# CEMC based rank aggregation

### Description

Performs Cross Entropy Monte Carlo simulations for generating combined ranked list using CEMC, taking into account the different spaces of ranked input lists.

### Usage

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### Arguments

`input` |
A list of several |

`space` |
A list of the same structure as the input list. Contains underlying spaces for the top- |

`k` |
Desired length of combined list |

`dm` |
Distance measure, "s" for Spearman, "k" for Kendall (p=0) |

`kp` |
Partial distance used in Kendall's tau distance measure |

`N` |
Number of samples generated in each iterate |

`N1` |
Number of samples retained after each iterate |

`rho` |
Proportion of samples used to estimate a new probability matrix |

`e1` |
Stopping criterion with respect to the l1-norm of the difference of the two probability matrices between the current and previous iterations |

`e2` |
Stopping criterion with respect to the difference in the obtimizing criterion (e.g. the generalized Kemeny guideline) between the current and the previous iterations |

`w` |
Weight of the new probability vector for the next iterate |

`b` |
Parameter used in blur function - this is for finding starting values for the algorithem |

`init.m` |
Initialization method, see the function |

`init.w` |
Probability matrix initialization. (See Details) |

`d.w` |
Weights for distances from different input lists |

`input.par` |
Input parameters in a data.frame |

`extra` |
Number of additional items to be included in the combined ranked list during the calculation |

### Details

The algorithm implemented is the Order Explicit Algorithm, which is an iterative procedure to maximize an objective function (either based on Kendall's distance (dm="k") or Spearman's distance (dm="s")).

init.w: probability matrix initialization: (1-init.w) * uniform + init.w * estimated from input lists

### Value

A list containing three components:

`TopK` |
A vector giving the aggregate ranked list. |

`ProbMatrix` |
A matrix, with each column represent the probability vector of a multinomial distribution and thus sum to 1. |

`input.par` |
A vector containing tuning parameters used in the current run. User may edit this vector and use it as input for a more refined analysis. |

### Author(s)

Jie Ding <jding@jimmy.harvard.edu>, Shili Lin <shili@stat.osu.edu>

### References

Lin, S. and Ding, J. (2009). Integration of ranked lists via Cross Entropy Monte Carlo with applications to mRNA and microRNA studies. Biometrics, 65, 9-18.

### Examples

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