Efficient Optimization of the Adaptive ICA Function with Estimating the Number of Non-Gaussian Sources

We propose a new method for efficiently estimating the number of non-Gaussian sources in independent component analysis (ICA). While PCA can find only a few principal components incrementally in the order of significance, ICA has to estimate all the sources after giving the number of them in advance. Then, the appropriate number of sources is determined after the estimation if necessary. Here, we use the adaptive ICA function (AIF), which has been derived by using a simple probabilistic model. It is previously proved that the optimization of AIF with the Gram-Schmidt orthonormalization can find all the sources in descending order of the degree of non-Gaussianity. In this paper, we propose an efficient method for optimizing AIF in the deflation approach by combining fast ICA with the stochastic optimization. In addition, we propose a threshold for determining whether an estimated source is Gaussian or not, which is derived by utilizing the Fisher information of the probabilistic model of AIF. By terminating the optimization when the currently estimated source is Gaussian, the number of sources is estimated efficiently. The experimental results on blind image separation problems verify the usefulness of the proposed method.