MC: Markov chain based rank aggregation

In TopKLists: Inference, Aggregation and Visualization for Top-K Ranked Lists

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.

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).

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

Author(s)

Shili Lin <[e-mail]>

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)

TopKLists documentation built on Sept. 1, 2022, 5:10 p.m.