Multivariate time-frequency analysis

Recent advances in time-frequency theory have led to the development of high resolution time-frequency algorithms, such as the empirical mode decomposition (EMD) and the synchrosqueezing transform (SST). These algorithms provide enhanced localization in representing time varying oscillatory components over conventional linear and quadratic time-frequency algorithms. However, with the emergence of low cost multichannel sensor technology, multivariate extensions of time-frequency algorithms are needed in order to exploit the inter-channel dependencies that may arise for multivariate data. Applications of this framework range from filtering to the analysis of oscillatory components. To this end, this thesis first seeks to introduce a multivariate extension of the synchrosqueezing transform, so as to identify a set of oscillations common to the multivariate data. Furthermore, a new framework for multivariate time-frequency representations is developed using the proposed multivariate extension of the SST. The performance of the proposed algorithms are demonstrated on a wide variety of both simulated and real world data sets, such as in phase synchrony spectrograms and multivariate signal denoising. Finally, multivariate extensions of the EMD have been developed that capture the inter-channel dependencies in multivariate data. This is achieved by processing such data directly in higher dimensional spaces where they reside, and by accounting for the power imbalance across multivariate data channels that are recorded from real world sensors, thereby preserving the multivariate structure of the data. These optimized performance of such data driven algorithms when processing multivariate data with power imbalances and inter-channel correlations, and is demonstrated on the real world examples of Doppler radar processing.Open Acces

Multivariate Signal Denoising Based on Generic Multivariate Detrended Fluctuation Analysis

We propose a generic multivariate extension of detrended fluctuation analysis (DFA) that incorporates interchannel dependencies within input multichannel data to perform its long-range correlation analysis. We next demonstrate the utility of the proposed method within multivariate signal denoising problem. Particularly, our denosing approach first obtains data driven multiscale signal representation via multivariate variational mode decomposition (MVMD) method. Then, proposed multivariate extension of DFA (MDFA) is used to reject the predominantly noisy modes based on their randomness scores. The denoised signal is reconstructed using the remaining multichannel modes albeit after removal of the noise traces using the principal component analysis (PCA). The utility of our denoising method is demonstrated on a wide range of synthetic and real life signals

Performance evaluation of the Hilbert–Huang transform for respiratory sound analysis and its application to continuous adventitious sound characterization

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/The use of the Hilbert–Huang transform in the analysis of biomedical signals has increased during the past few years, but its use for respiratory sound (RS) analysis is still limited. The technique includes two steps: empirical mode decomposition (EMD) and instantaneous frequency (IF) estimation. Although the mode mixing (MM) problem of EMD has been widely discussed, this technique continues to be used in many RS analysis algorithms. In this study, we analyzed the MM effect in RS signals recorded from 30 asthmatic patients, and studied the performance of ensemble EMD (EEMD) and noise-assisted multivariate EMD (NA-MEMD) as means for preventing this effect. We propose quantitative parameters for measuring the size, reduction of MM, and residual noise level of each method. These parameters showed that EEMD is a good solution for MM, thus outperforming NA-MEMD. After testing different IF estimators, we propose Kay¿s method to calculate an EEMD-Kay-based Hilbert spectrum that offers high energy concentrations and high time and high frequency resolutions. We also propose an algorithm for the automatic characterization of continuous adventitious sounds (CAS). The tests performed showed that the proposed EEMD-Kay-based Hilbert spectrum makes it possible to determine CAS more precisely than other conventional time-frequency techniques.Postprint (author's final draft

Spectro-spatial Profile for Gender Identification using Emotional-based EEG Signals

 Identifying gender has become essential specially to support automatic human-computer interface applications and to customize interactions based on affective responses. The electroencephalogram (EEG) has been adopted for recording the neuronal information as waveforms from the scalp. The objective of this study was twofold. First, to identify genders from four different emotional states using spectral relative power biomarkers. Second, to develop Spectro-spatial profiles that afford additional information for gender identification using emotional-based EEGs. The dataset has been collected from ten healthful volunteer students from the University of Vienna while watching short emotional audio-visual clips of angry, happiness, sadness, and neutral emotions. Wavelet (WT) has been used as a denoising technique, the spectral relative power features of delta (), theta (), alpha (), beta () and gamma () were extracted from each recorded EEG channel. In the subsequent steps, analysis of variance (ANOVA) and Pearson’s correlation analysis were performed to characterize the emotional-based EEG biomarkers towards developing the Spectro-spatial profile to identify gender differences. The results show that the spectral set of features may provide and convey reliable biomarkers for identifying Spectro-spatial profiles from four different emotional states. EEG biomarkers and profiles enable more comprehensive insights into various human behavior effects and as an intervention on the brain. The results revealed that almost high relative powers from all emotional states appear in females compared to males. Particularly,  was the most prominent for anger,  and  were widely observed in happiness,  was the most appears in sadness,  and  were the powers that appears widely in neutral. Moreover, in females, neut was correlated with and _ang, _neut was mostly correlated with _ang. Besides, _neut was correlated with _ang, _neut was correlated with _ang, _neut was mostly correlated with _sad. Moreover, in males, _neut showed a very strong correlation with _sadness whereas _neut was correlated with _hap and _neut was correlated with _hap. Therefore, the proposed system using the WT denoising method, spectral relative power markers, and the spectro-spatial profile plays a crucial role in characterizing the emotional-based EEGs towards gender identification. The classification results were 89.46% for SVM and 90% for the KNN. Therefore, the proposed system using the WT denoising method, spectral relative powers features, SVM, and KNN classifiers were crucial in gender identification and characterizing the emotional EEG signals

