Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis

Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time-frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).Comment: 49 pages, 16 figure

Joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a Bayesian sampling approach

International audienceWe propose a joint segmentation algorithm for piecewise constant autoregressive (AR) processes recorded by several independent sensors. The algorithm is based on a hierarchical Bayesian model. Appropriate priors allow to introduce correlations between the change locations of the observed signals. Numerical problems inherent to Bayesian inference are solved by a Gibbs sampling strategy. The proposed joint segmentation methodology yields improved segmentation results when compared to parallel and independent individual signal segmentations. The initial algorithm is derived for piecewise constant AR processes whose orders are fixed on each segment. However, an extension to models with unknown model orders is also discussed. Theoretical results are illustrated by many simulations conducted with synthetic signals and real arc-tracking and speech signals

시계열 데이터 패턴 분석을 위한 종단 심층 학습망 설계 방법론

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 컴퓨터공학부, 2019. 2. 장병탁.Pattern recognition within time series data became an important avenue of research in artificial intelligence following the paradigm shift of the fourth industrial revolution. A number of studies related to this have been conducted over the past few years, and research using deep learning techniques are becoming increasingly popular. Due to the nonstationary, nonlinear and noisy nature of time series data, it is essential to design an appropriate model to extract its significant features for pattern recognition. This dissertation not only discusses the study of pattern recognition using various hand-crafted feature engineering techniques using physiological time series signals, but also suggests an end-to-end deep learning design methodology without any feature engineering. Time series signal can be classified into signals having periodic and non-periodic characteristics in the time domain. This thesis proposes two end-to-end deep learning design methodologies for pattern recognition of periodic and non-periodic signals. The first proposed deep learning design methodology is Deep ECGNet. Deep ECGNet offers a design scheme for an end-to-end deep learning model using periodic characteristics of Electrocardiogram (ECG) signals. ECG, recorded from the electrophysiologic patterns of heart muscle during heartbeat, could be a promising candidate to provide a biomarker to estimate event-based stress level. Conventionally, the beat-to-beat alternations, heart rate variability (HRV), from ECG have been utilized to monitor the mental stress status as well as the mortality of cardiac patients. These HRV parameters have the disadvantage of having a 5-minute measurement period. In this thesis, human's stress states were estimated without special hand-crafted feature engineering using only 10-second interval data with the deep learning model. The design methodology of this model incorporates the periodic characteristics of the ECG signal into the model. The main parameters of 1D CNNs and RNNs reflecting the periodic characteristics of ECG were updated corresponding to the stress states. The experimental results proved that the proposed method yielded better performance than those of the existing HRV parameter extraction methods and spectrogram methods. The second proposed methodology is an automatic end-to-end deep learning design methodology using Bayesian optimization for non-periodic signals. Electroencephalogram (EEG) is elicited from the central nervous system (CNS) to yield genuine emotional states, even at the unconscious level. Due to the low signal-to-noise ratio (SNR) of EEG signals, spectral analysis in frequency domain has been conventionally applied to EEG studies. As a general methodology, EEG signals are filtered into several frequency bands using Fourier or wavelet analyses and these band features are then fed into a classifier. This thesis proposes an end-to-end deep learning automatic design method using optimization techniques without this basic feature engineering. Bayesian optimization is a popular optimization technique for machine learning to optimize model hyperparameters. It is often used in optimization problems to evaluate expensive black box functions. In this thesis, we propose a method to perform whole model hyperparameters and structural optimization by using 1D CNNs and RNNs as basic deep learning models and Bayesian optimization. In this way, this thesis proposes the Deep EEGNet model as a method to discriminate human emotional states from EEG signals. Experimental results proved that the proposed method showed better performance than that of conventional method based on the conventional band power feature method. In conclusion, this thesis has proposed several methodologies for time series pattern recognition problems from the feature engineering-based conventional methods to the end-to-end deep learning design methodologies with only raw time series signals. Experimental results showed that the proposed methodologies can be effectively applied to pattern recognition problems using time series data.시계열 데이터의 패턴 인식 문제는 4차 산업 혁명의 패러다임 전환과 함께 매우 중요한 인공 지능의 한 분야가 되었다. 이에 따라, 지난 몇 년간 이와 관련된 많은 연구들이 이루어져 왔으며, 최근에는 심층 학습망 (deep learning networks) 모델을 이용한 연구들이 주를 이루어 왔다. 시계열 데이터는 비정상, 비선형 그리고 잡음 (nonstationary, nonlinear and noisy) 특성으로 인하여 시계열 데이터의 패턴 인식 수행을 위해선, 데이터의 주요한 특징점을 추출하기 위한 최적화된 모델의 설계가 필수적이다. 본 논문은 대표적인 시계열 데이터인 생체 신호를 사용하여 여러 특징 벡터 추출 방법 (hand-crafted feature engineering methods)을 이용한 패턴 인식 기법에 대하여 논할 뿐만 아니라, 궁극적으로는 특징 벡터 추출 과정이 없는 종단 심층 학습망 설계 방법론에 대한 연구 내용을 담고 있다. 시계열 신호는 시간 축 상에서 크게 주기적 신호와 비주기적 신호로 구분할 수 있는데, 본 연구는 이러한 두 유형의 신호들에 대한 패턴 인식을 위해 두 가지 종단 심층 학습망에 대한 설계 방법론을 제안한다. 첫 번째 제안된 방법론을 이용해 설계된 모델은 신호의 주기적 특성을 이용한 Deep ECGNet이다. 심장 근육의 전기 생리학적 패턴으로부터 기록된 심전도 (Electrocardiogram, ECG)는 이벤트 기반 스트레스 수준을 추정하기 위한 척도 (bio marker)를 제공하는 유효한 데이터가 될 수 있다. 전통적으로 심전도의 심박수 변동성 (Herat Rate Variability, HRV) 매개변수 (parameter)는 심장 질환 환자의 정신적 스트레스 상태 및 사망률을 모니터링하는 데 사용되었다. 하지만, 표준 심박수 변동성 매개 변수는 측정 주기가 5분 이상으로, 측정 시간이 길다는 단점이 있다. 본 논문에서는 심층 학습망 모델을 이용하여 10초 간격의 ECG 데이터만을 이용하여, 추가적인 특징 벡터의 추출 과정 없이 인간의 스트레스 상태를 인식할 수 있음을 보인다. 제안된 설계 기법은 ECG 신호의 주기적 특성을 모델에 반영하였는데, ECG의 은닉 특징 추출기로 사용된 1D CNNs 및 RNNs 모델의 주요 매개 변수에 주기적 특성을 반영함으로써, 한 주기 신호의 스트레스 상태에 따른 주요 특징점을 종단 학습망 내부적으로 추출할 수 있음을 보였다. 실험 결과 제안된 방법이 기존 심박수 변동성 매개변수와 spectrogram 추출 기법 기반의 패턴 인식 방법보다 좋은 성능을 나타내고 있음을 확인할 수 있었다. 두 번째 제안된 방법론은 비 주기적이며 비정상, 비선형 그리고 잡음 특성을 지닌 신호의 패턴인식을 위한 최적 종단 심층 학습망 자동 설계 방법론이다. 뇌파 신호 (Electroencephalogram, EEG)는 중추 신경계 (CNS)에서 발생되어 무의식 상태에서도 본연의 감정 상태를 나타내는데, EEG 신호의 낮은 신호 대 잡음비 (SNR)로 인해 뇌파를 이용한 감정 상태 판정을 위해서 주로 주파수 영역의 스펙트럼 분석이 뇌파 연구에 적용되어 왔다. 통상적으로 뇌파 신호는 푸리에 (Fourier) 또는 웨이블렛 (wavelet) 분석을 사용하여 여러 주파수 대역으로 필터링 된다. 이렇게 추출된 주파수 특징 벡터는 보통 얕은 학습 분류기 (shallow machine learning classifier)의 입력으로 사용되어 패턴 인식을 수행하게 된다. 본 논문에서는 이러한 기본적인 특징 벡터 추출 과정이 없는 베이지안 최적화 (Bayesian optimization) 기법을 이용한 종단 심층 학습망 자동 설계 기법을 제안한다. 베이지안 최적화 기법은 초 매개변수 (hyperparamters)를 최적화하기 위한 기계 학습 분야의 대표적인 최적화 기법인데, 최적화 과정에서 평가 시간이 많이 소요되는 목적 함수 (expensive black box function)를 갖고 있는 최적화 문제에 적합하다. 이러한 베이지안 최적화를 이용하여 기본적인 학습 모델인 1D CNNs 및 RNNs의 전체 모델의 초 매개변수 및 구조적 최적화를 수행하는 방법을 제안하였으며, 제안된 방법론을 바탕으로 Deep EEGNet이라는 인간의 감정상태를 판별할 수 있는 모델을 제안하였다. 