison based evaluation

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rank aggregation

rank aggregation

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• 1. Comparison-based evaluationJose Antonio Martinez Torres
• 2. Problem
• 3. Law of Large number1 spin-\$5001000 spin\$100,000
• 4. 254
• 5. 432
• 6. Experiments• Movies Dataset– 100,000 ratings– 1000 users– 1700 movies• http://www.grouplens.org/node/73
• 7. True rating• Based on the law of large numbers, averagerating using this movies dataset can work verywell.• However, by using a small sample, averagerating would significantly differ from the truerating.
• 8. = { 2, 4, 5,5,4,4,5,3,3,4,5,4,5,4,5,4,5,4,3,2,3,3,4,5,4,4,5,5,3,4}True rating = 4= { 2, 4 }Rating = 3
• 9. Kendall tau• Statistic used to measure the degree ofsimilarity between two rankings.• Practical use:– Compare how close the top-10 results producedby Google and Bing are.
• 10. ABCDECDABERank 1 Rank 2T = 6 - 4 / ½ (5) (5-1) = 0.2Dissimilarity goes from 1 to -1 where 1 means the two rankings arethe same and -1 means one ranking is the reverse of the other
• 11. Movie1 = {3, 4, 5,4,5,3,2,4,4,5,4,3,4,5,4,3,2,3,4,4,4,5,4,3,3,2}Movie2 = {4, 3, 2,3,2,3,4,3,2,1,2,3,4,3,4,3,2,3,2,3,4,3,4,3,4,3}Movie3 = {3, 4, 2,4,5,3,2,4,,4,5,4,3,4,5,4,3,2,3,4,4,4,5,4,3,3,2}Movie4 = {2, 3, 4,5,3,4,4,4,5,4,3,3,2}Movie5 = {3, 4, 5,2,4,5,4,3,3,2}Movie6 = {5, 3, 4,3,3,5,4,3,3,2}Movie7 = {1, 3, 4,3,2,3,43,2,3,4,2,3,4,2,3,4,3,3,2}..Movie1700= {3, 4, 5,4,2,3,3,2,3,2,1,1,2,3}Ranking 1 = 3 , 4 , 3, 2, 3, 5, 1Ranking 2 = 3.5 ,3.5 , 3.5, 2.5, 3.5, 4, 2...Calculate 1 to n ranking n and true rating Kendall tau correlation
• 12. 0.40.50.60.70.80.911 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50KendalltvalueError rate k-distanceSerie…