A new vision of a simple 1D Convolutional Neural Networks (1D-CNN) with Leaky-ReLU function for ECG abnormalities classification

Artificial Intelligence (AI) is increasingly impacting the healthcare field, due to its computational power that reduces time, cost and efforts for both healthcare professionals and patients. Diagnosing cardiac abnormalities using AI represents a very attractive subject for both medical and technical professionals. Cardiac abnormalities are characterized by the ECG signal, which is known by its variable morphology and intense affection by noises and artifacts. In this context, the presented study aims to propose a simple yet efficient version of Convolutional Neural Networks (CNN) to classify those abnormalities. This version increases the ability to detect several heart rate arrhythmias and severe cardiac abnormalities based only on the original 1D format of the ECG signal, which reserve the main feature of this signal and can be very suitable for ready-to-use and real-time applications. The main used training datasets are the MIT-BIH arrhythmias and the PTB databases. The proposed architectures are mainly inspired by the most recent CNN models and introduce several modifications on functions and layers, such as the use of the Leaky-ReLU instead of the ReLU activation function. The results of the proposed model are varying from an accuracy of 97%–99% in classifying Normal (n), Supraventricular (s), Ventricular (v), Fusion of ventricular and normal (f), and noisy (q) beats, in addition to the Myocardial Infarction (MI) case. A continuous performance was achieved while testing the model on real data, and after its migration to real mobile devices

Overlapping Clusters and Support Vector Machines Based Interval Type-2 Fuzzy System for the Prediction of Peptide Binding Affinity

In the post-genome era, it is becoming more complex to process high dimensional, low-instance available, and nonlinear biological datasets. This paper aims to address these characteristics as they have adverse effects on the performance of predictive models in bioinformatics. In this paper, an interval type-2 Takagi Sugeno fuzzy predictive model is proposed in order to manage high-dimensionality and nonlinearity of such datasets which is the common feature in bioinformatics. A new clustering framework is proposed for this purpose to simplify antecedent operations for an interval type-2 fuzzy system. This new clustering framework is based on overlapping regions between the clusters. The cluster analysis of partitions and statistical information derived from them has identified the upper and lower membership functions forming the premise part. This is further enhanced by adapting the regression version of support vector machines in the consequent part. The proposed method is used in experiments to quantitatively predict affinities of peptide bindings to biomolecules. This case study imposes a challenge in post-genome studies and remains an open problem due to the complexity of the biological system, diversity of peptides, and curse of dimensionality of amino acid index representation characterizing the peptides. Utilizing four different peptide binding affinity datasets, the proposed method resulted in better generalization ability for all of them yielding an improved prediction accuracy of up to 58.2% on unseen peptides in comparison with the predictive methods presented in the literature. Source code of the algorithm is available at https://github.com/sekerbigdatalab

