## 4 Results
### Algorithms Comparison
Therefore, hierarchical algorithms are suitable in data filtering, i.e., in cases that atypical data need to be excluded from the data set. Also, atypical data may refer to the load of holidays, working days close to holidays and other days with special attributes. The potential of tracking special days is suitable in load profiling applications. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Empty Clusters** & **Outliers Tracking** \\ \hline K-means & No & No \\ Modified K-means\#1 & No & No \\ Modified K-means\#2 & No & No \\ WFA K-means & No & No \\ IWFA K-means & No & No \\ Hopfield K-means & No & No \\ minCEntropy & No & No \\ K-means\_A & No & No \\ K-means\_B & No & No \\ K-medoids & No & No \\ SL & No & Yes \\ CL & No & Yes \\ UFQMA & No & Yes \\ WPGMA & No & Yes \\ WPGMC & No & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Algorithms comparison in terms of empty clusters formation and outliers tracking. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Execution Time (s)** & **Ratio** \\ \hline K-means & 8.31 & 1 \\ Modified K-means\#1 & 978.81 & 117.78 \\ Modified K-means\#2 & 2 & 15.93 & 1.91 \\ WFA K-means & 8.44 & 1.01 \\ IWFA K-means 1 & 713.80 & 85.89 \\ Hopfield K-means & 495.53 & 5.96 \\ minCEntropy & 691.73 & 83.24 \\ K-means\_A & 8.27 & 0.99 \\ K-means\_B & 8.16 & 0.98 \\ K-medoids & 9.22 & 1.10 \\ SL & 3.59 & 0.43 \\ CL & 3.69 & 0.44 \\ UPGMA & 3.67 & 0.44 \\ WPGMA & 3.68 & 0.44 \\ WPGMC & 3.71 & 0.44 \\ UPGMC & 3.73 & 0.44 \\ MVM & 3.70 & 0.44 \\ FCM & 10.91 & 1.31 \\ IFCM & 13.32 & 1.60 \\ SOM (1D) & 1148 & 138.14 \\ AVQ 3 & 1244.70 & 149.78 \\ Hopfield & 44.69 & 5.37 \\ FDL & \textgreater{}\textgreater{}0 & \textgreater{}\textgreater{}1 \\ CLA 4 & 848.97 & 102.16 \\ IRC & 6.41 & 0.77 \\ BCEC1 5 & 6.83 & 0.82 \\ BCEC2 5 & 6.61 & 0.79 \\ CSC 5 & 6.53 & 0.78 \\ SVC & 27.54 & 3.31 \\ ISODATA & \textgreater{}\textgreater{}0 & \textgreater{}\textgreater{}1 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Required execution time per algorithm. Criterion#6 refers to software availability of the algorithms. Table 11 presents the software packages that include implementation of the algorithms. It can be noticed that most algorithms are available under commercial license or freely. In the cases of the K-means, K-medoids and hierarchical algorithms the Table presents the most common software. According to Table 11, there are lots of alternatives to implement these algorithms. The term \"Matlab 3 rd party code\" refers to unofficial Matlab code freely provided by the authors. The term \"In-house software\" refers to code developed by the authors of the respective paper and is not officially distributed. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Empty Clusters** & **Outliers Tracking** \\ \hline UPGMC & No & Yes \\ MVM & No & Yes \\ FCM & Yes & No \\ IECM & Yes & No \\ SOM & No & No \\ AVQ & Yes & No \\ Hopfield & No & No \\ FDL & No & Yes \\ CLA & Yes & No \\ IRC & No & Yes \\ BCEC1 & No & Yes \\ BCEC2 & No & Yes \\ CSC & No & Yes \\ SVC & No & Yes \\ ISODATA & Yes & No \\ \hline \hline \end{tabular}
\end{table} 
Table 10: _Cont._ \begin{table}
\begin{tabular}{c l} \hline \hline
**Algorithm** & **Availability** \\ \hline  & 1. Matlab \\  & 2. Mathematica \\  & 3. SPSS \\  & 4. SAS \\ K-means & 5. R \\  & 6. Weka \\  & 7. C++/C\# \\  & 8. Python \\  & 9. Matlab 3 rd party code \\ \hline Modified K-means\#1 & In-house software \\ \hline Modified K-means\#2 & In-house software \\ \hline WFA K-means & In-house software \\ \hline IWFA K-means & In-house software \\ \hline Hopfield K-means & In-house software \\ \hline minCEntropy & Matlab 3 rd party code \\ \hline K-means\_A & In-house software \\ \hline K-means\_B & In-house software \\ \hline  & 1. Matlab \\  & 2. Mathematica \\  & 3. SPSS \\  & 4. SAS \\ K-medoids & 5. R \\  & 6. Weka \\  & 7. C++/C\# \\  & 8. Python \\  & 9. Matlab 3 rd party code \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Software availability per algorithm [98; 99; 100; 101; 102].