In recent years, the intrinsic low rank structure of some datasets has been extensively exploited to reduce dimensionality, remove noise and complete the missing entries. As a well-known technique for dimensionality reduction and data compression, Generalized Low Rank Approximations of Matrices (GLRAM) claims its superiority on computation time and compression ratio over the SVD. However, GLRAM is very sensitive to sparse large noise or outliers and its robust version does not have been explored or solved yet. To address this problem, this paper proposes a robust method for GLRAM, named Robust GLRAM (RGLRAM). We first formulate RGLRAM as an l₁-norm optimization problem which minimizes the l₁-norm of the approximation errors. Secondly, we apply the technique of Augmented Lagrange Multipliers (ALM) to solve this l₁-norm minimization problem and derive a corresponding iterative scheme. Then the weak convergence of the proposed algorithm is discussed under mild conditions. Next, we investigate a special case of RGLRAM and extend RGLRAM to a general tensor case. Finally, the extensive experiments on synthetic data show that it is possible for RGLRAM to exactly recover both the low rank and the sparse components while it may be difficult for previous state-of-the-art algorithms. We also discuss three issues on RGLRAM: the sensitivity to initialization, the generalization ability and the relationship between the running time and the size/number of matrices. Moreover, the experimental results on images of faces with large corruptions illustrate that RGLRAM obtains the best denoising and compression performance than other methods.

Climate classification aims to divide a given region into distinct groups on the basis of meteorological variables, and it has important applications in fields such as agriculture and buildings. In this paper, we propose a novel spectral clustering–based method to partition 661 meteorological stations in China into several zones. First, the correlations are analyzed among five meteorological variables: daily average temperature, average relative humidity, sunshine hours, diurnal temperature range, and atmospheric pressure. The resulting weak linear correlation supports the classification under multiple views. Next, a similarity matrix/graph is constructed by combining the advantages of k-nearest-neighbor and sparse subspace representation. The blocking effect of the similarity matrix confirms the rationality of the classification. Then, we consider respectively the climate classification under a single view and multiple views. For the single view, atmospheric pressure has the highest imbalance degree, and sunshine hours and diurnal temperature range have the strongest classification consistency. The consistency rates are improved evidently in a multiple-view situation. Afterward, we propose a determining method for the number of clusters and make a sensitivity analysis on various parameters. Finally, we provide a further statistical analysis on the classification results and compare the consistency with another climate dataset. All experimental results show that the proposed classification method is feasible and effective in the climate zoning of China.

Forecasting the output power of solar PV systems is required for the good operation of the power grid and the optimal management of energy fluxes occurring in the solar system. Before forecasting the solar system’s output, it is essential to focus on the prediction of solar irradiance. In this paper, the solar radiation data collected for two years in a certain place in Jiangsu in China are investigated. The objective of this paper is to improve the ability of short-term solar radiation prediction. Firstly, missing data are recovered through the means of matrix completion. Then the completed data are denoised via robust principal component analysis. To reduce the influence of weather types on solar radiation, spectral clustering is adopted by fusing sparse subspace representation and k-nearest-neighbor to partition the data into three clusters. Next, for each cluster, four neural networks are established to predict the short-term solar radiation. The experimental results show that the proposed method can enhance the solar radiation accuracy.