## 1 Introduction
### Literature Survey and Contributions
In [34], the single distance hierarchical algorithm is applied to the daily load curves of a Brazilian hospital. The purpose is to classify the load curves in clusters and afterwards employ a statistical analysis per clusters in order to gather information about the demand patterns and consumption levels per cluster. The scope is to exploit the load profiling outcome to build an energy management system for the hospital. In [35], the authors propose a new load data representation technique different from the time-domain one, using symbolic representation of the demand (i.e., letter characters). While the proposed representation technique seems promising in terms of expressing the daily load curves with a reduced set of features, it does not provide the optimal results in terms of low clustering compared with Sammon mapping, principal component analysis and others. Fuzzy clustering is a generalization of crisp or hard clustering; the patterns (i.e., load curves) are distributed in all clusters with membership degrees that express partial membership. This fact provides flexibility in cluster structure and definition. The FCM algorithm is considered in [36] to cluster a set of load curves of distribution feeders in Malaysia that cover the needs of various domestic, commercial and small size industries consumers. The FCM performance is checked by 2 validity indicators. The same data set and algorithm are examined in [37]. The data refer to aggregated feeder loads and thus, no large differences in the shapes of the load profiles of the different clusters are observed. After the initial execution of the FCM, the algorithm is executed again separately in the daily load curves of each cluster. This leads to the formation of an additional load profile per cluster, a fact that increases the final number of load profiles. In [38], the FCM is checked with 7 clustering validity indicators. The algorithm is applied to the daily load curves that cover a period of a full year and correspond to the consumption of a city located in China. According to the paper's findings, the value of the fuzziness parameter holds an important role in the FCM operation. This parameter is data specific, a fact that raise the need for several trial-and-error executions for its calibration. In [39], the authors investigate the influence of the fuzziness parameter in the FCM clustering outcome via a trial and error approach. According to the results, the increment of the parameter results in lower clustering errors. In [40], the experiments include different execution of the FCM in order to calibrate the fuzziness parameters. The results indicate that while the value increases, the clustering error, as measured by 3 validity indicators, decreases. In [41], the set contains 124 daily load curves of an educational building in Spain. The FCM is used to cluster the data. The emphasis of the paper is placed on similarity metrics on the clustering validation. The authors experiment with different similarity metrics such as Mahalanobis distance, Dynamic Time Wrapping distance and others and conclude that the type of the metric considerably influence the results. Another trend in the related literature is to combine the FCM with supervised machine learning algorithm and namely, artificial neural networks. The general approach is to assign the load profiles generated by the FCM to pre-defined types of consumers or activities. More specifically, in [42] a number of pre-defined consumer types is present. The FCM clusters the data and later a Probabilistic Neural Network (PNN) is used to classify the load profiles drawn by the FCM to the consumer types. In [43], the FCM is again combined with the PNN. The load profiles obtained by the FCM are used to train the PNN. The latter is used to categorize the load profiles in pre-defined activity types. The authors of [44] examine the application of FCM in a set of low voltage consumers. After the extraction of load profiles, a feed-forward neural network is used to assign the consumers to the clusters.