One of the challenges in data analysis is to distinguish between different sources of variability manifested in data. In this work, we consider the case of multiple sensors, measuring the same physical phenomenon, so that the properties of the physical phenomenon are manifested as a common source of variability (which we would like to extract) and each sensor has its own sensor-specific effects. We present a method based on alternating products of diffusion operators, and show that it extracts the common source of variability. Moreover, we show that this method extracts the common source of variability in a multi-sensor experiment as if it were a standard manifold-learning algorithm used to analyze a simple single-sensor experiment in which the common source of variability is the only source of variability.
This is joint work with Ronen Talmon.