Kernel Regression for Graph Signal Prediction in Presence of Sparse Noise
This work addresses signal prediction in graph-based applications like sensor networks, but it is incremental as it builds on existing kernel regression and sparse noise handling techniques.
The paper tackles the problem of predicting graph signals corrupted by sparse noise, such as missing samples or large perturbations, using kernel regression with a convex cost function combining ℓ₁ and ℓ₂ norms, and demonstrates its efficacy on real-world temperature data, particularly for limited training datasets.
In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The presence of sparse noise is handled using appropriate use of $\ell_1$-norm along-with use of $\ell_2$-norm in a convex cost function. For optimization of the cost function, we propose an iteratively reweighted least-squares (IRLS) approach that is suitable for kernel substitution or kernel trick due to availability of a closed form solution. Simulations using real-world temperature data show efficacy of our proposed method, mainly for limited-size training datasets.