21 research outputs found

    Dynamic Algorithms and Asymptotic Theory for Lp-norm Data Analysis

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    The focus of this dissertation is the development of outlier-resistant stochastic algorithms for Principal Component Analysis (PCA) and the derivation of novel asymptotic theory for Lp-norm Principal Component Analysis (Lp-PCA). Modern machine learning and signal processing applications employ sensors that collect large volumes of data measurements that are stored in the form of data matrices, that are often massive and need to be efficiently processed in order to enable machine learning algorithms to perform effective underlying pattern discovery. One such commonly used matrix analysis technique is PCA. Over the past century, PCA has been extensively used in areas such as machine learning, deep learning, pattern recognition, and computer vision, just to name a few. PCA\u27s popularity can be attributed to its intuitive formulation on the L2-norm, availability of an elegant solution via the singular-value-decomposition (SVD), and asymptotic convergence guarantees. However, PCA has been shown to be highly sensitive to faulty measurements (outliers) because of its reliance on the outlier-sensitive L2-norm. Arguably, the most straightforward approach to impart robustness against outliers is to replace the outlier-sensitive L2-norm by the outlier-resistant L1-norm, thus formulating what is known as L1-PCA. Exact and approximate solvers are proposed for L1-PCA in the literature. On the other hand, in this big-data era, the data matrix may be very large and/or the data measurements may arrive in streaming fashion. Traditional L1-PCA algorithms are not suitable in this setting. In order to efficiently process streaming data, while being resistant against outliers, we propose a stochastic L1-PCA algorithm that computes the dominant principal component (PC) with formal convergence guarantees. We further generalize our stochastic L1-PCA algorithm to find multiple components by propose a new PCA framework that maximizes the recently proposed Barron loss. Leveraging Barron loss yields a stochastic algorithm with a tunable robustness parameter that allows the user to control the amount of outlier-resistance required in a given application. We demonstrate the efficacy and robustness of our stochastic algorithms on synthetic and real-world datasets. Our experimental studies include online subspace estimation, classification, video surveillance, and image conditioning, among other things. Last, we focus on the development of asymptotic theory for Lp-PCA. In general, Lp-PCA for p\u3c2 has shown to outperform PCA in the presence of outliers owing to its outlier resistance. However, unlike PCA, Lp-PCA is perceived as a ``robust heuristic\u27\u27 by the research community due to the lack of theoretical asymptotic convergence guarantees. In this work, we strive to shed light on the topic by developing asymptotic theory for Lp-PCA. Specifically, we show that, for a broad class of data distributions, the Lp-PCs span the same subspace as the standard PCs asymptotically and moreover, we prove that the Lp-PCs are specific rotated versions of the PCs. Finally, we demonstrate the asymptotic equivalence of PCA and Lp-PCA with a wide variety of experimental studies

    Diagnosis of the sleep apnea-hypopnea syndrome : a comprehensive approach through an intelligent system to support medical decision

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    [Abstract] This doctoral thesis carries out the development of an intelligent system to support medical decision in the diagnosis of the Sleep Apnea-Hypopnea Syndrome (SAHS). SAHS is the most common disorder within those affecting sleep. The estimates of the disease prevalence range from 3% to 7%. Diagnosis of SAHS requires of a polysomnographic test (PSG) to be done in the Sleep Unit of a medical center. Manual scoring of the resulting recording entails too much effort and time to the medical specialists and as a consequence it implies a high economic cost. In the developed system, automatic analysis of the PSG is accomplished which follows a comprehensive perspective. Firstly an analysis of the neurophysiological signals related to the sleep function is carried out in order to obtain the hypnogram. Then, an analysis is performed over the respiratory signals which have to be subsequently interpreted in the context of the remaining signals included in the PSG. In order to carry out such a task, the developed system is supported by the use of artificial intelligence techniques, specially focusing on the use of reasoning mechanisms capable of handling data imprecision. Ultimately, it is the aim of the proposed system to improve the diagnostic procedure and help physicians in the diagnosis of SAHS.[Resumen] Esta tesis aborda el desarrollo de un sistema inteligente de apoyo a la decisión clínica para el diagnóstico del Síndrome de Apneas-Hipopneas del Sueño (SAHS). El SAHS es el trastorno más común de aquellos que afectan al sueño. Afecta a un rango del 3% al 7% de la población con consecuencias severas sobre la salud. El diagnóstico requiere la realización de un análisis polisomnográfico (PSG) en una Unidad del Sueño de un centro hospitalario. El análisis manual de dicha prueba resulta muy costoso en tiempo y esfuerzo para el médico especialista, y como consecuencia en un elevado coste económico. El sistema desarrollado lleva a cabo el análisis automático del PSG desde una perspectiva integral. A tal efecto, primero se realiza un análisis de las señales neurofisiológicas vinculadas al sueño para obtener el hipnograma, y seguidamente, se lleva a cabo un análisis neumológico de las señales respiratorias interpretándolas en el contexto que marcan las demás señales del PSG. Para lleva a cabo dicha tarea el sistema se apoya en el uso de distintas técnicas de inteligencia artificial, con especial atención al uso mecanismos de razonamiento con soporte a la imprecisión. El principal objetivo del sistema propuesto es la mejora del procedimiento diagnóstico y ayudar a los médicos en diagnóstico del SAHS.[Resumo] Esta tese aborda o desenvolvemento dun sistema intelixente de apoio á decisión clínica para o diagnóstico do Síndrome de Apneas-Hipopneas do Sono (SAHS). O SAHS é o trastorno máis común daqueles que afectan ao sono. Afecta a un rango do 3% ao 7% da poboación con consecuencias severas sobre a saúde. O diagnóstico pasa pola realización dunha análise polisomnográfica (PSG) nunha Unidade do Sono dun centro hospitalario. A análise manual da devandita proba resulta moi custosa en tempo e esforzo para o médico especialista, e como consecuencia nun elevado custo económico. O sistema desenvolvido leva a cabo a análise automática do PSG dende unha perspectiva integral. A tal efecto, primeiro realizase unha análise dos sinais neurofisiolóxicos vinculados ao sono para obter o hipnograma, e seguidamente, lévase a cabo unha análise neumolóxica dos sinais respiratorios interpretándoos no contexto que marcan os demais sinais do PSG. Para leva a cabo esta tarefa o sistema apoiarase no uso de distintas técnicas de intelixencia artificial, con especial atención a mecanismos de razoamento con soporte para a imprecisión. O principal obxectivo do sistema proposto é a mellora do procedemento diagnóstico e axudar aos médicos no diagnóstico do SAHS

