This experiment, as stated earlier, utilizes paired combinations of 10 preprocessors and 6 learners on various 10 data sets. To ensure that we have data with conclusive answers to test on, the leave-one-out method is used on each of its respective data set 7 times. Each repetition represents a different error measure (AR, MRE, MER, MdMRE, MRE, PRED(25), and MIBRE), each explained in the experiment specification section. These measures are used to calculate both wins and loss for both data sets and algorithms (preprocessor, learner combinations). The summed measures are organized with the fewest losses and, inversely, the most wins. \\
  
Though the results extracted from this follow up do vary slightly from the previous experiment that we have emulated, the results are essentially the same.  All the sorted algorithms' performance can be seen in Figure \fig{DataLosses}. From our experiment, the SWReg/1NN combination was ranked the best in the terms of fewest losses, and the PCA/SLReg combination was ranked the worst. These correspond to the previous study's results. \\

\begin{figure}[H]
\begin{center} \includegraphics[width=3in]{vincent/ranking.jpg} \end{center}
\caption{All permutations of data miners and learner pairs, ordered from least amount of loss measures to the most.}\label{fig:SortedAlgorithms}
\end{figure}

\begin{figure}[H]
\begin{center} \includegraphics[width=3in]{vincent/DataSetLossValues.pdf} \end{center}
\caption{The seventy two algorithms, sorted
by their percentage of maximum possible losses (so 100\% = 4970). }\label{fig:DataLosses}
\end{figure}

To get proper percentages of loss over the algorithms, the sum of losses for one algorithm over all error measures is divided by the total possible losses which is the counts of: \[ comparisons made * error measures * datasets =\] \[ 71 * 7 * 10 = 4,970 \] The results of such findings are located in Figure \fig{AlgorithmLosses}. Which resemble the figure of Algorithm Losses provided by the paper ICSE paper.

As for the percentages of Loss over a Data Set, a very similar equation is used where all numbers gathered for a data set are summed together with all data collected for each error measure. That is then divided by the total possible amount of losses for that data set which is the count of: \[ comparisons made * error measures * algorithms = \]
\[71 * 7 * 72 = 35,784 \]

\begin{figure}[H]
\begin{center} \includegraphics[width=3in]{vincent/AlgorithmLossValues.pdf} \end{center}
\caption{The seventy two algorithms, sorted
by their percentage of maximum possible losses (so 100\% = 5040). }\label{fig:AlgorithmLosses}
\end{figure}

\begin{figure}[H]
\includegraphics[width=1.5in]{vincent/DataSetWinValues.pdf}\includegraphics[width=1.9in]{vincent/AlgorithmWinValues.pdf}
\caption{Algorithms and datasets, sorted as per 
but this
time showing their percentage of 
maximum {\em wins} over all performance measures.}
\label{fig:WinValues}
\end{figure}

\begin{figure}[H]
\includegraphics[width=1.5in]{vincent/pred25DataSetWinValues.pdf}\includegraphics[width=1.9in]{vincent/pred25AlgorithmWinValues.pdf} 
\caption{Algorithms and datasets, sorted as per 
\fig{DataLosses} and \fig{AlgorithmLosses}, 
but this time showing their percentage of 
maximum {\em wins} over {\em just the PRED(25)} performance measures.}\label{fig:WinValues_pred25}
\end{figure}

While the visible trend may seem convincing, it beckons for more evidence. Unfortunately, when the opposite graph to the Losses \fig{DataLosses} is constructed in the Wins \fig{WinValues}, the trend is very jagged and hard to get an accurate reading. These graphs are are similar to the Wins Figures in the Ekrem paper, and demonstrate the same need for more empirical studies. The Wins \fig{WinValues_pred25} demonstrates that there is correlation between the error measure values gathered, if only one. \\

\begin{figure}[H]
\begin{center} \includegraphics[width=3in]{vincent/AllLossPercentages.jpg} \end{center}
\caption{
The 19 data sets and 52 methods are expressed on this graph in percentages of maximum possible losses for one algorithm for one data set = \# of Error Measures * \# of comparisons made. (100\% = 108, 50\% = 54, 25\% = 28, 12.5\% = 14) and based on these number both the columns and rows are sorted by their sum.}
\label{fig:AllLosses}
\end{figure} 



