markov {raincin}

Google's PageRank algorithm for Rating and Ranking

Description

Calculate ratings and provide rankings using Google's PageRank algorithm

Usage

markov(
  jpMat,
  method = "markovvl",
  dampingFactor = 0.85,
  ties.method = "average"
)

Arguments

jpMat

a Judge-Presenter matrix, or a User-Movie matrix

method

a character string specifying Markov's method, including "markov", "markovvl", "markovlvpd", "markovwlvp".

dampingFactor

the PageRank theory holds that an imaginary surfer who is randomly clicking on links will eventually stop clicking. The probability, at any step, that the person will continue is a damping factor. Web 0.85, NFL 0.60, NCAA basketball 0.50

ties.method

a character string specifying how ties are treated, including "average", "first", "last", "random", "max", "min", from base::rank

Details

1. markov: Markov's method, voting with losses, equivalent to markovvl

2. markovvl: Markov's method, voting with losses

3. markovlvpd: Markov's method, losers vote with point differentials

4. markovwlvp: Markov's method, winners and losers vote with points

Author(s)

Jiangtao Gou

References

Brin, S. and Page, L. (1998). The anatomy of a large-scale hypertextual web search engine. Computer Networks and ISDN Systems 30, 107-117. Proceedings of the Seventh International World Wide Web Conference.

Gou, J. and Wu, S. (2020). A Judging System for Project Showcase: Rating and Ranking with Incomplete Information. Technical Report.

Langville, A. N. and Meyer, C. D. (2012). Who's Number 1?: The Science of Rating and Ranking. Princeton University Press.

Examples

jpMat <- matrix(data=c(5,4,3,0, 5,5,3,1, 0,0,0,5, 0,0,2,0, 4,0,0,3, 1,0,0,4),
nrow=6,
byrow=TRUE)
result <- markov(jpMat, 
method='markovvl', 
dampingFactor=0.85, 
ties.method='average')
print(result)