Classification of EMG Signals using Wavelet Features and Fuzzy Logic Classifiers

Master'sMASTER OF ENGINEERIN

Sistema de inferência fuzzy geral do tipo-2 aplicado à classificação

This work proposes the development of a new tool based on general type-2 fuzzy sets to be applied to digital classification of data. The classification problem considered here regards the identification of areas of forest in satellite images. The goal is to assist users in tasks related to monitoring forest. The developed digital classifier employs an inference mechanism called "general type-2 scaled inference" to classify pixels in images according to their vegetation cover. Such classifier is innovative because, besides using general type-2 fuzzy sets, it can use specific and generic rules base (both in a hierarchical way) to reclassify pixels that remain unclassified. Such hierarquical reclassification leads to a compact rule base (with few rules). The reason why one should use type-2 fuzzy inference is that they present better performance than their type-1 counterparts, in spite of their bigger computational cost. The carried out tests showed, for sure, that the proposed system is better than the conventional fuzzy classifier usually employed in similar applications and its performance is comparable to the statistical likelihood classifier, proving to be an alternative choice to this last one.Propõe-se, nesta tese, o desenvolvimento de uma nova ferramenta baseada em conjuntos fuzzy gerais do tipo-2 para aplicação em processos de classificação digital de dados. O problema de classificação a ser considerado está relacionado à identificação de regiões de floresta em imagens de satélite com o objetivo de auxiliar em tarefas de monitoramento florestal. O classificador digital desenvolvido utiliza um mecanismo de inferência denominado de "inferência escalonada fuzzy geral do tipo-2" para classificar os pixels das imagens de satélite de acordo com sua cobertura vegetal. Tal classificador é inovador pois, além de utilizar conjuntos fuzzy tipo-2 gerais, pode utilizar tanto uma base de regras específica quanto uma base genérica (ambas de forma hierárquica) para reclassificar pontos que, do contrário, permaneceriam sem classificação. Isto permite a obtenção de uma base de regras compacta (composta de poucas regras). A justificativa para o uso de sistemas de inferência do tipo-2 é que estes, apesar do custo computacional maior, apresentam desempenho superior aos sistemas do tipo-1 equivalentes. Os testes realizados mostram que, de fato, o sistema proposto é melhor do que o classificador fuzzy convencional usualmente empregado em aplicações semelhantes e possui desempenho comparável ao classificador estatístico da máxima verossimilhança, sendo uma alternativa viável ao último

Análisis de señales biomédicas para aplicación de terapias en la fibrilación ventricular cardiaca

