Statistical Independence and Independent Component Analysis

2014 ◽  
Vol 553 ◽  
pp. 564-569
Author(s):  
Yaseen Unnisa ◽  
Danh Tran ◽  
Fu Chun Huang
Keyword(s):  
Independent Component Analysis ◽  
Component Analysis ◽  
Independent Component ◽  
Statistical Testing ◽  
P Value ◽  
Statistical Independence ◽  
Mixing Matrix ◽  
Recent Method ◽  
Novel Method ◽  
Source Signals

Independent Component Analysis (ICA) is a recent method of blind source separation, it has been employed in medical image processing and structural damge detection. It can extract source signals and the unmixing matrix of the system using mixture signals only. This novel method relies on the assumption that source signals are statistically independent. This paper looks at various measures of statistical independence (SI) employed in ICA, the measures proposed by Bakirov and his associates, and the effects of levels of SI of source signals on the output of ICA. Firstly, two statistical independent signals in the form of uniform random signals and a mixing matrix were used to simulate mixture signals to be anlysed byfastICApackage, secondly noise was added onto the signals to investigate effects of levels of SI on the output of ICA in the form of soure signals, the mixing and unmixing matrix. It was found that for p-value given by Bakirov’s SI statistical testing of the null hypothesis H0is a good indication of the SI between two variables and that for p-value larger than 0.05, fastICA performs satisfactorily.

scholarly journals Orthogonal Approach to Independent Component Analysis Using Quaternionic Factorization

2020 ◽  
Author(s):  
Adam Borowicz
Keyword(s):  
Independent Component Analysis ◽  
Additive Noise ◽  
Component Analysis ◽  
Independent Component ◽  
Actual Distribution ◽  
Rotation Matrices ◽  
Fastica Algorithm ◽  
Non Gaussian ◽  
Ica Algorithm ◽  
Source Signals

Abstract Independent component analysis (ICA) is a popular technique for demixing multi-channel data. The performance of typical ICA algorithm strongly depends on many factors such as the presence of additive noise, the actual distribution of source signals, and the estimated number of non-Gaussian components. Often a linear mixing model is assumed and the source signals are extracted by proceeding data whitening followed by a sequence of plane (Jacobi) rotations. In this article, we develop a four-unit, symmetric algorithm, based on the quaternionic factorization of the rotation matrices and the Newton-Raphson iterative scheme. Unlike conventional rotational techniques such as the JADE algorithm, our method exploits 4 x 4 rotation matrices and uses negentropy approximation as a contrast function. Consequently, the proposed method can be adapted to a given data distribution (e.g. super-Gaussians) by selecting the appropriate non-linear function that approximates the negentropy. Compared to the widely used, symmetric FastICA algorithm, the proposed method does not require an orthogonalization step and offers better numerical stability in the presence of multiple Gaussian sources.

Fast Independent Component Analysis (FastICA) in Separating Vocals and Instruments in the Art of Geguntangan

2020 ◽  
Vol 8 (3) ◽  
pp. 219
Author(s):  
Angga Pramana Putra ◽  
I Gede Arta Wibawa
Keyword(s):  
Independent Component Analysis ◽  
Component Analysis ◽  
Independent Component ◽  
Blind Signal Separation ◽  
Sound Sources ◽  
Blind Signal ◽  
Fast Independent Component Analysis ◽  
Fastica Algorithm ◽  
Mixing Matrix ◽  
Sound Separation

Geguntangan is pesantian in religious ceremonies in Bali accompanied by gamelan music. The human sense of hearing tends to have limitations, which causes not all vocals mixed with gamelan to be heard clearly. Therefore we need a system that can be used to separate vocals with gamelan in the geguntangan. Separation of sound sources is categorized as Blind Source Separation (BSS) or also called Blind Signal Separation, which means an unknown source. The algorithm used to handle BSS is the Fast Independent Component Analysis (FastICA) algorithm with a focus on separating the sound signal in a wav-format sound file. FastICA algorithm is used for the sound separation process with the value parameter used is Mean Square Error (MSE). From the simulation results show the results of MSE calculations using the mixing matrix [0.3816, 0.8678], [0.8534, -0.5853] obtained the results for the FastICA method, the MSE value is 3.60 x 10-5 for the vocal and 1.71 x 10-6 for the instrument.

Robust Method via Independent Component Analysis with Additive Noise

2010 ◽  
Vol 113-116 ◽  
pp. 272-275
Author(s):  
Yong Jian Zhao ◽  
Bo Qiang Liu ◽  
Hong Run Wang
Keyword(s):  
Independent Component Analysis ◽  
High Stability ◽  
Additive Noise ◽  
Group Structure ◽  
Processing System ◽  
Component Analysis ◽  
Independent Component ◽  
Signal Processing System ◽  
Mixing Matrix ◽  
Simulation Results

Blind source separation via independent component analysis (ICA) has received increasing attention because of its potential application in signal processing system. The existing ICA methods can not give a consistent estimator of the mixing matrix because of additive noise. Based on interpretation and properties of the vectorial spaces of sources and mixtures, a new ICA method is presented in this paper that may constructively reject noise so as to estimate the mixing matrix consistently. This procedure may capture the underlying source dynamics effectively even if additive noise exists. The simulation results show that this method has high stability and reliability in the process of revealing the undering group structure of extracted ICA components.

