## 5 Experiments  
All the experiments are performed on multi-label datasets available at [19]. Table 1 exhibits basic statistics, such as the number of examples and labels, along with the statistics that are relevant to the label sets [16].  
Multi-Label classification problem can be solved in different ways [2]. Problem transformation methods allow converting a multi-label problem to a single-label one. Below is the list of the most frequently used approaches:  
* Binary Relevance. One builds a classifier for each label, which will make a decision about this label.
* Label Power-set transformation. One builds a multiclass classifier, where each class corresponds to a set of labels associated with a document.
* One _vs._ one. One trains a classifier for each pair of labels. The decision is made by voting.  
We use Binary Relevance transformation because of the nature of the data (Table 1). The last column shows the number of classes in case of Label Power-set transformation. This transformation can work on Scene, Genbase and Medical. In other datasets, the number of classes will be rather large so the number of training examples for each class will be low and classification performance will be poor as well.  
It is also rather hard to build one versus one flat classifier. There will be \(100,000\) classifiers for Corel5k. It is much easier to use it in a hierarchy, and we plan to do it in our future work.  
Each dataset is divided into the training and test parts in the proportion \(2\) to \(1\), respectively. There are no any other transformations of the datasets. In particular, there is no attribute selection. The first four datasets are used in all experiments and the last five are used only with the PHOCS-2.  
The decision tree algorithm \(C4.5\)[18] is chosen as the basic multi-label classifier. The \(K\)-means algorithm is used for clustering and building hierarchies. The micro and macro measures of classification accuracy (precision (P), recall (R) and \(F1\)-measure) are used [20].  
The parameter values for the PHOCS are chosen as \(k_{min}=2\) and \(k_{max}=10\). Such \(k_{max}\) is chosen since the number of labels in our experiments has the order of \(100\), so the hierarchy contains at least \(2\) layers.  
The experiment results are represented in Table 2.  
We removed the external parameter, so the PHOCS-2 has only two parameters: \(k_{min}\), which should always equal \(2\), and \(k_{max}\), which can be the only external parameter in the ideal case. We got a better \(F1\)-measure in comparison with the results from [4] for all four datasets that we used there. In all cases the current version of the algorithm demonstrated the best performance (\(F1\)-measure).  
The experimental study of the PHOCS-2 performance on nine multi-label datasets justifies its effectiveness. We got significantly better results in five of them compared with the flat case. It was difficult to improve the result of the Genbase, because its performance is already \(0.97\), and we have not improved the performance in the Mediamill and the Yeast. HOMER [15] was tested only on two datasets. One of them is Mediamill and we can compare results. There is no baseline in [15]. PHOCSv2 outperforms HOMER by \(10\%\) in \(F1\)-measure on Mediamill dataset.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Name** & **Docs** & **Labels** & **Bound of labelsets** & **Actual labelsets** \\ \hline Mediamill & 43907 & 101 & 43907 & 6555 \\ Bibtex & 7395 & 159 & 7395 & 2856 \\ Medical & 978 & 45 & 978 & 94 \\ Enron & 1702 & 53 & 1702 & 753 \\ Yeast & 2417 & 14 & 2417 & 198 \\ Genbase & 662 & 27 & 662 & 32 \\ Corel5k & 5000 & 374 & 5000 & 3175 \\ CAL500 & 502 & 174 & 502 & 502 \\ Scene & 2407 & 6 & 64 & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Multi-Label Datasets and Their Statistics.  
In most cases, our algorithm provides better F1 due to better Recall. We are able to optimize other measures as well. It is useful when one has specific requirements to a classifiers performance.