La muerte súbita es una muerte natural, inesperada y rápida en un tiempo límite de 24 horas después del comienzo de un proceso patológico. Las causas más comunes de la muerte súbita son las enfermedades Cardiovasculares (ECV) que resultan estar entre las principales causas de muerte en todo el mundo. En 2012, la Organización Mundial de la Salud (OMS) registró 17,5 millones de muertes por ECV, que representan el 31 % de todas las muertes registradas en el mundo . Una de las enfermedades cardiovasculares con mayor mortalidad es la Fibrilación Ventricular (FV), que es una arritmia cardíaca producida por una actividad eléctrica desorganizada del corazón. Durante la FV, los ventrículos se contraen de forma asíncrona con ausencia de latido efectivo, fallando el bombeo sanguíneo, lo que produce la muerte súbita en el paciente, si no se trata de forma adecuada en un plazo de pocos minutos. Las desfibrilación es el único tratamiento definitivo posible de la FV, que consiste en la aplicación de un choque eléctrico de alta energía sobre el pecho del paciente, facilitando así el reinicio de la actividad eléctrica cardíaca normal. El éxito de la desfibrilación es inversamente proporcional al intervalo de tiempo desde el comienzo del episodio hasta la aplicación de la descarga. Aparecen muchas dificultades a la hora de diagnosticar la FV: por una parte están las características intrínsecas de la FV (falta de organización, irregularidad, etc.), y por otra, la gran similitud entre la FV y otras patologías cardíacas entre ellas la Taquicardia Ventricular (TV). La diferenciación entre la TV y la FV es bastante complicada: el diagnóstico de la TV como FV en un paciente puede ocasionarle graves lesiones a la hora de aplicarle la terapia correspondiente a FV (descarga eléctrica de alto voltaje), es más, puede causarle una FV. Por el contrario, si la FV se interpreta incorrectamente como TV, el resultado puede ser también peligroso para la vida. Por lo tanto, un método de detección eficaz para distinguir FV de TV tiene mucha importancia en la investigación clínica. Con el fin de diagnosticar y tratar las enfermedades cardiovasculares (FV por ejemplo), se establecen dos grandes grupos de métodos diagnósticos en cardiología: métodos diagnósticos invasivos y no invasivos. Las técnicas invasivas requieren introducir catéteres en el organismo, con el objetivo de medir presiones de las cavidades cardíacas, para registrar la actividad eléctrica. Las técnicas no invasivas están enfocadas a caracterizar el estado fisiopatológico del corazón a través de electrodos colocados directamente sobre la piel del paciente. El electrocardiograma (ECG) es un examen no invasivo, de bajo costo, que se ha utilizado como el método básico de diagnóstico de desórdenes cardíacos de conducción eléctrica, mediante el estudio de la frecuencia cardíaca y la morfología de diferentes ondas que constituyen el ciclo cardíaco. El análisis ECG constituye una buena fuente de información a partir de la cual se pueden detectar diferentes tipos de enfermedades cardíacas. Debido a que la señal de ECG es una señal aleatoria no estacionaria, el análisis en el dominio del tiempo no resulta ser suficientemente sensible a las distorsiones de las formas de la onda ECG. Sin embargo estos métodos no siempre presentan todas las informaciones que pueden ser extraídas de las señales ECG, con lo cual, se pierde la información sobre la frecuencia, la cual muestra una información más adicional de la señal. El diagnóstico en el dominio de la frecuencia utiliza métodos como la transformada de Fourier. Por lo tanto, el análisis en el dominio de la frecuencia permite determinar las frecuencias de la señal. Por otro lado, se pierde la información de tipo temporal de la señal, con lo cual es un método muy limitado y no es útil para el análisis de señales no estacionarias. Varios estudios han utilizado modelos matemáticos que combinan la información temporal y espectral en la misma representación. Esta técnica Representación Tiempo-Frecuencia (RTF) es muy importante en el tratamiento de las señales no estacionarias como la señal de ECG, ya que distribuye la energía de la señal en el espacio bidimensional tiempo-frecuencia. Además, múltiples factores alteran la adquisición y registro de la señal ECG: por un lado está la influencia del medio ambiente (la interferencia de red 50-60 Hz, la línea base, etc.), y por otro lado están las perturbaciones de origen fisiológico como los de la electromiografía (EMG). La reducción del ruido en el ECG ha sido uno de los principales campos de investigación en las últimas décadas, ya que una adecuada reducción permite realizar un buen pre-procesado de la señal, extrayendo de ésta la máxima cantidad de