Approximate Diagonalization Of Eigenmatrices Research Articles

Cloud based multivariate signal based heart abnormality detection

This paper discusses the rate of heartbeat monitoring with the help of face tracking, extraction of forehead region and separation of blind source. Separation of blind source is applied for three RGB color channel. Independent Component Analysis (ICA) is a powerful tool for such acquisitions. There are mainly four ICA algorithms and these algorithms have been described in the literature. In this paper contribution of two main common ICA algorithms has been studied. These methods are compared to each other in terms of their ability to obtain independent signal from standard RGB signal of forehead region. These methods are Joint Approximate Diagonalization of Eigen matrices (JADE) and Fixed-point ICA (FastICA). Same RGB data set have been applied to these common ICA algorithms and compared with the results of blood volume pulse (BVP) sensor readings. Both methods provide equally consistent results. However, FastICA has shown better results for heart rate measurement compared to JADE.

Electroencephalogram Signal Eye Blink Rejection Improvement Based on the Hybrid Stone Blind Origin Separation and Particle Swarm Optimization Technique

Electroencephalogram (EEG) extraction has widely used Stone's Blind Source Separation (Stone's BSS) algorithm. However, Stone's BSS algorithm is sensitive to the initial half-life (hlong, hshort) and weight vector W parameters, which affect the convergence of the algorithm. This paper proposes a hybridization of Stone's BSS with Particle Swarm Optimization (PSO) to boost the separation process. An improved Stone's BSS (ISBSS) method is employed to reject eye blinking from the electroencephalogram (EEG) mixture. The electroencephalogram (EEG) mixed-signal is first centralized and whitened; then, it is incorporated into the particle swarm optimization (PSO) iterative algorithm to process the initial (hlong, hshort) and generate the weight vector W parameters randomly. Finally, the generalized eigenvalue decomposition (GEVD) method is applied to extract EEG singles to obtain a clean EEG signal. A clinical EEG database is used to test the improved and other algorithms. The GEVD method estimates the measurement performance of the proposed algorithm using a carrier-to-interference ratio and integral square error and compares the proposed algorithm with the conventional Stone's BSS, fast independent component analysis (FastICA), evolutionary fast independent component analysis (EFICA), and joint approximate diagonalization of eigen matrices (JADE) algorithms to check its effectiveness. The results show that the suggested hybrid method has a better performance and decreasing elapsed time than conventional Stone's BSS and other algorithms.

Effective Hybrid Method for the Detection and Rejection of Electrooculogram (EOG) and Power Line Noise Artefacts From Electroencephalogram (EEG) Mixtures

Electrooculogram (EOG) and power line noise artefact detection and rejection have commonly utilized Stone's blind source separation (Stone's BSS) algorithm. The paper suggests a hybrid method between particle swarm optimization (PSO) and Stone's BSS for the detection and rejection of electrooculogram (EOG) and power line noise in the single-channel without the use of a notch filter. The proposed method contains three major steps: centralizing and whitening of the input EEG signal, incorporating the processing EEG signal into the iterative algorithm of the particle swarm optimization (PSO) to randomly generate the optimal value of (h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">short</sub> , h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">long</sub> ) and weight vector W parameters, and applying Stone's BSS using the generalized eigenvalue decomposition (GEVD) method to eliminate electrooculogram (EOG) and power line noise artefacts to obtain a clean EEG signal. The authors assess the robustness of the suggested method evaluated using real and simulated electroencephalogram (EEG) data sets. The simulated electroencephalogram (EEG) data and electrooculogram (EOG) and line noise (LN) artefacts are produced and mixed randomly in the MATLAB program; two types of real EEG data are taken in 9 and 19 channels. Evaluation results show the proposed algorithms as effective techniques for extracting both the power line noise and electrooculogram (EOG) artefacts from brain mixtures compared to specific BSS algorithms (e.g., Stone's BSS, evolutionary fast independent component analysis (EFICA), fast independent component analysis (FastICA), and joint approximate diagonalization of Eigen matrices (JADE)) while preserving the clinical features of the reconstructed EEG signal.

