A combination of supervised dimensionality reduction and learning methods to forecast solar radiation

Machine learning is routinely used to forecast solar radiation from inputs, which are forecasts of meteorological variables provided by numerical weather prediction (NWP) models, on a spatially distributed grid. However, the number of features resulting from these grids is usually large, especially if several vertical levels are included. Principal Components Analysis (PCA) is one of the simplest and most widely-used methods to extract features and reduce dimensionality in renewable energy forecasting, although this method has some limitations. First, it performs a global linear analysis, and second it is an unsupervised method. Locality Preserving Projection (LPP) overcomes the locality problem, and recently the Linear Optimal Low-Rank (LOL) method has extended Linear Discriminant Analysis (LDA) to be applicable when the number of features is larger than the number of samples. Supervised Nonnegative Matrix Factorization (SNMF) also achieves this goal extending the Nonnegative Matrix Factorization (NMF) framework to integrate the logistic regression loss function. In this article we try to overcome all these issues together by proposing a Supervised Local Maximum Variance Preserving (SLMVP) method, a supervised non-linear method for feature extraction and dimensionality reduction. PCA, LPP, LOL, SNMF and SLMVP have been compared on Global Horizontal Irradiance (GHI) and Direct Normal Irradiance (DNI) radiation data at two different Iberian locations: Seville and Lisbon. Results show that for both kinds of radiation (GHI and DNI) and the two locations, SLMVP produces smaller MAE errors than PCA, LPP, LOL, and SNMF, around 4.92% better for Seville and 3.12% for Lisbon. It has also been shown that, although SLMVP, PCA, and LPP benefit from using a non-linear regression method (Gradient Boosting in this work), this benefit is larger for PCA and LPP because SMLVP is able to perform non-linear transformations of inputs.