New approximations of differential entropy for independent component analysis and projection pursuit
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Neural Computation
Advances in Independent Component Analysis
Advances in Independent Component Analysis
Mean-field approaches to independent component analysis
Neural Computation
Linear and nonlinear ICA based on mutual information: the MISEP method
Signal Processing - Special issue on independent components analysis and beyond
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
Neural Computation
A Variational Method for Learning Sparse and Overcomplete Representations
Neural Computation
Learning Overcomplete Representations
Neural Computation
Source separation in post-nonlinear mixtures
IEEE Transactions on Signal Processing
Blind source separation-semiparametric statistical approach
IEEE Transactions on Signal Processing
MISEP Method for Postnonlinear Blind Source Separation
Neural Computation
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In this letter, we propose a noisy nonlinear version of independent component analysis (ICA). Assuming that the probability density function (p. d. f.) of sources is known, a learning rule is derived based on maximum likelihood estimation (MLE). Our model involves some algorithms of noisy linear ICA (e. g., Bermond & Cardoso, 1999) or noise-free nonlinear ICA (e. g., Lee, Koehler, & Orglmeister, 1997) as special cases. Especially when the nonlinear function is linear, the learning rule derived as a generalized expectation-maximization algorithm has a similar form to the noisy ICA algorithm previously presented by Douglas, Cichocki, and Amari (1998). Moreover, our learning rule becomes identical to the standard noise-free linear ICA algorithm in the noiseless limit, while existing MLE-based noisy ICA algorithms do not rigorously include the noise-free ICA. We trained our noisy nonlinear ICA by using acoustic signals such as speech and music. The model after learning successfully simulates virtual pitch phenomena, and the existence region of virtual pitch is qualitatively similar to that observed in a psychoacoustic experiment. Although a linear transformation hypothesized in the central auditory system can account for the pitch sensation, our model suggests that the linear transformation can be acquired through learning from actual acoustic signals. Since our model includes a cepstrum analysis in a special case, it is expected to provide a useful feature extraction method that has often been given by the cepstrum analysis.