Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Breathing pattern characterization in patients with respiratory and cardiac failure

El objetivo principal de la tesis es estudiar los patrones respiratorios de pacientes en proceso de extubación y pacientes con insuficiencia cardiaca crónica (CHF), a partirde la señal de flujo respiratorio. La información obtenida de este estudio puede contribuir a la comprensión de los procesos fisiológicos subyacentes,y ayudar en el diagnóstico de estos pacientes. Uno de los problemas más desafiantes en unidades de cuidados intensivos es elproceso de desconexión de pacientes asistidos mediante ventilación mecánica. Más del 10% de pacientes que se extuban tienen que ser reintubados antes de 48 horas. Una prueba fallida puede ocasionar distrés cardiopulmonar y una mayor tasa de mortalidad. Se caracterizó el patrón respiratorio y la interacción dinámica entre la frecuenciacardiaca y frecuencia respiratoria, para obtener índices no invasivos que proporcionen una mayor información en el proceso de destete y mejorar el éxito de la desconexión.Las señales de flujo respiratorio y electrocardiográfica utilizadas en este estudio fueron obtenidas durante 30 minutos aplicando la prueba de tubo en T. Se compararon94 pacientes que tuvieron éxito en el proceso de extubación (GE), 39 pacientes que fracasaron en la prueba al mantener la respiración espontánea (GF), y 21 pacientes quesuperaron la prueba con éxito y fueron extubados, pero antes de 48 horas tuvieron que ser reintubados (GR). El patrón respiratorio se caracterizó a partir de las series temporales. Se aplicó la dinámica simbólica conjunta a las series correspondientes a las frecuencias cardiaca y respiratoria, para describir las interacciones cardiorrespiratoria de estos pacientes. Técnicas de "clustering", ecualización del histograma, clasificación mediante máquinasde soporte vectorial (SVM) y técnicas de validación permitieron seleccionar el conjunto de características más relevantes. Se propuso una nueva métrica B (índice de equilibrio) para la optimización de la clasificación con muestras desbalanceadas. Basado en este nuevo índice, aplicando SVM, se seleccionaron las mejores características que mantenían el mejor equilibrio entre sensibilidad y especificidad en todas las clasificaciones. El mejor resultado se obtuvo considerando conjuntamente la precisión y el valor de B, con una clasificación del 80% entre los grupos GE y GF, con 6 características. Clasificando GE vs. el resto de los pacientes, el mejor resultado se obtuvo con 9 características, con 81%. Clasificando GR vs. GE y GR vs. el resto de pacientes la precisión fue del 83% y 81% con 9 y 10 características, respectivamente. La tasa de mortalidad en pacientes con CHF es alta y la estratificación de estospacientes en función del riesgo es uno de los principales retos de la cardiología contemporánea. Estos pacientes a menudo desarrollan patrones de respiraciónperiódica (PB) incluyendo la respiración de Cheyne-Stokes (CSR) y respiración periódica sin apnea. La respiración periódica en estos pacientes se ha asociadocon una mayor mortalidad, especialmente en pacientes con CSR. Por lo tanto, el estudio de estos patrones respiratorios podría servir como un marcador de riesgo y proporcionar una mayor información sobre el estado fisiopatológico de pacientes con CHF. Se pretende identificar la condición de los pacientes con CHFde forma no invasiva mediante la caracterización y clasificación de patrones respiratorios con PBy respiración no periódica (nPB), y patrón de sujetos sanos, a partir registros de 15minutos de la señal de flujo respiratorio. Se caracterizó el patrón respiratorio mediante un estudio tiempo-frecuencia estacionario y no estacionario, de la envolvente de la señal de flujo respiratorio. Parámetros relacionados con la potencia espectral de la envolvente de la señal presentaron losmejores resultados en la clasificación de sujetos sanos y pacientes con CHF con CSR, PB y nPB. Las curvas ROC validan los resultados obtenidos. Se aplicó la "correntropy" para una caracterización tiempo-frecuencia mas completa del patrón respiratorio de pacientes con CHF. La "corretronpy" considera los momentos estadísticos de orden superior, siendo más robusta frente a los "outliers". Con la densidad espectral de correntropy (CSD) tanto la frecuencia de modulación como la dela respiración se representan en su posición real en el eje frecuencial. Los pacientes con PB y nPB, presentan diferentesgrados de periodicidad en función de su condición, mientras que los sujetos sanos no tienen periodicidad marcada. Con único parámetro se obtuvieron resultados del 88.9% clasificando pacientes PB vs. nPB, 95.2% para CHF vs. sanos, 94.4% para nPB vs. sanos.The main objective of this thesis is to study andcharacterize breathing patterns through the respiratory flow signal applied to patients on weaning trials from mechanicalventilation and patients with chronic heart failure (CHF). The aim is to contribute to theunderstanding of the underlying physiological processes and to help in the diagnosis of these patients. One of the most challenging problems in intensive care units is still the process ofdiscontinuing mechanical ventilation, as over 10% of patients who undergo successfulT-tube trials have to be reintubated in less than 48 hours. A failed weaning trial mayinduce cardiopulmonary distress and carries a higher mortality rate. We characterize therespiratory pattern and the dynamic interaction between heart rate and breathing rate toobtain noninvasive indices that provide enhanced information about the weaningprocess and improve the weaning outcome. This is achieved through a comparison of 94 patients with successful trials (GS), 39patients who fail to maintain spontaneous breathing (GF), and 21 patients who successfully maintain spontaneous breathing and are extubated, but require thereinstitution of mechanical ventilation in less than 48 hours because they are unable tobreathe (GR). The ECG and the respiratory flow signals used in this study were acquired during T-tube tests and last 30 minute. The respiratory pattern was characterized by means of a number of respiratory timeseries. Joint symbolic dynamics applied to time series of heart rate and respiratoryfrequency was used to describe the cardiorespiratory interactions of patients during theweaning trial process. Clustering, histogram equalization, support vector machines-based classification (SVM) and validation techniques enabled the selection of the bestsubset of input features. We defined a new optimization metric for unbalanced classification problems, andestablished a new SVM feature selection method, based on this balance index B. The proposed B-based SVM feature selection provided a better balance between sensitivityand specificity in all classifications. The best classification result was obtained with SVM feature selection based on bothaccuracy and the balance index, which classified GS and GFwith an accuracy of 80%, considering 6 features. Classifying GS versus the rest of patients, the best result wasobtained with 9 features, 81%, and the accuracy classifying GR versus GS, and GR versus the rest of the patients was 83% and 81% with 9 and 10 features, respectively.The mortality rate in CHF patients remains high and risk stratification in these patients isstill one of the major challenges of contemporary cardiology. Patients with CHF oftendevelop periodic breathing patterns including Cheyne-Stokes respiration (CSR) and periodic breathing without apnea. Periodic breathing in CHF patients is associated withincreased mortality, especially in CSR patients. Therefore it could serve as a risk markerand can provide enhanced information about thepathophysiological condition of CHF patients. The main goal of this research was to identify CHF patients' condition noninvasively bycharacterizing and classifying respiratory flow patterns from patients with PB and nPBand healthy subjects by using 15-minute long respiratory flow signals. The respiratory pattern was characterized by a stationary and a nonstationary time-frequency study through the envelope of the respiratory flow signal. Power-related parameters achieved the best results in all of the classifications involving healthy subjects and CHF patients with CSR, PB and nPB and the ROC curves validated theresults obtained for the identification of different respiratory patterns. We investigated the use of correntropy for the spectral characterization of respiratory patterns in CHF patients. The correntropy function accounts for higher-order moments and is robust to outliers. Due to the former property, the respiratory and modulationfrequencies appear at their actual locations along the frequency axis in the correntropy spectral density (CSD). The best results were achieved with correntropy and CSD-related parameters that characterized the power in the modulation and respiration discriminant bands, definedas a frequency interval centred on the modulation and respiration frequency peaks,respectively. All patients, i.e. both PB and nPB, exhibit various degrees of periodicitydepending on their condition, whereas healthy subjects have no pronounced periodicity.This fact led to excellent results classifying PB and nPB patients 88.9%, CHF versushealthy 95.2%, and nPB versus healthy 94.4% with only one parameter.Postprint (published version