información posible y eliminando la no deseable. El uso de imágenes de representación de tiempo-frecuencia (t-f) como la entrada directa al clasificador es lo novedoso de esta tesis doctoral. Se plantea la hipótesis de que este método facilita mejorar los resultados de la clasificación ya que permite eliminar la extracción de características típicas, y su correspondiente pérdida de información, que además se utilizan para la evaluación y la comparación con otros autores. Materiales y Métodos: se ha utilizado las bases de datos estándar del MIT-BIH Malignant Ventricular Arrhytmia Data base y AHA (2000 series) para obtener los registros de las señales ECG, creando a partir de ellos un conjunto de entrenamiento y uno de prueba para los algoritmos de clasificación empleados. Un total de 24 registros de monitorización continua (22 registros de MIT-BIH más dos adicionales de la base de datos AHA) se ha empleado, con frecuencia de muestreo de 125 Hz. Como método se ha implementado un algoritmo de filtro, con el fin de reducir la línea base, se desarrolla un enventanado que indica el comienzo de la Ventana de tiempo (Vt) de la señal del ECG. A cada ventana obtenida se le aplicó la Transformada de Hilbert (TH), después se le aplicó la RTF como entrada a los cinco clasificadores: las Redes Neuronales Artificiales de clasificación (ANNC-Artificial Neural Networks Classification), máquina de vector de soporte de tipo Smooth (SSVM-Smooth Support Vector Machine), (BAGG-Bagging), regresión logística (L2_RLR-L_2-Regularized Logistic Regression) y K vecinos más cercanos (KNN-K Nearest Neighbors). Se realizó sus respectivos entrenamientos y pruebas individuales eligiendo el clasificador KNN por su mejor calidad de detección. La RTF fue convertida en Imagen de RTF (IRTF) e IRTF de dimensionalidad reducida mediante técnicas de reducción del tamaño de imágenes (Media de la Intensidad de los Píxeles (MIP), KNN, Bilineal, Bicúbica) y de la técnica de Selección de Características (SC) de tipo (SFS-Sequential Forward Selection). Se realizaron combinaciones de los algoritmos de clasificación al aplicarse sobre un mismo conjunto de datos (IRTF, IRTF reducida, SC), con el fin de comparar el comportamiento entre ellos y con los resultados logrados de los clasificadores individuales. Estas estrategias y metodologías utilizadas fueron comparadas con diferentes métodos citados en la bibliografía y así comprobar en qué medida los resultados obtenidos apoyan nuestra hipótesis. Resultados: usando parámetros de evaluación del rendimiento (sensibilidad, especificidad y exactitud) como metodología para validar los resultados que obtuvo cada una de las estrategias empleadas, se encontró que el clasificador KNN alcanza el mejor rendimiento para RTF. Se logró para ‘FV’ una sensibilidad del 94,97% y una especificidad global del 99,27%, exactitud global del 98,47 %, y para ‘TV’ una sensibilidad del 93,47%, especificidad global del 99,39%, exactitud global del 98,97% y un tiempo de ejecución 0,1763s. Los principales resultados de la clasificación para la detección de FV obtenidos usando la técnica IRTF reducida (MIP) como entrada al clasificador KNN, mostraron un 88,27% de sensibilidad, 98,22% de especificidad global y 96,35% de exactitud global. En el caso de ‘TV’ 88,31% de sensibilidad, 98,80% de especificidad global, 98,05% de exactitud global y un tiempo de ejecución 0,024s. Al realizar combinaciones de los clasificadores, se obtuvo que la combinación ANNC_KNN_ANNC al utilizar el Método de Jerárquica (MJ) dieron una sensibilidad del 92,14%, especificidad del 98,07% y 97,07% de exactitud global para ‘FV’, una sensibilidad del 89,03%, una especificidad del 80,78%, 98,08% de exactitud global para ‘TV’ y un tiempo de ejecución entre [0,0239s; 0,0241s]. Conclusiones: la clasificación realizada en la discriminación de FV y TV demostró cómo se comportan los distintos algoritmos de clasificación tanto individuales como combinados al aplicarse sobre un mismo conjunto de características. Los resultados obtenidos mediante el algoritmos de combinación ANNC_KNN_ANNC usando los datos de IRTF reducidas fueron mejores en la detección comparado con los obtenidos mediante los algoritmos utilizados individualmente y otros multiclasificadores aplicando sobre un mismo conjunto de datos de IRTF reducidas. Además al comparar los resultados de la combinación con los obtenidos mediante KNN empleando la RTF y IRTF no reducidas son ligeramente inferiores en combinación, pero en cambio se obtiene un tiempo de ejecución menor, por lo que es de mejor utilidad para sistemas de detección en tiempo real. Después de un largo análisis es posible concluir que la metodología propuesta brinda información útil para la detección de