Background Extraction by Fast Independent Component Analysis in Video Surveillance

2014 ◽  
Vol 936 ◽  
pp. 2286-2290
Author(s):  
Ding Rui ◽  
Tang Jin ◽  
Wang Wei
Keyword(s):  
Independent Component Analysis ◽  
Video Surveillance ◽  
Component Analysis ◽  
Independent Component ◽  
Background Signal ◽  
Dynamic Background ◽  
Fast Independent Component Analysis ◽  
Background Extraction ◽  
Source Signals ◽  
Background Image

To solve dynamic background extraction in complicated outdoor surveillance, a method of background extraction based on fast independent component analysis (FastICA) is presented. Since foreground regions and background in an image are considered to be independent, and background images in video show a high correlation coefficient, the method can directly recover the background signal without recover other source signals. In this paper, the principle of FastICA are introduced, and the detailed processes of the method and results are given, which show that the method can realize extracting background image .

Bearing fault diagnosis based on kernel independent component analysis and antlion optimization

2021 ◽  
pp. 014233122110384
Author(s):  
Hong Zhong ◽  
Jingxing Liu ◽  
Liangmo Wang ◽  
Yang Ding ◽  
Yahui Qian
Keyword(s):  
Fault Diagnosis ◽  
Independent Component Analysis ◽  
Blind Source Separation ◽  
Component Analysis ◽  
Independent Component ◽  
Bearing Fault ◽  
Bearing Fault Diagnosis ◽  
Kernel Independent Component Analysis ◽  
Antlion Optimization ◽  
Source Signals

Fault diagnosis of gearboxes based on vibration signal processing is challenging, as vibration signals collected by acceleration sensors are typically a nonlinear mixture of unknown signals. Furthermore, the number of source signals is usually larger than that of sensors because of the practical limitation on sensor positions. Hence, the fault characterization is actually a nonlinear underdetermined blind source separation (NUBSS) problem. In this paper, a novel NUBSS algorithm based on kernel independent component analysis (KICA) and antlion optimization (ALO) is proposed to address the technical challenge. The mathematical model demonstrates the nonlinear mixing of source signals in the underdetermined cases. Ensemble empirical mode decomposition is used as a preprocessing tool to decompose the observed signals into a set of intrinsic mode functions that suffers from the problem of redundant components. The correlation coefficient is utilized to eliminate the redundant components. An adaptive threshold singular value decomposition method is proposed to estimate the number of source signals. Then a whitening process is carried out to transform the overdetermined blind source separation (BSS) into determined BSS, which can be solved by the KICA method. However, the reasonable selection of parameters in KICA limits its application to some extent. Therefore, ALO and Fisher’s linear discriminant analysis are adopted to further enhance the accuracy of the KICA method. The separation performance of the proposed method is assessed through simulation. The numerical results show that the proposed method can accurately estimate the number of source signals and attains a higher separation quality in tackling nonlinear mixed signals when compared with the existing methods. Finally, the inner ring fault experiment is conducted to preliminarily validate the practicability of the proposed method in bearing fault diagnosis.

SN Ratio Estimation and Speech Segment Detection of Extracted Signals Through Independent Component Analysis

2010 ◽  
Vol 14 (4) ◽  
pp. 364-374
Author(s):  
Takeshi Koya ◽  
◽  
Nobuo Iwasaki ◽  
Takaaki Ishibashi ◽  
Go Hirano ◽  
...  
Keyword(s):  
Independent Component Analysis ◽  
Real World ◽  
Transfer Functions ◽  
Signal To Noise Ratio ◽  
Component Analysis ◽  
Independent Component ◽  
Snr Estimation ◽  
Speech Segment ◽  
Speech Segments ◽  
Source Signals

In real world environments where acoustic signals are contaminated with various noises, it is difficult to estimate the Signal-to-Noise Ratio (SNR) only from signals observed at microphones; the knowledge of acoustic transfer functions and original source signals is inevitable for SNR estimation. The present paper proposes a method to estimate SNR approximately in the real world environments without the knowledge of transfer functions and source signals: SNR is estimated after application of Independent Component Analysis (ICA) to the signals observed at microphones. Our proposed method also works as a speech segment detector since detection of speech segments are necessarily carried out in the course of SNR estimation. From several experimental results, the proposed method has been confirmed to be valid.

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