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This paper proposes efficient batch-based and online strategies for kernel regression over graphs (KRG). The proposed algorithms do not require the input signal to be a graph signal, whereas the target signal is defined over the graph. We first use random Fourier features (RFF) to tackle the complexity issues associated with kernel methods employed in the conventional KRG. For batch-based approaches, we also propose an implementation that reduces complexity by avoiding the inversion of large matrices. Then, we derive two distinct online strategies using RFF, namely, the mini-batch gradient KRG (MGKRG) and the recursive least squares KRG (RLSKRG). The stochasticgradient KRG (SGKRG) is introduced as a particular case of the MGKRG. The MGKRG and the SGKRG are low-complexity algorithms that employ stochastic gradient approximations in the regression-parameter update. The RLSKRG is a recursive implementation of the RFF-based batch KRG. A detailed stability analysis is provided for the proposed online algorithms, including convergence conditions in both mean and mean-squared senses. A discussion on complexity is also provided. Numerical simulations include a synthesized-data experiment and real-data experiments on temperature prediction, brain activity estimation, and image reconstruction. Results show that the RFF-based batch implementation offers competitive performance with a reduced computational burden when compared to the conventional KRG. The MGKRG offers a convenient trade-off between performance and complexity by varying the number of mini-batch samples. The RLSKRG has a faster convergence than the MGKRG and matches the performance of the batch implementation.

This work proposes the use and analyzes the viability of graph Fourier transform (GFT) for light-field compression. GFT is employed in place of discrete-cosine transform (DCT) in a simplified compression system based on high-efficiency video coding (HEVC). The effect on GFT efficiency of different implementations for prediction procedure is analyzed, as well as different methods for computing GFT given residual images. Results indicate that the prediction scheme is sensitive to the type of light field being compressed, and a preliminary method for selecting the best prediction scheme is explored. Moreover, considering multiple residual images when computing GFT, instead of only one central image, improves compression rate and makes compression more uniform across multiple views. GFT achieves reduction of up to 21.92% in number of transform coefficients when compared to DCT-based compression, while providing better or equal mean squared reconstruction error.