Fault Diagnosis of Bearings Based on KJADE and VNWOA-LSSVM Algorithm

In order to accurately diagnose the faulty parts of the rolling bearing under different operating conditions, the KJADE (Kernel Function Joint Approximate Diagonalization of Eigenmatrices) algorithm is proposed to reduce the dimensionality of the high-dimensional feature data. Then, the VNWOA (Von Neumann Topology Whale Optimization Algorithm) is used to optimize the LSSVM (Least Squares Support Vector Machine) method to diagnose the fault type of the rolling bearing. The VNWOA algorithm is used to optimize the regularization parameters and kernel parameters of LSSVM. The low-dimensional nonlinear features contained in the multidomain feature set are extracted by KJADE and compared with the results of PCA, LDA, KPCA, and JADE methods. Finally, VNWOA-LSSVM is used to identify bearing faults and compare them with LSSVM, GA-LSSVM, PSO-LSSVM, and WOA-LSSVM. The results show that the recognition rate of fault diagnosis is up to 98.67% by using VNWOA-LSSVM. The method based on KJADE and VNWOA-LSSVM can diagnose and identify fault signals more effectively and has higher classification accuracy.

Decoupling of Multiple Concurrent Faults for Diagnosing Coal Cutter Gearboxes: An Extensive Experimental Investigation With Multichannel Sensor Measurements

Abstract Due to harsh operating environments in underground coal seams, the key components (e.g., gear pairs and bearings) in the power transmission systems of coal cutters suffer from extreme wear and functional damages. To guarantee the safe and reliable operation of the coal cutters, it is important to monitor the condition of their transmission systems and detect possible faults in a timely manner. A challenging task here is to diagnose multiple concurrent faults. A literature review indicates that the current interests lie on the decoupling of multiple co-existing faults and that the very limited work has been done to deal with the dependence/correlation between the fault signals. To address this issue, this work extends our previous work on gear crack detection using the bounded component analysis (BCA) and proposes an improved BCA-based approach for decoupling hybrid faults with high dependence/correlation in coal cutter transmission systems. The proposed approach incorporates the Vold–Kalman order tracking and spectral kurtosis into an improved BCA framework (OTBCA-SK). Owing to the uniform sampling of order tracking, the influence of background noise and rotational speed variation on vibration signals can be effectively reduced. Since BCA is capable of handling vibration sources that are statistically dependent, OTBCA-SK can decouple both independent and dependent source signals. As a result, the vibration sources excited by hybrid faults, although maybe dependent/correlated, can be fully decoupled into single-fault vibration source signals. Three specially designed case studies were used to evaluate the effectiveness of the proposed OTBCA-SK approach in decoupling hybrid gear faults. The analysis results demonstrate better performance of hybrid fault decoupling using OTBCA-SK than that of three representative techniques, i.e., Erdogan's BCA (E-BCA), joint approximate diagonalization of eigen matrices (JADE) and fast independent component analysis (FastICA). These case studies also suggest that the proposed OTBCA-SK approach can retain the physical meaning of the original vibration and is hence suitable for hybrid fault diagnosis in practical applications.

Blind Equalization Based on JADE in PDM-CO-OFDM

Optical orthogonal frequency division multiplexing (OOFDM) significantly reduces frequency overhead in data transmission. Channel equalization (CE) is an approach used to estimate the channel state, and generally with inserting periodic training symbols (TS) to assist channel estimation. By study the technique of independent component analysis, a blind CE method based on joint approximate diagonalization of eigen-matrices with only one-tap in each subcarrier and without TS for polarization division multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) is proposed. This method has a faster convergence speed than the conventional CE technique in PDM-CO-OFDM. For the free of TS, it also enhances the spectral efficiency of the systems. The given approach may offer an efficient technique in the fields such as data transmission in high speed and burst communication, as well as OFDM system. Simulation results indicate that our method is effective for blind CE in OOFDM.

