Diffusion maps for signal processing: A deeper look at manifold-learning techniques based on kernels and graphs

Signal processing methods have significantly changed over the last several decades. Traditional methods were usually based on parametric statistical inference and linear filters. These frameworks have helped to develop efficient algorithms that have often been suitable for implementation on digital signal processing (DSP) systems. Over the years, DSP systems have advanced rapidly, and their computational capabilities have been substantially increased. This development has enabled contemporary signal processing algorithms to incorporate more computations. Consequently, we have recently experienced a growing interaction between signal processing and machine-learning approaches, e.g., Bayesian networks, graphical models, and kernel-based methods, whose computational burden is usually high.