scholarly journals What Is the Relation Between Slow Feature Analysis and Independent Component Analysis?

2006 ◽  
Vol 18 (10) ◽  
pp. 2495-2508 ◽  
Author(s):  
Tobias Blaschke ◽  
Pietro Berkes ◽  
Laurenz Wiskott
Keyword(s):  
Time Delay ◽  
Independent Component Analysis ◽  
Time Delays ◽  
Component Analysis ◽  
Second Order ◽  
Independent Component ◽  
Feature Analysis ◽  
Analytical Comparison ◽  
Slow Feature Analysis

We present an analytical comparison between linear slow feature analysis and second-order independent component analysis, and show that in the case of one time delay, the two approaches are equivalent. We also consider the case of several time delays and discuss two possible extensions of slow feature analysis.

scholarly journals Adaptive Complex-Valued Independent Component Analysis Based on Second-Order Statistics

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yanfei Jia ◽  
Xiaodong Yang
Keyword(s):  
Independent Component Analysis ◽  
Cost Function ◽  
Order Statistics ◽  
Component Analysis ◽  
Second Order ◽  
Independent Component ◽  
Second Order Statistics ◽  
The Cost ◽  
Source Signals ◽  
Complex Valued

This paper proposes a two-stage fast convergence adaptive complex-valued independent component analysis based on second-order statistics of complex-valued source signals. The first stage constructs a cost function by extending the real-valued whiten cost function to a complex-valued domain and optimizes the cost function using a complex-valued gradient. The second stage uses the restriction that the pseudocovariance matrix of the separated signal is a diagonal matrix to construct the cost function and the geodesic method is used to optimize the cost function. Compared with other adaptive complex-valued independent component analysis, the proposed method shows a faster convergence rate and smaller error. Computer simulations were performed on synthesized signals and communications signals. The simulation results demonstrate the validity of the proposed algorithm.

Independent Slow Feature Analysis and Nonlinear Blind Source Separation

2007 ◽  
Vol 19 (4) ◽  
pp. 994-1021 ◽  
Author(s):  
Tobias Blaschke ◽  
Tiziano Zito ◽  
Laurenz Wiskott
Keyword(s):  
Independent Component Analysis ◽  
Blind Source Separation ◽  
Source Separation ◽  
Second Order ◽  
Feature Analysis ◽  
Statistical Independence ◽  
Sufficient Criterion ◽  
Nonlinear Case ◽  
Separation Problem ◽  
Slow Feature Analysis

In the linear case, statistical independence is a sufficient criterion for performing blind source separation. In the nonlinear case, however, it leaves an ambiguity in the solutions that has to be resolved by additional criteria. Here we argue that temporal slowness complements statistical independence well and that a combination of the two leads to unique solutions of the nonlinear blind source separation problem. The algorithm we present is a combination of second-order independent component analysis and slow feature analysis and is referred to as independent slow feature analysis. Its performance is demonstrated on nonlinearly mixed music data. We conclude that slowness is indeed a useful complement to statistical independence but that time-delayed second-order moments are only a weak measure of statistical independence.

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