## 1 Introduction
### Literature Survey and Contributions
The algorithms that have been proposed in the related literature can be divided to the following categories: (a) Partitional algorithms such as the K-means, K-medoids and others; (b) hierarchical agglomerative algorithms such as the Ward's algorithm and others; (c) fuzzy algorithms, such as the Fuzzy C-Means (FCM) and others (d) neural network based algorithms such as the Self-Organizing Map (SOM), Hopfield neural network and others and (e) algorithms that do not belong to the above classes, such as the Support Vector Clustering (SVC), the modified \"follow-the-leader\" (FDL), Renyi Entropy Clustering and others [11; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78]. The algorithms differ in terms of efficiency, computational complexity, speed and others. The performance of an algorithm is evaluated by a set of clustering validity indicators [17]. In the majority of load profiling problems, the number of clusters is not known, i.e., external expertise information is absent. Therefore, a load profiling problem can be viewed as purely unsupervised machine learning task. This means that an algorithm should be executed for different number of clusters. For each number, the score on the validity indicator is checked. The clustering process is data driven and thus, external norms have to be considered to obtain the optimal number of clusters. A validity indicator is used for this purpose. It should be noted that increasing the number of clusters leads to better clustering. Yet, a high number of clusters is not preferable since it corresponds to increased complexity on the exploitation of clustering results. For example, a large number of consumer clusters may lead to difficulties in tariff design. On the other hand, a small number is also not desirable since it refers to poor clustering, i.e., high clustering errors. The data may refer to public buildings, a mix of residential, commercial and industrial consumers, single consumers, distribution feeders and others. The existing works in the literature can be distinguished into 2 general types: The 1 st type refers to the sole application of a clustering algorithm, while the 2 nd type refers to a comparative analysis of algorithms of different type. The sole application of the K-means algorithm is tested in [30]. The scope is to formulate the seasonal load profiles of 103 residential consumers with data measured per minute and covering a period of a full year. The results of the K-means are combined with homeowner's survey data in order to track correlations between the consumption and other parameters like income, education level and others. In [31], the authors propose via the K-means the concept of dynamic clustering in Spanish residential consumers. This refers to clustering the full load time series (i.e., the total load sequence) instead of using daily curves. In [32], the data under examination are obtained from metering systems of a large utility in South Korea. The K-means is applied separately to the data corresponding to different consumer types such as residential, general high-voltage, industrial high-voltage and others. The optimal number of clusters per category varies. The study also includes a statistical analysis to obtain some key information of the consumption per cluster. In [33], the data set includes a set of households that is charged with time-of-use rates and another set with real-time pricing tariffs. The authors apply the principal component analysis to derive the principal components of household variables like solar heating, number of persons, building age and others. The K-means is applied in the set of principal components to cluster the variables and track households with similar variables. Hierarchical agglomerative clustering is used in [34; 35].