Semi-nonnegative Independent Component Analysis: The (3, 4)-SENICAexp Method

To solve the Independent Component Analysis (ICA) problem under the constraint of nonnegative mixture, we propose an iterative algorithm, called (3,4)-SENICAexp. This method profits from some interesting properties enjoyed by third and fourth order statistics in the presence of mixed independent processes, imposing the nonnegativity of the mixture by means of an exponential change of variable. This process allows us to obtain an unconstrained problem, optimized using an ELSALS-like procedure. Our approach is tested on synthetic magnetic resonance spectroscopic imaging data and compared to two existing ICA methods, namely SOBI and CoM2.

[1]  D. Brie,et al.  Separation of Non-Negative Mixture of Non-Negative Sources Using a Bayesian Approach and MCMC Sampling , 2006, IEEE Transactions on Signal Processing.

[2]  Yin Zhang,et al.  Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems , 2005 .

[3]  P. Comon,et al.  Blind Identification of Overcomplete MixturEs of sources (BIOME) , 2004 .

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

[5]  Lucas C. Parra,et al.  Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain , 2004, IEEE Transactions on Medical Imaging.

[6]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[7]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[8]  Christophe Ladroue,et al.  Independent component analysis for automated decomposition of in vivo magnetic resonance spectra , 2003, Magnetic resonance in medicine.

[9]  R. Plemmons,et al.  Optimality, computation, and interpretation of nonnegative matrix factorizations , 2004 .

[10]  P. Comon,et al.  Tensor decompositions, alternating least squares and other tales , 2009 .

[11]  Christian Jutten,et al.  Detection de grandeurs primitives dans un message composite par une architecture de calcul neuromime , 1985 .

[12]  Pierre Comon,et al.  Handbook of Blind Source Separation: Independent Component Analysis and Applications , 2010 .

[13]  Michael W. Berry,et al.  Algorithms and applications for approximate nonnegative matrix factorization , 2007, Comput. Stat. Data Anal..

[14]  Michael R. Lyu,et al.  Nonnegative independent component analysis based on minimizing mutual information technique , 2006, Neurocomputing.