Remaining Useful Life Prediction of Rolling Bearings Using PSR, JADE, and Extreme Learning Machine

Rolling bearings play a pivotal role in rotating machinery. The degradation assessment and remaining useful life (RUL) prediction of bearings are critical to condition-based maintenance. However, sensitive feature extraction still remains a formidable challenge. In this paper, a novel feature extraction method is introduced to obtain the sensitive features through phase space reconstitution (PSR) and joint with approximate diagonalization of Eigen-matrices (JADE). Firstly, the original features are extracted from bearing vibration signals in time and frequency domain. Secondly, the PSR is applied to embed the original features into high dimensional phase space. The between-class and within-class scatter (SS) are calculated to evaluate the feature sensitivity through the phase point distribution of different degradation stages and then different weights are assigned to the corresponding features based on the calculatedSS. Thirdly, the JADE is employed to fuse the weighted features to obtain the advanced features which can better reflect the bearing degradation process. Finally, the advanced features are input into the extreme learning machine (ELM) to train the RUL prediction model. A set of experimental case studies are carried out to verify the effectiveness of the proposed method. The results show that the extracted advanced features can better reflect the degradation process compared to traditional features and could effectively predict the RUL of bearing.

Residual life prediction for ball bearings based on joint approximate diagonalization of eigen matrices and extreme learning machine

Data-driven approaches have been proved effective for remaining useful life estimation of key components (bearings for example) in rotating machinery. In such approaches, it is important to determine an appropriate degradation indicator from the collected run-to-failure life cycle data. In this paper, a new degradation indicator is introduced based on the joint approximate diagonalization of eigen matrices algorithm. First, a matrix consisting of time domain, frequency domain, and time–frequency domain features extracted from the collected data instances is created. Then a two-layer joint approximate diagonalization of eigen matrices is introduced to transform the matrix to the advanced features (a vector) that represents the behavior of the bearing’s degradation. As an independent component analysis method, the designed two-layer joint approximate diagonalization of eigen matrices is able to eliminate the redundancy of the directly extracted features. Further, the obtained vector is input into an extreme learning machine to train a remaining useful life prediction model. Finally, a set of experimental cases are utilized to verify the presented method. Results show that the two-layer joint approximate diagonalization of eigen matrices is capable of exploring features that reflects the trend of bearing’s degradation state much better. And due to the easy parameter configuration and fast learning speed, the extreme learning machine is capable of training a model that can effectively predict the remaining useful life of the bearings.

Comparison of JADE and canonical correlation analysis for ECG de-noising.

This paper explores differences between two methods for blind source separation within frame of ECG de-noising. First method is joint approximate diagonalization of eigenmatrices, which is based on estimation of fourth order cross-cummulant tensor and its diagonalization. Second one is the statistical method known as canonical correlation analysis, which is based on estimation of correlation matrices between two multidimensional variables. Both methods were used within method, which combines the blind source separation algorithm with decision tree. The evaluation was made on large database of 382 long-term ECG signals and the results were examined. Biggest difference was found in results of 50 Hz power line interference where the CCA algorithm completely failed. Thus main power of CCA lies in estimation of unstructured noise within ECG. JADE algorithm has larger computational complexity thus the CCA perfomed faster when estimating the components.

EYEBLINK ARTEFACT REMOVAL FROM EEG USING INDEPENDENT COMPONENT ANALYSIS

The electrical activity of the human brain is recorded using Electroencephalogram (EEG). Most Often, an EEG signal is contaminated with some unwanted signals called artefact. Artefacts are due to eyeblink (EB), eyeball movement, sweat, power line and muscle. It is very essential to remove such artifact from an EEG signal without losing integrity. In this project, detection and removal of eyeblink artefact has been carried out. Linear feature has been taken to detect an EB artefact in an EEG signal and it’s been validated with Spectrogram. Using independent component analysis (ICA), EB artifacts are removed. This project uses some of the algorithms like Algorithm for multiple unknown source extraction (AMUSE), Second order blind identification (SOBI), Joint approximate diagonalization of Eigen matrices (JADE) and Second order non stationary source separation (SONS) which performs ICA for removal of EB artifact. Correlation coefficient is calculated between an original signals and reconstructed signals which are obtained using the above four algorithms. It is found that SOBI and JADE algorithm performs better when compared to other two algorithms.

