TopKLists (version 1.0.2)

MC: Markov chain based rank aggregation

Description

Aggregating ranked lists using three Markov chain algorithms.

Usage

MC(input, space = NULL, k = NULL, a = 0.15, delta = 10^-15)

Arguments

input

A list containing individual ranked lists.

space

A list containing the underlying spaces. If not explicitly specified, all lists are treated as coming from a common space defined by the union of all input lists.

k

An integer specifying the number of items in the output top-k list.

a

Tuning parameter to make sure Markov Chain with the transition matrix is ergodic; default set to 0.15.

delta

Convergence criterion for stationary distribution; default set to 10^-15.

Value

• A list of elements, two for each of the MC algorithms:
• MC1.TopK
  A vector of aggregate ranked elements based on MC1 algorithm.
• MC1.Prob
  Stationary probability distribution: a vector of probabilities corresponding to the ranked elements in MC1.TopK
• MC2.TopK
  A vector of aggregate ranked elements based on MC2 algorithm.
• MC2.Prob
  Stationary probability distribution: a vector of probabilities corresponding to the ranked elements in MC2.TopK
• MC3.TopK
  A vector of aggregate ranked elements based on MC3 algorithm.
• MC3.Prob
  Stationary probability distribution: a vector of probabilities corresponding to the ranked elements in MC3.TopK

Details

Constructs ergodic Markov Chain based on ranking data from individual lists. A larger probability in the stationary distribution corresponds to a higher rank of the corresponding element. The algorithm are considered: MC1 (spam sensitive), MC2 (majority rule), and MC3 (proportional).

References

Lin, S. (2010). Space oriented rank-based data integration. Statistical Applications in Genetics and Molecular Biology 9, Article 20.

See Also

Borda, CEMC, MC.plot

Examples

#get sample data
data(TopKSpaceSampleInput)
outMC=MC(input,space) #underlying space-dependent
outMCa=MC(input,space=input) #top-k spaces
MC.plot(outMC)