Multi-context blind source separation by error-gated Hebbian rule

Modeling the Repetition-Based Recovering of Acoustic and Visual Sources With Dendritic Neurons

In natural auditory environments, acoustic signals originate from the temporal superimposition of different sound sources. The problem of inferring individual sources from ambiguous mixtures of sounds is known as blind source decomposition. Experiments on humans have demonstrated that the auditory system can identify sound sources as repeating patterns embedded in the acoustic input. Source repetition produces temporal regularities that can be detected and used for segregation. Specifically, listeners can identify sounds occurring more than once across different mixtures, but not sounds heard only in a single mixture. However, whether such a behavior can be computationally modeled has not yet been explored. Here, we propose a biologically inspired computational model to perform blind source separation on sequences of mixtures of acoustic stimuli. Our method relies on a somatodendritic neuron model trained with a Hebbian-like learning rule which was originally conceived to detect spatio-temporal patterns recurring in synaptic inputs. We show that the segregation capabilities of our model are reminiscent of the features of human performance in a variety of experimental settings involving synthesized sounds with naturalistic properties. Furthermore, we extend the study to investigate the properties of segregation on task settings not yet explored with human subjects, namely natural sounds and images. Overall, our work suggests that somatodendritic neuron models offer a promising neuro-inspired learning strategy to account for the characteristics of the brain segregation capabilities as well as to make predictions on yet untested experimental settings.

On the Achievability of Blind Source Separation for High-Dimensional Nonlinear Source Mixtures

For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world data that involve nonlinear source mixtures. This work theoretically validates that a cascade of linear PCA and ICA can solve a nonlinear BSS problem accurately-when the sensory inputs are generated from hidden sources via nonlinear mappings with sufficient dimensionality. Our proposed theorem, termed the asymptotic linearization theorem, theoretically guarantees that applying linear PCA to the inputs can reliably extract a subspace spanned by the linear projections from every hidden source as the major components-and thus projecting the inputs onto their major eigenspace can effectively recover a linear transformation of the hidden sources. Then subsequent application of linear ICA can separate all the true independent hidden sources accurately. Zero-element-wise-error nonlinear BSS is asymptotically attained when the source dimensionality is large and the input dimensionality is sufficiently larger than the source dimensionality. Our proposed theorem is validated analytically and numerically. Moreover, the same computation can be performed by using Hebbian-like plasticity rules, implying the biological plausibility of this nonlinear BSS strategy. Our results highlight the utility of linear PCA and ICA for accurately and reliably recovering nonlinearly mixed sources and suggest the importance of employing sensors with sufficient dimensionality to identify true hidden sources of real-world data.