여러 실험을 통해 제안된 모델이 기존의 주파수 특징 벡터 (band power feature) 추출 기법 기반의 전통적인 감정 패턴 인식 방법보다 좋은 성능을 나타내고 있음을 확인할 수 있었다. 결론적으로 본 논문은 시계열 데이터를 이용한 패턴 인식문제를 여러 특징 벡터 추출 기법 기반의 전통적인 방법을 통해 설계하는 방법부터, 추가적인 특징 벡터 추출 과정 없이 원본 데이터만을 이용하여 종단 심층 학습망을 설계하는 방법까지 제안하였다. 또한, 다양한 실험을 통해 제안된 방법론이 시계열 신호 데이터를 이용한 패턴 인식 문제에 효과적으로 적용될 수 있음을 보였다.Chapter 1 Introduction 1 1.1 Pattern Recognition in Time Series 1 1.2 Major Problems in Conventional Approaches 7 1.3 The Proposed Approach and its Contribution 8 1.4 Thesis Organization 10 Chapter 2 Related Works 12 2.1 Pattern Recognition in Time Series using Conventional Methods 12 2.1.1 Time Domain Features 12 2.1.2 Frequency Domain Features 14 2.1.3 Signal Processing based on Multi-variate Empirical Mode Decomposition (MEMD) 15 2.1.4 Statistical Time Series Model (ARIMA) 18 2.2 Fundamental Deep Learning Algorithms 20 2.2.1 Convolutional Neural Networks (CNNs) 20 2.2.2 Recurrent Neural Networks (RNNs) 22 2.3 Hyper Parameters and Structural Optimization Techniques 24 2.3.1 Grid and Random Search Algorithms 24 2.3.2 Bayesian Optimization 25 2.3.3 Neural Architecture Search 28 2.4 Research Trends related to Time Series Data 29 2.4.1 Generative Model of Raw Audio Waveform 30 Chapter 3 Preliminary Researches: Patten Recognition in Time Series using Various Feature Extraction Methods 31 3.1 Conventional Methods using Time and Frequency Features: Motor Imagery Brain Response Classification 31 3.1.1 Introduction 31 3.1.2 Methods 32 3.1.3 Ensemble Classification Method (Stacking & AdaBoost) 32 3.1.4 Sensitivity Analysis 33 3.1.5 Classification Results 36 3.2 Statistical Feature Extraction Methods: ARIMA Model Based Feature Extraction Methodology 38 3.2.1 Introduction 38 3.2.2 ARIMA Model 38 3.2.3 Signal Processing 39 3.2.4 ARIMA Model Conformance Test 40 3.2.5 Experimental Results 40 3.2.6 Summary 43 3.3 Application on Specific Time Series Data: Human Stress States Recognition using Ultra-Short-Term ECG Spectral Feature 44 3.3.1 Introduction 44 3.3.2 Experiments 45 3.3.3 Classification Methods 49 3.3.4 Experimental Results 49 3.3.5 Summary 56 Chapter 4 Master Framework for Pattern Recognition in Time Series 57 4.1 The Concept of the Proposed Framework for Pattern Recognition in Time Series 57 4.1.1 Optimal Basic Deep Learning Models for the Proposed Framework 57 4.2 Two Categories for Pattern Recognition in Time Series Data 59 4.2.1 The Proposed Deep Learning Framework for Periodic Time Series Signals 59 4.2.2 The Proposed Deep Learning Framework for Non-periodic Time Series Signals 61 4.3 Expanded Models of the Proposed Master Framework for Pattern Recogntion in Time Series 63 Chapter 5 Deep Learning Model Design Methodology for Periodic Signals using Prior Knowledge: Deep ECGNet 65 5.1 Introduction 65 5.2 Materials and Methods 67 5.2.1 Subjects and Data Acquisition 67 5.2.2 Conventional ECG Analysis Methods 72 5.2.3 The Initial Setup of the Deep Learning Architecture 75 5.2.4 The Deep ECGNet 78 5.3 Experimental Results 83 5.4 Summary 98 Chapter 6 Deep Learning Model Design Methodology for Non-periodic Time Series Signals using Optimization Techniques: Deep EEGNet 100 6.1 Introduction 100 6.2 Materials and Methods 104 6.2.1 Subjects and Data Acquisition 104 6.2.2 Conventional EEG Analysis Methods 106 6.2.3 Basic Deep Learning Units and Optimization Technique 108 6.2.4 Optimization for Deep EEGNet 109 6.2.5 Deep EEGNet Architectures using the EEG Channel Grouping Scheme 111 6.3 Experimental Results 113 6.4 Summary 124 Chapter 7 Concluding Remarks 126 7.1 Summary of Thesis and Contributions 126 7.2 Limitations of the Proposed Methods 128 7.3 Suggestions for Future Works 129 Bibliography 131 초 록 139Docto

