# Evaluation and Comparison of Spatial Clustering for Solar Irradiance Time Series
## 1 Introduction
Reviews papers such as References [18; 19] present states-of-the-art in the last decade that introduces some fundamental concepts of time-series analysis, classification, and clustering methods based on observations, time and frequency, and the similarity between series and dimensionality reduction. Focusing now on the clustering in renewable energy sources, [PERSON] et al. [20] described various AI techniques applied to different renewable energies, particularly photovoltaic ones. They realized a clustering of datasets for analyzing the most suitable location of solar plants according to the study of similar meteorological conditions. [PERSON] [21] compared various methods to categorize clear, cloudy, and partiality cloudy sky days, using a one-year solar-irradiance dataset from Budapest (Hungary). Six methods were compared deterministically and non-deterministically (k-means clustering, Fuzzy c-Means, and Multiple Fuzzy C-Means) with different temporal resolutions. The comparison aimed to reveal the strengths and weaknesses of the applied methods. Unfortunately, the results obtained with the implemented methods are limited, as they are susceptible to the input data, and the categorization is often inconsistent among them. In Reference [22], the authors aimed to predict the global hourly solar radiation of the next day and used clustering. The k-means clustering algorithm was proposed to classify four kinds of days: clear, cloudy, cloudy in the morning, and cloudy in the afternoon. They were combined with regression algorithms (decision trees, support vector machines, and artificial neural networks) to estimate the day-ahead clearness index in Malaga, Spain. [PERSON] et al. [23] proposed a solar irradiance classification of 98 stations with solar irradiance sensors and 562 stations without irradiance data. A k-means and a support-vector-machine genetic algorithm were used to perform this clustering. Models were developed by introducing geographical parameters, including latitude and altitude. [PERSON] et al. [24] sought to predict hourly global irradiance profiles from daily global irradiance records from six sites in the North African Sahara. They started from a prior categorization of the hourly observations by using a k-means clustering algorithm, followed by a nonparametric approximation of the function, using the multilayer perceptron artificial neural network. [PERSON] et al. [25] studied the relationship between the solar resource and the climatology in Uruguay (condition of the phenomenon called Nino or Nina). The input information consisted of global-horizontal-irradiance (GHI) estimations from daily satellite images and regionalization of the meteorological stations based on the geographical position of the station. A Principal Component Analysis (PCA) was used to decrease the dimensionality of the series. The clustering algorithm, based on the changes in the station for different years, was a k-means/ward. [PERSON] et al. [26] applied a k-means clustering to satellite-based daily global horizontal irradiation for spatial-variability analysis and regionalization in different regions of Vietnam. [PERSON] et al. [27] proposed a methodology to characterize and cluster the spatiotemporal daily global horizontal solar-resource variability in the Spanish territory. They used a hierarchical clustering technique to classify the spatial data, and different time windows were subsequently evaluated. The parameters used in this study are averaged (yearly, seasonal, and monthly) values of daily horizontal global irradiances. An unsupervised clustering-based (UC-based) solar forecasting method was developed by [PERSON] et al. [28] for short-term (1-h-ahead) global horizontal irradiance forecasting. The daily GHI time series is clustered by an Optimized Cross-Validated Clustering (OC-CUR) method. [PERSON] et al. [29] proposed a novel short-term (2-h-ahead) solar forecasting approach that uses a clustering (k-medoid clustering method) on the basis of cloud parameters as a preprocessing step.