2.5 Combination of k-means and NAR

K-means algorithm is a partition-based data clustering approach, which iteratively relocates data points among clusters for clustering optimization [10]. Nonlinear autoregressive (NAR) forecasting is based on the nonlinear relation between the past outputs and the predicted outputs, which and can be defined by a high-order diversity measure [11].

Benmouiza [12] proposes a hybrid of k-means clustering and NAR neural networks for short-term solar radiation forecasting. In this method, k-means algorithm is applied to extract useful information from the input data. By clustering the data, k-means recognizes patterns of the input space, which provides better training for the neural network and improves the forecasting results. The proposed hybrid method first uses the mutual information (MI) approach to identify the suitable time delay and reconstitutes the phase space of solar radiation time series. The false nearest neighbors (FNN) algorithm is then used to determine the minimum embedding dimension for reconstructing the nonlinear dynamics from a time series. The next phase involves the k-means clustering to cluster the input patterns into k groups with similar characteristics. The silhouette method is applied to select the most suitable number of clusters. A NAR neural network is then trained for each cluster as a sub-predictor for the corresponding subset of the input pattern. Finally, another NAR network is applied as a global predictor for the solar radiation time-series data. Taking advantage of both k-means and NAR, the proposed forecasting method provides satisfactory results.
