## 4 Results  
### Algorithms Comparison  
The data set under study correspond to a small industrial consumer and cover a period of a complete year. The dimension of patterns is \(D=24\), i.e., hourly measurements of active load are available. The data are normalized according to (1) and the set \(Y\) is obtained. Criterion#1 and Criterion#2 are indicators of algorithms' complexity. Apart from the number of clusters that are needed to be obtained by an algorithm, other parameters may be needed such as number of iterations, threshold values and others. The fact that an algorithm demands many parameters leads to extra effort from the user to carefully select the parameters. These parameters may be extracted after experimentation or defined directly from the user, based on expertise and previous experience. Tables 2-6 present the parameters that partitional, hierarchical, fuzzy, neural-network based and other algorithms need prior to their execution, respectively. K-means requires 3 parameters, namely the maximum number of iterations, the initial centroids and the threshold of the objective function. The initial centroids are optional, i.e., the conventional edition of the algorithm selects automatically the centroids in a random manner. All partitional algorithms, apart from the number of clusters, require 3 parameters. It should be noted, that while all algorithms require 3 parameters, in many cases the required calibration time differs. This fact will be shown in Criterion#4. For example, while K-means and Modified K-means#1 need the same number of parameters, it is a more demanding effort to extract the optimal coefficients \(\{a,b\}\) compared to the initial centroids. According to Criterion#1 (i.e., minimum number of parameters that need to be specified), all partitional algorithms are similar in terms of complexity. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Parameters for Determination** \\ \hline \multirow{3}{*}{K-means} & 1. Maximum number of iterations \\  & 2. Initial centroids (_optional_) \\  & 3. Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{Modified K-means\#1} & 1. Maximum number of iterations \\  & 2. Optimal coefficients \(\{a,b\}\) \\  & 3. Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{Modified K-means\#2} & 1. Maximum number of iterations \\  & 2. Coefficients \(\{a_{i},b_{i}\}\) \\  & 3. Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{WFA K-means} & 1. Maximum number of iterations \\  & 2. Initial centroids (_optional_) \\  & 3. Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{IWFA K-means} & 1. Maximum number of iterations \\  & 2. Optimal coefficients \(\{a,b\}\) \\  & 3. Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{Hopfield K-means} & 1. Maximum number of iterations for Hopfield ANN \\  & 2. Maximum number of iterations K-means \\  & 3. Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{minCEntropy} & 1. Maximum number of iterations \\  & 2. Parameter \(\sigma\) \\  & 3. Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{K-means\_A} & 1. Maximum number of iterations \\  & 2.Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{K-means\_B} & 1. Maximum number of iterations \\  & 2.Minimum objective function improvement threshold \\ \hline \multirow{3}{*}{K-medoids} & 1. Maximum number of iterations \\  & 2. Initial centroids (_optional_) \\ \cline{1-1}  & 3.Minimum objective function improvement threshold \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the partitional algorithms.