Audio Signal Processing Using Time-Frequency Approaches: Coding, Classification, Fingerprinting, and Watermarking

Audio signals are information rich nonstationary signals that play an important role in our day-to-day communication, perception of environment, and entertainment. Due to its non-stationary nature, time- or frequency-only approaches are inadequate in analyzing these signals. A joint time-frequency (TF) approach would be a better choice to efficiently process these signals. In this digital era, compression, intelligent indexing for content-based retrieval, classification, and protection of digital audio content are few of the areas that encapsulate a majority of the audio signal processing applications. In this paper, we present a comprehensive array of TF methodologies that successfully address applications in all of the above mentioned areas. A TF-based audio coding scheme with novel psychoacoustics model, music classification, audio classification of environmental sounds, audio fingerprinting, and audio watermarking will be presented to demonstrate the advantages of using time-frequency approaches in analyzing and extracting information from audio signals.</p

A Network-Based Enhanced Spectral Diversity Approach for TOPS Time-Series Analysis

For multitemporal analysis of synthetic aperture radar (SAR) images acquired with a terrain observation by progressive scan (TOPS) mode, all acquisitions from a given satellite track must be coregistered to a reference coordinate system with accuracies better than 0.001 of a pixel (assuming full SAR resolution) in the azimuth direction. Such a high accuracy can be achieved through geometric coregistration, using precise satellite orbits and a digital elevation model, followed by a refinement step using a time-series analysis of coregistration errors. These errors represent the misregistration between all TOPS acquisitions relative to the reference coordinate system. We develop a workflow to estimate the time series of azimuth misregistration using a network-based enhanced spectral diversity (NESD) approach, in order to reduce the impact of temporal decorrelation on coregistration. Example time series of misregistration inferred for five tracks of Sentinel-1 TOPS acquisitions indicates a maximum relative azimuth misregistration of less than 0.01 of the full azimuth resolution between the TOPS acquisitions in the studied areas. Standard deviation of the estimated misregistration time series for different stacks varies from 1.1e-3 to 2e-3 of the azimuth resolution, equivalent to 1.6-2.8 cm orbital uncertainty in the azimuth direction. These values fall within the 1-sigma orbital uncertainty of the Sentinel-1 orbits and imply that orbital uncertainty is most likely the main source of the constant azimuth misregistration between different TOPS acquisitions. We propagate the uncertainty of individual misregistration estimated with ESD to the misregistration time series estimated with NESD and investigate the different challenges for operationalizing NESD