FV con un bajo tiempo de cómputo, la cual la puede separar satisfactoriamente del resto de patologías cardiacas a la hora de diagnosticar, mejorando significativamente las posibilidades del paciente de ser manejado eficazmente al presentar un episodio con alguna de estas arritmias, lo que convierte a este trabajo en una fuente de aporte clínico en la ayuda para el diagnóstico de arritmias.Sudden death is a natural, unexpected and rapid death that occurs within a time frame of 24 Hours after the beginning of the pathological process. The most common causes of sudden death are Cardiovascular Diseases (CVD) that happen to be among the leading causes of death worldwide. In 2012, the World Health Organization (WHO) recorded 17.5 million CVD deaths, accounting for 31% of all deaths recorded in the world. One of the cardiovascular diseases with the highest mortality is Ventricular Fibrillation (VF), which is a cardiac arrhythmia caused by a disorganized electrical activity in the heart. During VF, the ventricles contract asynchronously causing an absence of an effective beat as well as a failure of blood pumping. This could result in a sudden death of the patient, if not treated properly within a few minutes. Defibrillation is the only definitive treatment of VF. It consists of the application of a high-energy electric shock to the patient's chest, thus restarting the normal cardiac electrical activity. The success of defibrillation is Inversely proportional to the interval of time it takes from the beginning of the episode to the application of the electrical charge. There are many difficulties in diagnosing VF: on the one hand there are some Intrinsic characteristics of the VF (lack of organization, irregularity, etc.), and on the other, there is a great similarity between VF and other cardiac pathologies including Ventricular Tachycardia (VT). The differentiation between VT and VF is quite complex. A wrongful diagnosis of VT instead of VF can cause serious injuries when applying the therapy to the patient. VT treatment consist of giving a high voltage electric shock to the patient, which could cause a VF. Conversely, if the VT is incorrectly interpreted as a VF, the result might be also dangerous for the patient´s life. Therefore, an effective detection method to distinguish VF from VT is very important in clinical research. In order to diagnose and treat cardiovascular diseases (for example VF), two major groups of diagnostic methods are established in cardiology: Invasive and noninvasive diagnoses. Invasive techniques require the introduction of catheters into the body, to measure the pressures in the cardiac chambers in order to record the electrical activity. Non-invasive techniques are focused on characterizing the pathophysiological state of the heart through electrodes placed directly on the patient's skin. The electrocardiogram (ECG) is a non invasive, low cost, examination which has been used as the basic diagnostic method for cardiac conduction disorders, by studying the frequency and the morphology of different waves that constitute the cardiac cycle. The ECG analysis is a good source of information to detect different types of heart disease. Due to the fact that the ECG signal is a non-stationary random signal, the time domain analysis does not prove to be sufficiently sensitive to the distortions of the waveforms on the ECG. However, these methods not always show all the information that can be extracted from ECG signals. Thereby, the frequency information, which shows additional data from the signal, is lost. Diagnosis within the frequency domain uses methods such as the fourier transform.Therefore, an analysis in the frequency domain allows to determine the frequencies within the ECG signal. On the other hand, using a frequency domain method losses the time information from the signal, resulting in a very limited method which is not useful for the analysis of non-stationary signals. Several studies have used mathematical models that combine time and spectral information in the same representation. This is Time-Frequency Representation (TFR) technique, very important in the treatment of non-stationary signals such as the ECG signal, as it distributes signal energy in a two-dimensional time-frequency space. In addition, multiple factors affect the acquisition and recording of the ECG signal: on the one hand there is the influence of the environment (50-60 Hz interference from the electrical grid, baseline, etc.), and on the other hand, physiological disturbances such as an electromyography (EMG). In the last decades, ECG noise reduction has been one of the main fields of research, since an adequate reduction of noise allows a good pre-processing