## 4 Results
### Algorithms Selection  
The selection of the most proper algorithm for a given application is done using TOPSIS. The scope is to select an algorithm that maximizes the clustering benefit, i.e., the optimal segmentation of a given load data set. The initial phase of TOPSIS is the setting of the weights of each criterion. The sum of weights equals 1. The higher the weight of a criterion, the higher the importance this criterion has in the overall decision. While only clustering validity indicators are regarded in the load profiling literature, the weight of Criterion#3 is set with the higher value. Also, since smart metering installations and load data collections continue to increase, Criterion#4 has the next highest value. All the other criteria are equally valued. More specifically, let \(w_{\text{CR(i)}}\) be the value of the \(i\)th criterion, \(I=1,\,\ldots,\,6\). The weights that are set to criteria are: \(w_{\text{CR(I)}}=0.10\), \(w_{\text{CR(2)}}=0.10\), \(w_{\text{CR(3)}}=0.40\), \(w_{\text{CR(4)}}=0.20\), \(w_{\text{CR(5)}}=0.10\) and \begin{table}
\begin{tabular}{c c} \hline
**Algorithm** & **Availability** \\ \hline  & 1. Matlab \\  & 2. Mathematica \\  & 3. SPSS \\  & 4. SAS \\ Hierarchical algorithms & 5. R \\  & 6. Weka \\  & 7. C++/C\# \\  & 8. Python \\  & 9. Matlab 3 rd party code \\ \hline  & 1. Matlab \\  & 2. Mathematica \\ FCM & 3. R \\  & 4. C++/C\# \\  & 5. Python \\  & 6. Matlab 3 rd party code \\ \hline IFCM & In-house software \\ \hline  & 1. Matlab \\  & 2. R \\ SOM & 3. Weka \\  & 4. C++/C\# \\  & 5. Python \\  & 6. Matlab 3 rd party code \\ \hline  & 1. Matlab \\ AVQ & 2. Weka \\  & 3. Python \\ \hline  & 1. Matlab \\  & 2. R \\ Hopfield & 3. C++/C\# \\  & 4. Python \\  & 5. Matlab 3 rd party code \\ \hline FDL & In-house software \\ \hline CLA & Matlab 3 rd party code \\ \hline IRC & In-house software \\ \hline BCEC1 & In-house software \\ \hline BCEC2 & In-house software \\ \hline CSC & In-house software \\ \hline  & 1. R \\ SVC & 2. Python \\  & 2. Matlab 3 rd party code \\  & 3. In-house software \\ \hline  & 1. R \\ ISODATA & 2. Python \\  & 2. Matlab 3 rd party code \\  & 3. In-house software \\ \hline \end{tabular}
\end{table} 
Table 11: _Cont._\(w_{\text{CR}(6)}=0.10\). Let C#i, I = 1,..., 6 the indicator of criterion. Regarding the scores of the solution, the scale presented in Table 12 is taken into account. The decision matrix is shown in Table 13. Criterion#1, Criterion#2 and Criterion#4 need to be \"minimized.\" This means that an algorithm should score as less as possible. The ideal value is 1. This concept is reversed in Criterion#3, Criterion#5 and Criterion#6. In these cases, the ideal value is 9. In order to provide objective scores in Criterion#1, the actual number of parameters are set as scores. In Criterion#2, score \"1\" is matched to no requirements for parameter updating and score \"2\" is matched to 1 parameter. Additionally, scores \"3\" and \"7\" correspond to the actual numbers of parameters. Regarding Criterion#3, the following scores are taken under consideration: No presence in the ranking of Table 8 \(\to\) 1, 1 presence in the ranking of Table 8 \(\to\) 3, more than 1 presence in the ranking of Table 8 \(\to\) 5, 1 presence and 1 higher rank in the ranking of Table 8 \(\to\) 7 and more than 1 presence and more than 1 higher ranks in the ranking of Table 8 \(\to\) 9. In Criterion#4, the actual execution durations in seconds are regarded. It should be noted that in TOPSIS, real numbers can also be considered as scores that do lie outside to the ordinary [1,2,... 9] scale. According to the results presented in Table 9, the FDL and ISODATA algorithm require large time that is considerable larger than the other algorithms. In order to express it in scale terms, they are considered to demand twice the time of the slowest algorithm, i.e., the AVQ. With reference to Criterion#5, the following scores are placed in {Empty clusters, Outlier tracking} pair: {Yes, No} \(\to\) 1, {Yes, Yes} \(\to\) 2, {No, No} \(\to\) 3 and {No, Yes} \(\to\) 4.