# MC: Markov chain based rank aggregation In TopKLists: Inference, Aggregation and Visualization for Top-K Ranked Lists

## Description

Aggregating ranked lists using three Markov chain algorithms.

## Usage

 `1` ```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 <[email protected]>

## References

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

`Borda`, `CEMC`, `MC.plot`

## Examples

 ```1 2 3 4 5``` ```#get sample data data(TopKSpaceSampleInput) outMC=MC(input,space) #underlying space-dependent outMCa=MC(input,space=input) #top-k spaces MC.plot(outMC) ```

### Example output

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TopKLists documentation built on May 31, 2017, 1:46 a.m.