Fast independent component analysis algorithm with a simple closed-form solution

2018 ◽  
Vol 161 ◽  
pp. 26-34 ◽  
Author(s):  
P. Spurek ◽  
J. Tabor ◽  
Ł. Struski ◽  
M. Śmieja
Keyword(s):  
Independent Component Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Component Analysis ◽  
Form Solution ◽  
Independent Component ◽  
Analysis Algorithm ◽  
Fast Independent Component Analysis ◽  
Independent Component Analysis Algorithm

An Alternative Perspective on Adaptive Independent Component Analysis Algorithms

1998 ◽  
Vol 10 (8) ◽  
pp. 2103-2114 ◽  
Author(s):  
Mark Girolami
Keyword(s):  
Independent Component Analysis ◽  
Closed Form ◽  
Gaussian Mixture Model ◽  
Score Function ◽  
Component Analysis ◽  
Gaussian Mixture ◽  
Independent Component ◽  
Analysis Algorithm ◽  
Alternative Perspective ◽  
Independent Component Analysis Algorithm

This article develops an extended independent component analysis algorithm for mixtures of arbitrary subgaussian and supergaussian sources. The gaussian mixture model of Pearson is employed in deriving a closed-form generic score function for strictly subgaussian sources. This is combined with the score function for a unimodal supergaussian density to provide a computationally simple yet powerful algorithm for performing independent component analysis on arbitrary mixtures of nongaussian sources.

Research of improved fast independent component analysis algorithm in rectal diagnosis signal preprocessing

2019 ◽  
Vol 42 (11) ◽  
pp. 636-644
Author(s):  
Peng Zan ◽  
Yingjie Xue ◽  
Meihan Chang
Keyword(s):  
Independent Component Analysis ◽  
Signal Sequence ◽  
Component Analysis ◽  
Independent Component ◽  
Artificial Organ ◽  
Anal Sphincters ◽  
Analysis Algorithm ◽  
Fast Independent Component Analysis ◽  
Reconstructed Signal ◽  
Independent Component Analysis Algorithm

With the maturity of artificial organ technology, the use of artificial anal sphincters was proposed to help patients who suffered anal incontinence for various causes reconstruct rectal perception, monitor rectal pressure and diagnose rectal lesion. Aimed at the lack of signal pretreatment in the artificial anal sphincter system, we find a way to solve it, that is, the multi-dimensional reconstruction of the intestinal one-dimensional pressure signal sequence by using phase space reconstruction, and the separation of the reconstructed signal by using the improved fast independent component analysis algorithm. We did some relevant experiments, further extracted the features of the isolated rectal signal, and used back propagation neural network to diagnose the rectal lesions. Experiments show that the method can pretreat the rectal signal, and further analyze the separated signal to diagnose of rectal function. The improved fast independent component analysis algorithm has few iterations, fast convergence, short run time, low requirements on initial weights and good diagnosis. This study lays a foundation for the diagnosis of rectal function by using artificial anal sphincters.

scholarly journals A Fast Independent Component Analysis Algorithm for Geochemical Anomaly Detection and Its Application to Soil Geochemistry Data Processing

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Bin Liu ◽  
Si Guo ◽  
Youhua Wei ◽  
Zedong Zhan
Keyword(s):  
Independent Component Analysis ◽  
Anomaly Detection ◽  
Data Processing ◽  
Component Analysis ◽  
Independent Component ◽  
Geochemical Data ◽  
Frequency Method ◽  
Analysis Algorithm ◽  
Fast Independent Component Analysis ◽  
Independent Component Analysis Algorithm

A fast independent component analysis algorithm (FICAA) is introduced to process geochemical data for anomaly detection. In geochemical data processing, the geological significance of separated geochemical elements must be explicit. This requires that correlation coefficients be used to overcome the limitation of indeterminacy for the sequences of decomposed signals by the FICAA, so that the sequences of the decomposed signals can be correctly reflected. Meanwhile, the problem of indeterminacy in the scaling of the decomposed signals by the FICAA can be solved by the cumulative frequency method (CFM). To classify surface geochemical samples into true anomalies and false anomalies, assays of the 1 : 10 000 soil geochemical data in the area of Dachaidan in the Qinghai province of China are processed. The CFM and FICAA are used to detect the anomalies of Cu and Au. The results of this research demonstrate that the FICAA can demultiplex the mixed signals and achieve results similar to actual mineralization when 85%, 95%, and 98% are chosen as three levels of anomaly delineation. However, the traditional CFM failed to produce realistic results and has no significant use for prospecting indication. It is shown that application of the FICAA to geochemical data processing is effective.

scholarly journals Stochastic Trapping in a Solvable Model of On-Line Independent Component Analysis

2002 ◽  
Vol 14 (2) ◽  
pp. 421-435 ◽  
Author(s):  
Magnus Rattray
Keyword(s):  
Independent Component Analysis ◽  
Fixed Points ◽  
Solvable Model ◽  
Closed Form Solution ◽  
Component Analysis ◽  
Form Solution ◽  
Independent Component ◽  
Initial Learning ◽  
On Line ◽  
Gaussian Sources

Previous analytical studies of on-line independent component analysis (ICA) learning rules have focused on asymptotic stability and efficiency. In practice, the transient stages of learning are often more significant in determining the success of an algorithm. This is demonstrated here with an analysis of a Hebbian ICA algorithm, which can find a small number of nongaussian components given data composed of a linear mixture of independent source signals. An idealized data model is considered in which the sources comprise a number of nongaussian and gaussian sources, and a solution to the dynamics is obtained in the limit where the number of gaussian sources is infinite. Previous stability results are confirmed by expanding around optimal fixed points, where a closed-form solution to the learning dynamics is obtained. However, stochastic effects are shown to stabilize otherwise unstable suboptimal fixed points. Conditions required to destabilize one such fixed point are obtained for the case of a single nongaussian component, indicating that the initial learning rate η required to escape successfully is very low (η = O (N−2) where N is the datadimension), resulting in very slow learning typically requiring O (N3) iterations. Simulations confirm that this picture holds for a finite system.

A Periodic Noise Separation Method Research of well Field Three-Dimensional Drill String Vibration Signal

2013 ◽  
Vol 318 ◽  
pp. 27-32
Author(s):  
Hao Cheng Wu ◽  
Yong Shou Dai ◽  
Wei Feng Sun ◽  
Li Gang Li ◽  
Ya Nan Zhang
Keyword(s):  
Independent Component Analysis ◽  
Vibration Signal ◽  
Component Analysis ◽  
Drill String ◽  
Independent Component ◽  
Analysis Algorithm ◽  
String Vibration ◽  
Periodic Noise ◽  
Well Field ◽  
Independent Component Analysis Algorithm

Periodic noise is an important manifestation of the drill string vibration signal noise. In order to extract the characteristics of the signals which reflect the situation of the tools in drilling, the periodic components which influence the original drill string vibration signal in the well field were researched and the independent component analysis algorithm which is on the basis of negative entropy for periodic vibration noise separation was adopted. At the same time, the effect of algorithm demixing was improved where periodic noise components which existed in three directions of drill string vibration signals were used, combining with the improved particle swarm optimization algorithm to seek the optimal mixed matrix by which the multi-channel mixed-signal of independent component analysis algorithm could be structured. This method in operation was fast. And after separation each signal was of high similarity. Through the experimental simulation, the method was proven effective in the drill string vibration periodic noise signal separation.

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