of the signal, extracting from it the maximum amount of relevant information while eliminating the irrelevant one. The use of time-frequency representation images (t-f) as the direct input to the classifier is the novelty of this doctoral thesis. It is hypothesized that this method makes it easier to improve the classification results by eliminating the extraction of typical characteristics, and their corresponding loss of information. They are also used for evaluation and comparison with other authors. Materials and Methods: MIT-BIH´s Malignant Ventricular Arrhytmia and AHA (2000 series) standard data bases have been used to obtain the records of ECG signals, creating from them one set for training and one for testing the classification algorithms used. A total of 24 monitoring records (22 MIT-BIH records plus two additional from the AHA data) have been used, with a sampling frequency of 125 Hz. As part of the method a filter algorithm has been implemented in order to reduce the base line. A report that indicates the beginning of the time Window (tW) of the ECG signal is developed. First, the Hilbert Transform (HT) was applied to each window obtained. Then the RTF was applied as input to the five classifiers: Artificial Neural Networks Classification (ANNC), Smooth-type support vector machine (SSVM), bagging (BAGG), \u1d43f2Regularized Logistic Regression (L2_RLR) and K Nearest Neighbors (KNN).Their respective training and individual tests were made by choosing the KNN classifier for best quality detection. The RTF was converted into an IRTF and a reduced dimensionality IRTF by means of image size reduction techniques (Average Intensity of the Pixels (AIP), KNN, Bilineal, Bicubic) and the techniques of Selection of Characteristics (SC), specifically the Sequential Forward Selection technique (SFS). Combinations of the classification algorithms were performed when applied over the same set of data (TFRI, reduced TFRI, SC), in order to compare their behavior with the results obtained from the individual classifiers. These strategies and methodologies were compared with different methods cited in the literature to verify to what extent the results obtained support our hypothesis. Results: using performance evaluation parameters (sensitivity, specificity and accuracy) as a methodology to validate the results obtained by each one of the strategies employed, it was found that the KNN classifier achieves the best performance for TFR. For 'VF' it was obtained a sensitivity of 94.97% an overall specificity of 99.21%, and an overall accuracy of 98.47%. Whereas for 'VT, it was obtained a Sensitivity of 93.47%, an overall specificity of 99.39%, and an overall accuracy of 98.97% within a time of execution 0,1763s. The main results of the classification for the detection of VF obtained using the reduced TFRI technique (AIP) as input to the KNN classifier, showed an 88.27% of sensitivity, a 98.22% of overall specificity and a 96.35% of overall accuracy. For ´VT', it was obtained an 88.31% sensitivity, a 98.80% for global specificity, and a 98.05% of global accuracy within a runtime of 0.024s. When the classifiers were combined, it resulted that the ANNC_KNN_ANNC combination when using the Hierarchical Method (MJ) gave a sensitivity of 92.6%, a specificity of 98.68% and an overall accuracy of 97.52% for 'VF'. Whereas a Sensitivity of 89.3%, a specificity of 99.01%, and a 98.32% of overall accuracy for 'VT 'were obtained with a runtime between [0,0487s; 0,0492s]. Conclusions: the classification of VF and VT discrimination showed how the different classification algorithms (both individual and combined) behave over the same set of characteristics. The results obtained by the ANNC_KNN_ANNC combination of algorithms using the reduced TFRI data were better at detection when compared to those obtained by the algorithms used individually as well as to other multi classifiers applied over a single set of reduced TFRI data. In addition, when comparing the results of the combination with those obtained by the KNN using the non-reduced TFR and the TFRI, the latter are slightly lower. On the other hand, a shorter execution time is obtained, so the method is more useful for Real-time detection systems. After a long analysis it is possible to conclude that the proposed methodology provides useful information for the detection of VF with a low computation time. Furthermore it can separate satisfactorily the VF from the rest of cardiac pathologies at the time of diagnosis, significantly improving the patient's ability to be effectively treated when presenting an episode with one of these arrhythmias. Thus making this work a source of clinical help in the diagnosis of arrhythmias

