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.

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 a typical ICA algorithm strongly depends on 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 source signals are extracted by data whitening followed by a sequence of plane (Jacobi) rotations. In this article, we develop a novel algorithm, based on the quaternionic factorization of rotation matrices and the Newton-Raphson iterative scheme. Unlike conventional rotational techniques such as the JADE algorithm, our method exploits $4 \times 4$ rotation matrices and uses approximate negentropy as a contrast function. Consequently, the proposed method can be adjusted to a given data distribution (e.g. super-Gaussians) by selecting a suitable non-linear function that approximates the negentropy. Compared to the widely-used, the symmetric FastICA algorithm, the proposed method does not require an orthogonalization step and is more accurate in the presence of multiple Gaussian sources.

Independent component analysis of EEG data for EGI system

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Anna Gajos ◽  
Grzegorz M. Wójcik
Keyword(s):  
Independent Component Analysis ◽  
High Performance ◽  
Linear Representation ◽  
Component Analysis ◽  
Independent Component ◽  
Signal Acquisition ◽  
Main Function ◽  
Eeg Signal ◽  
Non Gaussian ◽  
Ica Algorithm

AbstractComponent analysis is one of the most important methods used for electroencephalographic (EEG) signal decomposition, and the so-called independent component analysis (ICA) is commonly used. The main function of the ICA algorithm is to find a linear representation of non-Gaussian data whose elements are statistically independent or at least as independent as possible. There are many commercial solutions for EEG signal acquisition. Usually, together with the EEG, one gets a dedicated software to handle the signal. However, quite often, the software does not provide researchers with all necessary functions. A high-performance, dense-array EGI-EEG system is distributed with the NetStation software. Although NetStation is a powerful tool, it does not have any implementation of the ICA algorithm. This causes many problems for researchers who want to export raw data from the amplifier and then work on it using some other tools such as EEGLAB for MATLAB, as these data are not fully compatible with the EGI format. We will present the C++ implementation of ICA that can handle filtered data from the EGI with better affordability. Our tool offers visualization of raw signal and ICA algorithm results and will be distributed under Freeware license.

scholarly journals Improved Process Monitoring Scheme Using Multi-Scale Independent Component Analysis

2021 ◽  
Author(s):  
K Ramakrishna Kini ◽  
Muddu Madakyaru
Keyword(s):  
Fault Detection ◽  
Independent Component Analysis ◽  
Component Analysis ◽  
Independent Component ◽  
Noisy Environment ◽  
Process Data ◽  
Multi Scale ◽  
Efficient Information ◽  
Non Gaussian

AbstractThe task of fault detection is crucial in modern chemical industries for improved product quality and process safety. In this regard, data-driven fault detection (FD) strategy based on independent component analysis (ICA) has gained attention since it improves monitoring by capturing non-gaussian features in the process data. However, presence of measurement noise in the process data degrades performance of the FD strategy since the noise masks important information. To enhance the monitoring under noisy environment, wavelet-based multi-scale filtering is integrated with the ICA model to yield a novel multi-scale Independent component analysis (MSICA) FD strategy. One of the challenges in multi-scale ICA modeling is to choose the optimum decomposition depth. A novel scheme based on ICA model parameter estimation at each depth is proposed in this paper to achieve this. The effectiveness of the proposed MSICA-based FD strategy is illustrated through three case studies, namely: dynamic multi-variate process, quadruple tank process and distillation column process. In each case study, the performance of the MSICA FD strategy is assessed for different noise levels by comparing it with the conventional FD strategies. The results indicate that the proposed MSICA FD strategy can enhance performance for higher levels of noise in the data since multi-scale wavelet-based filtering is able to de-noise and capture efficient information from noisy process data.

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.

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