Solving the chaotic source separation problem

The cocktail party problem, which involves trying to pick out a single voice from a room full of overlapping conversations, is a real-world example of source separation. The applications of source separation in scientific research are abundant and wide-ranging. For instance, the neuroscience equivalent of the cocktail party problem is extracting the electrical activity of single neurons in the brain while recording millions of others firing at the same time.

Typically, finding a solution requires several assumptions about the signals and how they overlap. A new article proposes a novel approach to source separation that is general enough to extract sources without knowledge of the underlying equational forms. Instead of assuming the sources are linear, as many previous methods have done, this framework considers them as two autonomously evolving chaotic systems.

The researchers realized the chaotic source separation problem can be thought of as a nonlinear state-observer problem, with a naïve intermediate system playing the role of state-observer. The intermediate system can then take on the difficult responsibility of finding out where the signal of interest comes from.

As an in silico demonstration, they created a computer simulation with a square tank of water as an intermediate system trained by a supervised learning method. The mixed signal was propagated onto the surface of the water through three randomly generated filters. They recorded the water’s reaction to the mixed signal and used the trained function to successfully disentangle the chaotic source trajectories from their mixture.

In terms of future work, the authors wish to study what properties of the intermediate system affect its ability to deal with more complex mixtures, such as those that contain signals from many sources.

Source: “Supervised chaotic source separation by a tank of water,” by Zhixin Lu, Jason Z. Kim, and Danielle S. Bassett, Chaos (2020). The article can be accessed at http://doi.org/10.1063/1.5142462 .