## 1 Introduction
### Literature Survey and Contributions
The output layer of the neural network includes the fuzzy membership degrees of the consumers to the clusters. The SOM provides a visual interpretation of the formulated clusters. The input patterns are organized in a 1 or 2-Dimensional (D) map. The patterns that are topologically close, i.e., in the same neighbourhood of coordinates, are characterized by high similarity. Ref. [45] describes the findings after the application of a 2D SOM to Spanish consumers. The time-domain representation is compared with a representation approach that refers to load shape factors, such as the ratios of average to maximum daily load, average to maximum load of daylight hours and others and with frequency-domain representation, i.e., indices that have been obtained after the application of Discrete Fourier Transform. The 3 representation approaches are compared in terms of their influence on clustering composition. In Reference [46] the data includes the load curves of 2 consumers, namely a medium sized industry and a university. Prior to clustering, the SOM is used for data filtering, i.e., removal of abnormal data such as missing data and outliers. In Reference [47], the authors deal with a large number of residential consumers in Ireland. After the clustering, an analysis takes place in order to examine the distribution of home characteristics such as number of rooms, etc. and occupants features such as age, etc. in the clusters. In Reference [48], the authors argue that a macro-categorization should take place to distinguish the consumers to residential, commercial and others. Afterwards, for the macro-category under study, clustering should be applied. In this study, the 2D SOM is utilized and the clustering performance is checked by 4 adequacy measures or clustering validity indicators. In Reference [49], prior to SOM application a macro-categorization to consumer types is held. This information is passed in the SOM as an identification index. For instance, the values \"1\" and \"2\" are assigned to medium industries, \"3\" to warehouses and others. A SOM of different dimensions is used to cluster the electricity market prices. The purpose is to correlate the consumer and the price clusters in order to design real-time pricing schemes for the consumers in the different clusters. In Reference [50], the data include 183 substations. The input vector for SOM is composed by 5 elements. Each element refers to the portion of a specific type of load among the five that the substation serves. The authors test various maps but no validity indicator is used. Contrary to the 1D map, a 2D map results in a large number of centroids. This fact is addressed in the literature by combing a 2D map with another clustering algorithm. A combination of the K-means and the SOM is presented in Reference [51] on a set of low voltage consumers of a Portuguese utility. The K-means is used to perform the clustering of the SOM output units and obtain final clusters. Reference [52] proposes an electricity consumer characterization framework based on knowledge discovery in databases procedure. The concept of the framework is a combination of unsupervised and supervised techniques. The unsupervised learning stage consists of a SOM that reduces the dimensionality of the initial data set and the K-means algorithm which is used to group the weight vectors of SOM and obtain the final clusters centres. Then, the classification process takes place where the generated clusters are assigned to the predefined classes of a Portuguese distribution company. These classes are defined by various indices like the activity type, contracted power, supply voltage level, etc. The framework is tested on a set of low voltage consumers and the recorded data refer to a six-month period. In [53], the combination of SOM and K-means is used to cluster the daily load curves of 2 years of the national system of Algeria. In [54], the authors deal with the extraction of the load profiles of a load data sample of a utility in Finland.