    노래 신호의 자동 전사

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    학위논문 (박사)-- 서울대학교 융합과학기술대학원 융합과학부, 2017. 8. 이교구.Automatic music transcription refers to an automatic extraction of musical attributes such as notes from an audio signal to a symbolic level. The symbolized music data are applicable for various purposes such as music education and production by providing higher-level information to both consumers and creators. Although the singing voice is the easiest one to listen and play among various music signals, traditional transcription methods for musical instruments are not suitable due to the acoustic complexity in the human voice. The main goal of this thesis is to develop a fully-automatic singing transcription system that exceeds existing methods. We first take a look at some typical approaches for pitch tracking and onset detection, which are two fundamental tasks of music transcription, and then propose several methods for each task. In terms of pitch tracking, we examine the effect of data sampling on the performance of periodicity analysis of music signals. For onset detection, the local homogeneity in the harmonic structure is exploited through the cepstral analysis and unsupervised classification. The final transcription system includes feature extraction and probabilistic model of the harmonic structure, and note transition based on the hidden Markov model. It achieved the best performance (an F-measure of 82%) in the note-level evaluation including the state-of-the-art systems.Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Definitions 5 1.2.1 Musical keywords 5 1.2.2 Scientific keywords 7 1.2.3 Representations 7 1.3 Problems in singing transcription 9 1.4 Topics of interest 10 1.5 Outline of the thesis 13 Chapter 2 Background 16 2.1 Pitch estimation 17 2.1.1 Time-domain methods 17 2.1.2 Frequency-domain methods 18 2.2 Note segmentation 20 2.2.1 Onset detection 20 2.2.2 Offset detection 23 2.3 Singing transcription 24 2.4 Evaluation methodology 26 2.4.1 Pitch estimation 26 2.4.2 Note segmentation 27 2.4.3 Dataset 28 2.5 Summary 31 Chapter 3 Periodicity Analysis by Sampling in the Time/Frequency Domain for Pitch Tracking 32 3.1 Introduction 32 3.2 Data sampling 34 3.3 Sampled ACF/DF in the time domain 37 3.4 Sampled ACF/DF in the frequency domain 38 3.5 Iterative F0 estimation 40 3.6 Experimental setup 42 3.7 Result 46 3.8 Summary 49 Chapter 4 Note Onset Detection based on Harmonic Cepstrum regularity 50 4.1 Introduction 50 4.2 Cepstral analysis 52 4.3 Harmonic cepstrum regularity 56 4.3.1 Harmonic quefrency selection 57 4.3.2 Sub-harmonic regularity function 58 4.3.3 Adaptive thresholding 59 4.3.4 Picking onsets 59 4.4 Experiments 61 4.4.1 Dataset description 61 4.4.2 Evaluation results 62 4.5 Summary 64 Chapter 5 Robust Singing Transcription System using Local Homogeneity in the Harmonic Structure 66 5.1 Introduction 66 5.2 F0 tracking 71 5.3 Feature extraction 72 5.4 Mixture model 76 5.5 Note detection 80 5.5.1 Transition boundary detection 81 5.5.2 Note boundary selection 83 5.5.3 Note pitch decision 84 5.6 Evaluation 86 5.6.1 Dataset 86 5.6.2 Criteria and measures 87 5.6.3 Experimental setup 89 5.7 Results and discussions 90 5.7.1 Failure analysis 95 5.8 Summary 97 Chapter 6 Conclusion and Future Work 99 6.1 Contributions 99 6.2 Future work 103 6.2.1 Precise partial tracking using instantaneous frequency 103 6.2.2 Linguistic model for note segmentation 105 Appendix 108 Derivation of the instantaneous frequency 108 Bibliography 110 초 록 124Docto
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