Adaptive Lateral Inhibition for Non-negative Ica

We consider the problem of decomposing an observed input matrix (or vector sequence) into the product of a mixing matrix with a component matrix , i.e. , where (a) the elements of the mixing matrix and the component matrix are non-negative, and (b) the underlying components are considered to be observations from an independent source. This is therefore a problem of non-negative independent component analysis. Under certain reasonable conditions, it appears to be sufficient simply to ensure that the output matrix has diagonal covariance (in addition to the non-negativity constraints) to find the independent basis. Neither higher-order statistics nor temporal correlations are required. The solution is implemented as a neural network with error-correcting forward/backward weights and linear anti-Hebbian lateral inhibition, and is demonstrated on small artificial data sets including a linear version of the Bars problem.