The Application of Computer Techniques to ECG Interpretation

This book presents some of the latest available information on automated ECG analysis written by many of the leading researchers in the field. It contains a historical introduction, an outline of the latest international standards for signal processing and communications and then an exciting variety of studies on electrophysiological modelling, ECG Imaging, artificial intelligence applied to resting and ambulatory ECGs, body surface mapping, big data in ECG based prediction, enhanced reliability of patient monitoring, and atrial abnormalities on the ECG. It provides an extremely valuable contribution to the field

Ventricular Fibrillation detection using time-frequency and the KNN classifier without parameter extraction

[ES] Este trabajo propone la detección de FV y su discriminación de TV y otros ritmos cardiacos basándose en la representación tiempo-frecuencia del ECG y su conversión en imágen como entrada a un clasificador de vecinos más cercanos (KNN) sin necesidad de extracción de parámetros adicionales. Tres variantes de datos de entrada al clasificador son evaluados. Los resultados clasifican la señal en cuatro clases diferentes: ’Normal’ para latidos con ritmo sinusal, ’FV’ para fibrilación ventricular, ’TV’ para taquicardia ventricular y ’Otros’ para el resto de ritmos. Los resultados para detección de FV mostraron 88,27% de sensibilidad y 98,22% de especificidad para la entrada de imágen equivalente reducida que es la más rápida computacionalmente a pesar de obtener resultados de clasificación ligeramente inferiores a las representaciones no reducidas. En el caso de TV, se alcanzó un 88,31% de sensibilidad y 98,80% de especificidad, un 98,14% de sensibilidad y 96,82% de especificidad para ritmo sinusal normal y 96,91% de sensibilidad con 99,06% de especificidad para la clase ’Otros’. Finalmente, se realiza una comparación con otros algoritmos.[EN] This work describes new techniques to improve VF detection and its separation from Ventricular Tachycarida (VT) and other rhythms. It is based on time-frequency representation of the ECG and its use as input in an automatic classifier (K-nearest neighbours - KNN) without any further signal parameter extraction or additional characteristics. For comparison purposes, three time-frequency variants are analysed: pseudo Wigner-Ville representation (RTF), grey-scale image obtained from RTF (IRTF), and reduced image from IRTF (reduced IRTF). Four types of rhythms (classes) are defined: ’Normal’ for sinus rhythm, ’VT’ for ventricular tachycardia, ’VF’ for ventricular fibrillation and ’Others’ for the rest of rhythms. Classification results for VF detection in case of reduced IRTF are 88.27% sensitivity and 98.22% specificity. In case of VT, 88.31% sensitivity and 98.80% specificity is obtained, 98.14% sensitivity and 96.82% specificity for normal rhythms, and 96.91% sensitivity and 99.06% specificity for other rhythms. Finally, results are compared with other authors.Mjahad, A.; Rosado Muñoz, A.; Bataller Mompeán, M.; Francés Víllora, JV.; Guerrero Martínez, JF. (2017). Detección de Fibrilación Ventricular Mediante Tiempo-Frecuencia y Clasificador KNN sin Extracción de Parámetros. Revista Iberoamericana de Automática e Informática industrial. 15(1):124-132. https://doi.org/10.4995/riai.2017.8833OJS124132151Classen, T. A. C. M., Mecklenbrauker, W. F. G., 1980. The Wigner Distribution: A Tool for Time-Frequency Signal Analysis - Part 2: Discrete-Time Signals. Philips Journal of Research 35, 276-350.Cohen, L., Jul 1989a. Time frequency distributions a review. Proceedings of the IEEE 77 (7), 941-981. https://doi.org/10.1109/5.30749Cohen, L., 1989b. Time-frequency distributions-a review. Proceeding of the IEEE 77 (7), 941-981. https://doi.org/10.1109/5.30749Elhaj, F. A., Salim, N., Harris, A. R., Swee, T. T., Ahmed, T., 2016. Arrhythmia recognition and classification using combined linear and nonlinear features of ECG signals. Computer Methods and Programs in Biomedicine 127, 52- 63. https://doi.org/10.1016/j.cmpb.2015.12.024Hlawatsch, F., Boudreaux-Bartels, G. F., April 1992. Linear and quadratic time-frequency signal representations. IEEE Signal Processing Magazine 9 (2), 21-67. https://doi.org/10.1109/79.127284Ibaida, A., Khalil, I., Aug 2010. 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Type-2 fuzzy system for ECG arrhythmic classification

10.1109/FUZZY.2007.4295478IEEE International Conference on Fuzzy Systems-PIFS

Interval type-2 fuzzy system for ECG arrhythmic classification

10.1007/978-3-540-89968-6_15Studies in Fuzziness and Soft Computing242297-31