EEG-based emotion recognition using tunable Q wavelet transform and rotation forest ensemble classifier

Emotion recognition by artificial intelligence (AI) is a challenging task. A wide variety of research has been done, which demonstrated the utility of audio, imagery, and electroencephalography (EEG) data for automatic emotion recognition. This paper presents a new automated emotion recognition framework, which utilizes electroencephalography (EEG) signals. The proposed method is lightweight, and it consists of four major phases, which include: a reprocessing phase, a feature extraction phase, a feature dimension reduction phase, and a classification phase. A discrete wavelet transforms (DWT) based noise reduction method, which is hereby named multi scale principal component analysis (MSPCA), is utilized during the pre-processing phase, where a Symlets-4 filter is utilized for noise reduction. A tunable Q wavelet transform (TQWT) is utilized as feature extractor. Six different statistical methods are used for dimension reduction. In the classification step, rotation forest ensemble (RFE) classifier is utilized with different classification algorithms such as k-Nearest Neighbor (k-NN), support vector machine (SVM), artificial neural network (ANN), random forest (RF), and four different types of the decision tree (DT) algorithms. The proposed framework achieves over 93 % classification accuracy with RFE + SVM. The results clearly show that the proposed TQWT and RFE based emotion recognition framework is an effective approach for emotion recognition using EEG signals.</p

Inference of synchrosqueezing transform -- toward a unified statistical analysis of nonlinear-type time-frequency analysis

We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and non-null cases. The intricate nonlinear interaction of different quantities in the SST is quantified by carefully analyzing relevant multivariate complex Gaussian random variables. Several new results for such random variables are provided, and a central limit theorem result for the SST is established. The analysis sheds lights on bridging time-frequency analysis to time series analysis and diffusion geometry

Support matrix machine: A review

Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists in matrix format, which is given as input to SVM by reshaping the matrices into vectors. The process of reshaping disrupts the spatial correlations inherent in the matrix data. Also, converting matrices into vectors results in input data with a high dimensionality, which introduces significant computational complexity. To overcome these issues in classifying matrix input data, support matrix machine (SMM) is proposed. It represents one of the emerging methodologies tailored for handling matrix input data. The SMM method preserves the structural information of the matrix data by using the spectral elastic net property which is a combination of the nuclear norm and Frobenius norm. This article provides the first in-depth analysis of the development of the SMM model, which can be used as a thorough summary by both novices and experts. We discuss numerous SMM variants, such as robust, sparse, class imbalance, and multi-class classification models. We also analyze the applications of the SMM model and conclude the article by outlining potential future research avenues and possibilities that may motivate academics to advance the SMM algorithm

Towards Multiclass Damage Detection and Localization using Limited Vibration Measurements

Traditional vibration-based damage detection methods provide structural health information based on their measured data (i.e., acceleration and displacement response). Over the last few decades, various model-based and time-frequency methods have shown great promises for damage identification and localization. However, the existing methods are unable to perform satisfactorily in many situations, including the presence of limited sensor measurements and training data, detection of minor and progressive damage, and identification of multiclass damage, creating constraints to make them free of user-intervention and implemented using the modern sensors. The main objective of this thesis is to develop algorithms capable of damage identification and localization using limited measurements that can address the limitation of the traditional methods while providing a minimal to no user-intervention damage identification process. The proposed research in this thesis involves casting damage detection problems as non-parametric and autonomous with the least user intervention. Progressive damage identification is presented using novel time-frequency methods, such as synchrosqueezing transform and multivariate empirical mode decomposition, showing improved sensitivity of identifying minor damage over traditional methods. A basis-free method, such as multivariate empirical mode decomposition, is employed for damage localization using limited sensors. The acquired vibration measurement is decomposed into its mono components, and a damage localization index based on modal energy is proposed to overcome the need for a large number of sensors. The limited measurement aspect of damage localization is explored by selecting fewer sensors, and it is shown that with limited measurements, the proposed method is as effective as a total number of measurements equals the number of degrees of freedom of the model. To create an autonomous damage identification framework, Artificial Intelligence-based methods are explored the first time for multiclass damage classification and localization. Due to the lack of availability of a large amount of data, the acquired vibration data is augmented using windowing of the data per damage class. A novel window-based one-dimensional convolutional neural network is explored to classify sequential time-series of vibration measurements with only one hidden layer. The robustness of the proposed method is further evaluated by a suite of parametric and sensitivity analysis. Improvement of this method is further accomplished by implementing a windowed Long Short-term Memory network capable of learning long-term dependencies of the sequential data. Finally, the proposed methods are validated using a suite of experimental and full-scale studies, including a high-rate dynamics experimental testbed, a stadia prototype experimental setup, the MIT green building, and the Z24 bridge