PLRank is a collection of general purpose functions that provide a flexible set of tools for applying a wide range of label ranking methods based on Plackett-Luce model. PLRank includes evaluation methods, datasets and new algorithms I developed in my master thesis, "Generalized Plackett-Luce Model for Label Ranking", under the direction of Dr.Giorgio Corani and Dr.Alessandro Antonucci from the Swiss AI Lab IDSIA. Label ranking datasets in PLRank consist of training examples of a target function that has multiple binary target variables. In other words, each item of a label ranking dataset is annotated by many labels (classes). This is the nature of many real world problems such as web page categorization, music categorization, direct marketing, and etc. The typical usage scenario of PLRank would involve a machine learning researcher performing an empirical evaluation of one or more label ranking learning algorithms, based on one or more label ranking datasets, and a machine learning practitioner building a label ranking model using a training dataset and then applying it to a new (unlabeled) dataset, in order to obtain predictions.

Currently PLRank includes algorithms for performing major label ranking tasks and sample of datasets:

• Label ranking datasets, KEBI Data Repository hosted by the Philipps University of Marburg.

• Artificial ranking datasets. The functions to generate ranking datasets.

• Maximum likelihood estimation methods to estimate the parameters of Plackett-Luce model. Two MLE methods are available, MM and NR.

• Evaluation methods for label ranking problems. Calculate a variety of evaluation measures through k-folds cross validation.

Many examples concerning optimization tasks are provided in this section. In particular, we will present the optimization of well-known benchmark mathematical functions and label ranking problems in general. Hereafter, we assume that PLRank package is already installed and loaded in the current R session, for example by entering the following command:

R> library("PLRank")

We start by creating an artificail dataset from PL1 model. This is useful for performing inference tasks for ranking problems. Figure \ref{fig:R-genrank1V}, $$rank$ is the rankings randomly drawn from the known parameters $$para$

Usage:

genRank1v(nLabels, nObs)

Arguments:

nLabels number of labels to rank
nObs number of observations

Example: create artificial dataset with 4 labels to rank and 10 instances

R> lables = 4
R> observations = 10
R> genRank1v(lables, observations)

Creating an artificial dataset from PL2 model.Figure \ref{fig:R-genrank2V}, $$rank$ is the rankings randomly drawn from the known parameters $$para1$ and $$para2$, where the split point is defined at the second position.

#Usage
genRank2v(nLabels, nObs, L)

#Arguments
nLabels number of labels to rank
nObs number of observations
L split position between the first vase and the second vase

#Examples
Create artificial dataset with 4 labels to rank and 10 instances
R> lables = 4
R> observations = 10
R> L = 2
R> genRank2v(lables, observations, L)

This function uses the MM (minorization-maximization) algorithms to fit the Plackett-Luce model. The method was rewritten from the original Matlab code (plackmm) provided by [Hunter, 2004]. The method was modified by adding a stop criteria to prevent the estimates from approaching infinity.

#Usage
est.PL.MM(dset)

#Arguments
dset ranking dataset

#Examples
Create 2 ranks and 3 l a bel s
R> ranks = matrix (0 ,2 ,3) # rows : number of ranks, column : number of labels
R> ranks [1 , ] = c (1 ,2 ,3) # L1>L2>L3
R> ranks [2 , ] = c (3 ,1 ,2) # L3>L1>L2
R> est.PL.MM(ranks)

This function uses the NR algorithm to fit PL2 model. The function extends the original method fitting the one-vase Plackett-Luce model from PMR package by adding the two-vases model interpretation.

#Usage
est.PL2.NR( d se t , L )

#Arguments
dset ranking dataset
L split point between the first vase and the second vase

#Value
Estimated parameters and log-likelihood
Create 2 ranks and 3 l a bel s
R> ranks = matrix (0 ,2 ,3) # rows : number o f ranks , column : number o f l a b el s
R> ranks [1 , ] = c (1 ,2 ,3) # L1>L2>L3
R> ranks [2 , ] = c (3 ,1 ,2) # L3>L1>L2
R> est.PL2.NR( ranks , 1 )

This section illustrates the use of the cv.knn() function on two real datasets. The first one, Iris, is a well-known dataset in ranking study, which consists of measurements in centimeters of the variables sepal length and width and petal length and width, respectively, for each flowers from each of 3 species (3 labels).

The second one, Eurovision, presented in Jacques and Biernacki (2012), consists of the votes of European countries during the Euro- vision Song Contest. Both datasets are available in the Rankcluster package, as well as the three other datasets analysed and described in Jacques and Biernacki (2012): APA, quiz, sports.

Label ranking dataset consists of two main parts, the features and ranks. The latter forms a set of preference labels. At the moment, each instance only contains a complete ranking. Particularly, labels are assembled to a labek ranking by using the ">" sign. For example, L1 > L2 means that label 1 is preferred over label 2. It is not allowed to state one single label inside of an instance and thus there have to be at least two labels separated by the ">" character. The label ranking dataset will be automatically avaialble in the R environment once the PLRank package is loaded into the R session. For example, we can simply call the iris dataset by trying R > data.iris in the R console.

#Usage
cv.knn( dset , k = 10, nFolds = 10, nRuns = 10, alpha = 0.05)

#Arguments
dsetlabel ranking dataset
k the number of nearest neighbors to search . The defaul k value is set to 10
nFolds the number of folds for the cross validation
nRuns the number of runs for the cross validation
alpha the default value is set to 0.05

#Examples
Perform the 10 runs of 10 #folds cross validation on the Iris dataset
dset = data.iris
cv.knn(dset , k=15, nFolds=10, nRuns=10, alpha =0.05)