A FastICA Algorithm for Non-negative Independent Component Analysis

The non-negative ICA problem is here defined by the constraint that the sources are non-negative with probability one. This case occurs in many practical applications like spectral or image analysis. It has then been shown by [10] that there is a straightforward way to find the sources: if one whitens the non-zero-mean observations and makes a rotation to positive factors, then these must be the original sources. A fast algorithm, resembling the FastICA method, is suggested here, rigorously analyzed, and experimented with in a simple image separation example.

[1]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .

[2]  Erkki Oja,et al.  Blind Separation of Positive Sources by Globally Convergent Gradient Search , 2004, Neural Computation.

[3]  Ronald C. Henry,et al.  Multivariate receptor models—current practice and future trends , 2002 .

[4]  Kenji Kita,et al.  Dimensionality reduction using non-negative matrix factorization for information retrieval , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

[5]  Andreas Ziehe,et al.  Unmixing Hyperspectral Data , 1999, NIPS.

[6]  Mark D. Plumbley.  Algorithms for nonnegative independent component analysis , 2003, IEEE Trans. Neural Networks.

[7]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[8]  Erkki Oja,et al.  The nonlinear PCA learning rule in independent component analysis , 1997, Neurocomputing.

[9]  E. Oja,et al.  Independent Component Analysis , 2013 .

[10]  Daniel D. Lee,et al.  APPLICATION OF NON-NEGATIVE MATRIX FACTORIZATION TO DYNAMIC POSITRON EMISSION TOMOGRAPHY , 2001 .

[11]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[12]  Erkki Oja,et al.  A "nonnegative PCA" algorithm for independent component analysis , 2004, IEEE Transactions on Neural Networks.

[13]  Mark D. Plumbley.  Conditions for nonnegative independent component analysis , 2002, IEEE Signal Processing Letters.