Abstract

I give a detailed description of how the PageRank method and the Close Rankings method can be used to rank images in a much more dynamic way than the currently used Average-Point method. I show how the Close Rankings method can be used to rank images using both user rankings and vote relevance.

I introduce the Newcomer's Rush scenario and show how all three methods are aected by this problem. Furthermore I give a workaround that relaxes the eects of Newcomer's Rush.

When researching the PageRank method, I discovered a simple proof that the recursive computations used to solve the method converge, something that was not in (Page, 1999). I give a short description of the proof and show that the normalization described in the pseudocode in (Page, 1999) is unnecessary when dealing with the Random-Surfer model.

I show that the Close Rankings method has a problem with the way it compares votes, which implies that it might go in the complete opposite direction of what was intented without being punished. I propose a simple change in the objective function of the optimization problem which fixes this problem.

I show how the problem produced by the Close Rankings method can be solved using the Subgradient method combined with Golden Section Search.

Keywords

image ranking, group ranking, average point, page rank, pagerank, close rankings, comparison, weights, normalization, rank reversal, optimisation, optimization, golden section search, subgradient method