A parametric multiclass Bayes error estimator for the multispectral scanner spatial model performance evaluation

The author has identified the following significant results. The probability of correct classification of various populations in data was defined as the primary performance index. The multispectral data being of multiclass nature as well, required a Bayes error estimation procedure that was dependent on a set of class statistics alone. The classification error was expressed in terms of an N dimensional integral, where N was the dimensionality of the feature space. The multispectral scanner spatial model was represented by a linear shift, invariant multiple, port system where the N spectral bands comprised the input processes. The scanner characteristic function, the relationship governing the transformation of the input spatial, and hence, spectral correlation matrices through the systems, was developed

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

A Practical Approach: Design and Implementation of a Healthcare Software for Screening of Dysphonic Patients

Risk management in the development of medical software and devices is one of the most crucial processes in ensuring accurate diagnoses and treatment of disease. The consequences of wrong decisions that happen in our daily life might be unembellished. However, wrong decisions in healthcare based on unreliable evidence due to erroneous software could result in loss of life. Dysphonic patients suffering from various vocal fold disorders might have a threat of life due to inaccurate diagnosis. Some voice disorders, such as keratosis, are precancerous, and can become cancerous in cases that involve inaccurate diagnosis due to software failure. The objective of this paper is to design and implement a healthcare software for the detection of voice disorders in nonperiodic speech signals. Occurrences of potential risks during the design and development of the proposed software are taken into account to avoid failure. The software is implemented by applying the local binary pattern (LBP) operator on the textures of nonperiodic signals. The textures are obtained through the recurrence plot. The LBP operator computes the histograms for normal persons and dysphonic patients, and these histograms are used with the support vector machine for the automatic classification of dysphonic patients. The software is evaluated and tested by using the Massachusetts Eye and Ear Infirmary voice disorder database. The success rate of the proposed healthcare system is 97.73% ± 1.2, and the area under the receiver operating characteristic curve is 0.98 ± 0. The performance of the proposed healthcare system is much better than the existing commercial software used for screening dysphonic patients

Acoustic Scene Classification

This work was supported by the Centre for Digital Music Platform (grant EP/K009559/1) and a Leadership Fellowship (EP/G007144/1) both from the United Kingdom Engineering and Physical Sciences Research Council