Non Parametric Independent Component Analysis (NP-ICA)

Introduction

NP-ICA is a novel independent component analysis (ICA) algorithm, which is truly blind to the particular underlying distribution of the mixed signals. Based a non-parametric kernel density estimation technique, the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of the unmixing matrix. Following this approach, the blind signal separation framework can be posed as a non-linear optimization problem, where a closed form expression of the cost function is available, and only the elements of the unmixing matrix appear as unknowns. The resulting algorithm is non-parametric, data-driven, and does not require the definition of a specific model for the density functions. Monte Carlo simulations (see the results here)  involving linear mixtures of various source signals with different statistical characteristics and sample sizes demonstrate that NP-ICA consistently outperforms all state-of-the-art linear ICA methods. The increased computational complexity associated with the kernel density estimator is reduced through the adoption of a Fast Fourier Transform (FFT) based convolution technique.

Related Articles

R. Boscolo, H. Pan and V.P. Roychowdhury (December,2001), “Non-Parametric ICA”. In Proceedings of the Third International Symposium on Independent Component Analysis and Blind Signal Separation (ICA2001), 13--18, San Diego, California. [ps] [pdf]
R. Boscolo, H. Pan, and V.P. Roychowdhury (August,2002). “Beyond Comon's Identifiability Theorem for Independent Component Analysis”. In Proceedings of the 2002 International Conference on Artificial Neural Networks (ICANN 2002), Lecture Notes in Computer Science, Springer-Verlag, 2415:1119--1124, Madrid, Spain. [ps] [pdf]
R. Boscolo and V. P. Roychowdhury (April,2003). “On the Uniqueness of the Minimum of the Information-Theoretic Cost Function for the Separation of Mixtures of Nearly Gaussian Signals”. In Proceedings of the 4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA2003), 137--141, Nara, Japan. [pdf]
R. Boscolo, H. Pan, and V. P. Roychowdhury (2004). “Independent Component Analysis Based on Non-Parametric Density Estimation”. IEEE Transactions on Neural Networks, 15(1): 55-65. [ps] [pdf]


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Last updated on August 09 2004 by Riccardo Boscolo