## 1 Introduction
### Literature Survey and Contributions
First, there is a random initialization of the starting centroids. Each input feature is assigned to cluster based on the distance from the cluster's centroid. Afterwards, the WFA of each cluster is calculated and there is a new distribution of the features based this time on the distance from the WFA. The authors also propose an advanced version of the previous algorithm, namely the Improved Weight Fuzzy Average (IWFA) K-means. The centroids are not chosen randomly but with the initialization method of [27; 28; 67], where the calibrated parameters are chosen based on the optimal values of the adequacy measures. Next, the features are classified and there is a new calculation of the centroids, where they are actually the WFAs of the clusters. The authors demonstrated that the IWFA K-means surpass the performance of other algorithms. The authors of [73] propose a combination of the Hopfield neural network and the K-means. A comparison with other algorithms in taken place and the analysis is applied on a set of medium voltage consumers. Ref. [74] introduces 3 variants of Renyi entropy-based clustering procedures which show comparative performance with the common clustering algorithms in the most adequacy measures. The authors conclude that Renyi entropy-based clustering is suitable especially for large number of clusters. The authors of [75] introduce the Support Vector Clustering (SVC) and present a comparison with algorithms like the K-means, FCM, the modified FDL, the SOM and the hierarchical algorithms. They consider the classical K-means and they demonstrate the better performance of SVC over the other algorithms. In [76] the K-means is a part of a comparative analysis between several algorithms. The K-means shows comparable results with the other algorithms but its speed superiority is concluded. In [77] the K-medoids algorithm is introduced. The comparison includes the K-means and 7 hierarchical agglomerative algorithms. The K-medoids leads to lower errors in all validity indicators. The FCM is similar to K-means in regard to the initialization phase. The initial centroids are selected in a random manner. To overcome this limitation, an improved version of the FCM is proposed in [78] as a part of a demand side management methodology to manage the consumption of high voltage industrial consumers. The algorithms are compared with 4 validity indicators and in all cases, the improved version results in lower errors. The data set refers to the daily load curves of 2 high-voltage industrial consumers. The minCEntropy algorithm is introduced in [79]. This leads to lower errors compared to K-means, FCM, SOM and hierarchical clustering. In [80] the Iterative Refinement Clustering (IRC) is introduced. The authors discuss some limitations of FDL and hierarchical clustering. The authors compare IRC with 2 hierarchical algorithms, FCM, FDL and K-means. According to the results, IRC is ranked in the 3 rd place after average linkage hierarchical algorithm and FDL. In [81], the authors employ K-means, K-medoids and SOM to a set of households. After the extraction of the load profiles, the households' characteristics such as dwelling type, occupant behaviour and others are correlated with the load profiles. SOM results in better clustering compared to the K-means and K-medoids, according to the validity indicator used, namely the DBI. In [82], the K-means and hierarchical clustering are compared using a newly defined distance, namely the k-Sliding distance. Based on the above survey, the main conclusions can be summarized in the following:  
1. A considerable number of different algorithms have been employed in different sets ranging from residential consumers to distribution feeders and aggregate system loads. This fact highlights the importance of efficient clustering. The comparison between algorithms is favoured over the sole application since it leads to more reliable results. 2. In the majority of cases, the conclusions drawn from the comparison are influenced by the type of the validity indicator.