Natural gradient algorithm for blind separation of overdetermined mixture with additive noise

1999 ◽  
Vol 6 (11) ◽  
pp. 293-295 ◽  
Author(s):  
L.-Q. Zhang ◽  
A. Cichocki ◽  
S. Amari
Keyword(s):  
Additive Noise ◽  
Gradient Algorithm ◽  
Natural Gradient ◽  
Blind Separation

A Generalized Contrast Function and Stability Analysis for Overdetermined Blind Separation of Instantaneous Mixtures

2006 ◽  
Vol 18 (3) ◽  
pp. 709-728 ◽  
Author(s):  
Xiao-Long Zhu ◽  
Xian-Da Zhang ◽  
Ji-Min Ye
Keyword(s):  
Stability Analysis ◽  
Learning Algorithm ◽  
Gradient Algorithm ◽  
Natural Gradient ◽  
Blind Separation ◽  
Complete Case ◽  
Contrast Function ◽  
Mixing Matrix ◽  
Gradient Learning ◽  
Generalized Orthogonal

In this letter, the problem of blind separation of n independent sources from their m linear instantaneous mixtures is considered. First, a generalized contrast function is defined as a valuable extension of the existing classical and nonsymmetrical contrast functions. It is applicable to the overdetermined blind separation (m > n) with an unknown number of sources, because not only independent components but also redundant ones are allowed in the outputs of a separation system. Second, a natural gradient learning algorithm developed primarily for the complete case (m = n) is shown to work as well with an n × m or m × m separating matrix, for each optimizes a certain mutual information contrast function. Finally, we present stability analysis for a newly proposed generalized orthogonal natural gradient algorithm (which can perform the overdetermined blind separation when n is unknown), obtaining an expectable result that its local stability conditions are slightly stricter than those of the conventional natural gradient algorithm using an invertible mixing matrix (m = n).

Adaptive Blind Separation with an Unknown Number of Sources

2004 ◽  
Vol 16 (8) ◽  
pp. 1641-1660 ◽  
Author(s):  
Ji-Min Ye ◽  
Xiao-Long Zhu ◽  
Xian-Da Zhang
Keyword(s):  
Mutual Information ◽  
Full Column Rank ◽  
Gradient Algorithm ◽  
Local Minima ◽  
Natural Gradient ◽  
Blind Separation ◽  
Unknown Number ◽  
Mixing Matrix ◽  
Source Signals ◽  
Source Number

The blind source separation (BSS) problem with an unknown number of sources is an important practical issue that is usually skipped by assuming that the source number n is known and equal to the number m of sensors. This letter studies the general BSS problem satisfying m ≥ n. First, it is shown that the mutual information of outputs of the separation network is a cost function for BSS, provided that the mixing matrix is of full column rank and the m×m separating matrix is nonsingular. The mutual information reaches its local minima at the separation points, where the m outputs consist of n desired source signals and m−n redundant signals. Second, it is proved that the natural gradient algorithm proposed primarily for complete BSS (m n) can be generalized to deal with the overdetermined BSS problem (m>n), but it would diverge inevitably due to lack of a stationary point. To overcome this shortcoming, we present a modified algorithm, which can perform BSS steadily and provide the desired source signals at specified channels if some matrix is designed properly. Finally, the validity of the proposed algorithm is confirmed by computer simulations on artificially synthesized data.

A new adaptive variable step size natural gradient BSS algorithm

2021 ◽  
pp. 1-12
Author(s):  
Junqing Ji ◽  
Xiaojia Kong ◽  
Yajing Zhang ◽  
Tongle Xu ◽  
Jing Zhang
Keyword(s):  
Signal To Noise Ratio ◽  
Wavelet Coefficient ◽  
Gradient Algorithm ◽  
Variable Step Size ◽  
Natural Gradient ◽  
Threshold Method ◽  
Step Size ◽  
Morphological Component Analysis ◽  
Variable Step ◽  
Separation Degree

The traditional blind source separation (BSS) algorithm is mainly used to deal with signal separation under the noiseless model, but it does not apply to data with the low signal to noise ratio (SNR). To solve the problem, an adaptive variable step size natural gradient BSS algorithm based on an improved wavelet threshold is proposed in this paper. Firstly, an improved wavelet threshold method is used to reduce the noise of the signal. Secondly, the wavelet coefficient layer with obvious periodicity is denoised using a morphological component analysis (MCA) algorithm, and the processed wavelet coefficients are recombined to obtain the ideal model. Thirdly, the recombined signal is pre-whitened, and a new separation matrix update formula of natural gradient algorithm is constructed by defining a new separation degree estimation function. Finally, the adaptive variable step size natural gradient blind source algorithm is used to separate the noise reduction signal. The results show that the algorithm can not only adaptively adjust the step size according to different signals, but also improve the convergence speed, stability and separation accuracy.

Deformed exponentials and portfolio selection

2018 ◽  
Vol 29 (03) ◽  
pp. 1850029 ◽  
Author(s):  
Ana Flávia P. Rodrigues ◽  
Igor M. Guerreiro ◽  
Charles Casimiro Cavalcante
Keyword(s):  
Convergence Rate ◽  
Portfolio Selection ◽  
Heavy Tails ◽  
Time Instant ◽  
Gradient Algorithm ◽  
Natural Gradient ◽  
Economic Crises ◽  
Good Convergence ◽  
Markowitz Portfolio ◽  
Mean Variance

In this paper, we present a method for portfolio selection based on the consideration on deformed exponentials in order to generalize the methods based on the gaussianity of the returns in portfolio, such as the Markowitz model. The proposed method generalizes the idea of optimizing mean-variance and mean-divergence models and allows a more accurate behavior for situations where heavy-tails distributions are necessary to describe the returns in a given time instant, such as those observed in economic crises. Numerical results show the proposed method outperforms the Markowitz portfolio for the cumulated returns with a good convergence rate of the weights for the assets which are searched by means of a natural gradient algorithm.

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