## 5 Experimental Results  
### Model Implementation  
The solar radiation observation dataset was collected from a certain part of Jiangsu Province in 2018 and 2019. It can be formed into the matrix \(\mathbf{Z}=\left(z_{ij}\right)_{m\times n}\), where \(m=288\) is the total number of recordings per day, and \(n=728\) is the number of days for that selected two years.  
First of all, in view of the incompleteness of these solar radiation data, the matrix completion method is utilized to infer the missing elements. This procedure can further refine and calibrate these data. In 2018, 363 days are considered and there are 92 pieces of missing data in total. There are 365 days in 2019, and 28 pieces of data are missing. Taking 11 January 2018 as an example, there are 279 recordings and 9 missing values, and Figure 9 illustrates the completed data in that day. In this figure, the blue stars represent the observed values and the red filled circles are the recovered values by matrix completion. As we can see, the matrix completion has a good recovery performance in that day. In summary, 104,544 and 105,120 recording values, respectively, are obtained after completion.  
The recovered solar radiation data are further divided into four parts according to the four seasons, and RPCA is employed to denoise the completed data of each season. Figure 10 shows the solar radiation waveforms of 20 non-repeated days before and after denoising for each season, and different colors indicate different days. It can be seen that the solar radiation is zero before 6 a.m. and after 7 p.m. in most cases. It is especially important that the denoised data are convenient for us to grasp the real trend of the variation in solar radiation data, which is conducive to a better prediction of solar radiation.  
Figure 9: Recovered solar radiation data by matrix completion for one day.  
As can be seen from Figures 2 and 3, the differences of solar radiation intensity in the four seasons are particularly striking, and the sub-dataset of each season is disorganized without any seasonal characteristics and periodicity. For the solar radiation of each season, we utilize spectral clustering based on the fusion of k-nearest-neighbor and sparse subspace representation to divide all the days in each season into three clusters from the solar radiation intensity. In Figure 11, we cluster the radiation data of all days in each season  
Figure 10: Solar radiation waveform before and after denoising in four seasons. (**a**) Spring; (**b**) Summer; (**c**) Autumn; (**d**) Winter.  
into Cluster 1, Cluster 2 and Cluster 3 according to the solar radiation intensity from low to high. At the upper right of each subplot in Figure 11, the red asterisks, the blue hollow triangles and the green circles stand for Cluster 1, Cluster 2 and Cluster 3, respectively. Springs in Clusters 1, 2 and 3 have 60, 71 and 49 days, respectively, and summers have 55, 65 and 62 days. In autumn, there are 63, 68 and 51 days in the three clusters respectively, winters last 60, 71 and 49 days, respectively.  
When neural networks are used for predictions, we choose the solar radiation between 7 a.m. and 6 p.m. every day as the effective input data in order to improve the calculation speed and ensure the validity of the data. To enhance the short-term prediction ability of the proposed model, the solar radiation every two consecutive hours is selected as the training sample to predict that of the next moment. For each season, the last five days of each cluster are employed to construct the test set for final evaluation, and the remaining days are harnessed to train the neural networks. Attention should be paid as over-fitting may occur in the training process of the neural network, that is, the training error is small, but the generalization error is large. Therefore, in the experiment, we use the regularization technique for BP, RBF and ELM, and the dropout strategy for LSTM to prevent overfitting.