An Introduction to Energy-Based Blind Separating Algorithm for Speech Signals

We introduce the Energy-Based Blind Separating (EBS) algorithm for extremely fast separation of mixed speech signals without loss of quality, which is performed in two stages: iterative-form separation and closed-form separation. This algorithm significantly improves the separation speed simply due to incorporating only some specific frequency bins into computations. Simulation results show that, on average, the proposed algorithm is 43 times faster than the independent component analysis (ICA) for speech signals, while preserving the separation quality. Also, it outperforms the fast independent component analysis (FastICA), the joint approximate diagonalization of eigenmatrices (JADE), and the second-order blind identification (SOBI) algorithm in terms of separation quality.

On the blind channel identifiability of multiple-input multiple-output space-time block code systems using Joint Approximate Diagonalization of Eigenmatrices

Channel identifiability for multiple-input multiple-output space-time block code MIMO-STBC systems using Joint Approximate Diagonalization of Eigenmatrices JADE is studied in this paper. Compared with the previous blind MIMO-STBC channel estimation methods in literature, the method proposed in this paper is more suitable for non-cooperative scenario because it needs less prior information and can be applied to a general class of STBCs. The main contribution of the paper consists in the theoretical proof that, although the sources transmitted by different antennas of MIMO-STBC systems are not independent, they can be retrieved from the received data by directly using JADE in most cases. The conclusion is also demonstrated by a simulation. This shows that the classical JADE algorithm can be applied to a wider range of situations rather than strictly independent sources. Copyright © 2013 John Wiley & Sons, Ltd.

Feature Extraction of Turing Tool Wear Based on J-EEMD

In the monitoring of cutting tool state, a large number of redundant information is contained in the sensor signal. Therefore, it is obviously not conducive to pattern recognition, and difficult to classify the tool wear state correctly from the available sensors. The test platform that had real-time information collection of the vibration and acoustic emission signals in turning was built. Observed signals were adaptively processed using the method of ensemble empirical mode decomposition introduced joint approximate diagonalization of eigenmatrices (J-EEMD). This method is based on the characteristics of the signal itself decomposed into several intrinsic mode functions (IMF), and then transforms the energy ratio between the IMF. The white noise of each IMF component has been eliminated by introducing JADE algorithm during the signal decomposition. Compared with the EEMD algorithm, the decomposition efficiency is significantly improved. The experiments showed that the method could identify the different states of tool wear, if applied to feature extraction of vibration and acoustic emission signal in the cutting process. DOI: http://dx.doi.org/10.11591/telkomnika.v11i10.3423

Hyperspectral Blind Unmixing and Multiple Target Detection Using Linear Mixture Model

In this paper a blind source separation technique Joint Approximate Diagonalization of Eigen-matrices (JADE) is investigated to unmixing and multiple target detection for hyperspectral imagery data. Our targeted minerals are Alunite, Buddingtonite, Calcite and Kaolinite in ‘Cuprite’ scene data that has been widely used for research experiments in hyperspectral imagery. A comparative study is conducted to show the effectiveness of the JADE with Vertex Component Analysis. The results are evaluated with both full and reduced bands.

On the Performance Analysis of the ICA Algorithms with Maternal and Fetal ECG signals Inputs and Contaminated Noises

This paper evaluates the performance of some major Independent Component Analysis (ICA) algorithms like Cardoso’s Joint Approximate Diagonalization of Eigen matrices (JADE), Comon’s algorithm and Optimized Generalized Weighted Estimator (OGWE) ICA algorithm in a biomedical blind source separation problem. Independent signals representing Fetal ECG (FECG) and Maternal ECG (MECG) are generated and then mixed linearly in the presence of white or pink noise to simulate a recording of electrocardiogram. While ICA has been used to extract FECG, very little literature is available on its performance in clinical environment. So there is a need to evaluate performance of these algorithms in Biomedical. To quantify the performance of ICA algorithms, two scenarios, i.e., (a) different amplitude ratios of simulated maternal and fetal ECG signals, (b) different values of additive white Gaussian noise or pink noise, were investigated. Higher order and second order performances were measured by performance index and signal-to-error ratio respectively. The selected ICA algorithms separate the white and pink noises equally well. This paper reports on the performance of the ICA algorithms.

Theoretical studies and efficient algorithm of semi-blind ICI equalization for OFDM

The intercarrier interference (ICI) due to the Doppler frequency shift, sampling clock offset, time-varying multipath fading and local oscillator frequency offset becomes the major difficulty for the data transmission via the wireless orthogonal frequency division multiplexing (OFDM) systems. The existing ICI mitigation schemes involve the frequency-domain channel estimation/equalization or the additional coding and therefore require the pilot symbols which reduce the throughput. The frequency-domain channel estimation/equalization relies on the huge matrix inversion with high computational complexity especially for the OFDM technologies possessing many subcarriers such as digital video broadcasting (DVB) systems and wireless metropolitan-area networks (WMAN). In our previous work, we proposed a semi-blind ICI equalization scheme using the joint multiple matrix diagonalization (JMMD) algorithm and empirically showed that the proposed method significantly improved the symbol error rates for QPSK- and 16QAM-OFDM systems. In this paper, we discuss the sufficient condition for the theoretical ICI equalizability and also propose an alternative semi-blind ICI equalization method based on the joint approximate diagonalization of eigen-matrices (JADE) algorithm, which is much more computationally efficient than our previous method.

Detection of Indeterminacies in Corrected ECG Signals Using Parameterized Multidimensional Independent Component Analysis

Independent component analysis (ICA) is a new technique suitable for separating independent components from electrocardiogram (ECG) complex signals. The basic idea of using multidimensional independent component analysis (MICA) is to find stable higher dimensional source signal subspaces and to decompose each rotation into elementary rotations within all two‐dimensional planes spanned by the coordinate axes useful for diagnostic information of heart. In this paper, ability of ICA for parameterization of ECG signals was felt to reduce the amount of redundant ECG data. This work aims at finding an independent subspace analysis (ISA) model for ECG analysis that allows applicability to any random vectors available in an ECG data set. For the common standards for electrocardiography (CSE) based ECG data sets, joint approximate diagonalization of eigen matrices (Jade) algorithm is used to find smaller subspaces. The extracted independent components are further cleaned by statistical measures. In this study, it is also observed that the value of kurtosis coefficients for the independent components, which represents the noise component, can be further reduced using parameterized multidimensional ICA (PMICA) technique. The indeterminacies if available in the ECG data are to be analysed also using modified version of Jade algorithm to PMICA and parameterized standard ICA (PsICA) for comparative studies. The indeterminacies if available in the ECG data are reduced in PMICA better in comparison to the analysis done using PsICA. The simulation results obtained indicate that ICA definitely improves signal–noise ratio (SNR) like the other higher order digital filtering methods like Kalman, Butterworth etc. with minimum reconstruction errors. Here, it is also confirmed that re‐parameterization of the standard ICA model results into a ‘component model’ using MICA technique, which is geometric in spirit and free of indeterminacies existing in sICA model.

A least squares approach to blind beamforming

We present a least squares approach to blind beamforming. Two estimation criteria are derived. One turns out to coincide with the Comon (1990, 1994) criterion, whereas the other is a computationally simpler criterion similar in nature to the joint approximate diagonalization of eigenmatrices (JADE) criterion.