HMM-based Supervised Machine Learning Framework for the Detection of ECG R Peak Locations
چارچوب یادگیری ماشین نظارت شده مبتنی بر HMM مبتنی برای تشخیص مکان های اوج ECG-2019
Objective: Fetal Electro Cardiogram (fECG) provides critical information on the wellbeing of a foetus heart in its developing stages in the mother’s womb. The objective of this work is to extract fECG which is buried in a composite signal consisting of itself, maternal ECG (mECG) and noises contributed from various unavoidable sources. In the past, the challenge of extracting fECG from the composite signal was dealt with by Stochastic Weiner filter, model-based Kalman filter and other adaptive filtering techniques. Blind Source Separation (BSS) based Independent Component Analysis (ICA) has shown an edge over the adaptive filtering techniques as the former does not require a reference signal. Recently, data-driven machine learning techniques e.g., adaptive neural networks, adaptive neuro-fuzzy inference system, support vector machine (SVM) are also applied. Method: This work pursues hidden Markov model (HMM)-based supervised machine learning frame-work for the determination of the location of fECG QRS complex from the composite abdominal signal. HMM is used to model the underlying hidden states of the observable time series of the extracted and separated fECG data with its QRS peak location as one of the hidden states. The state transition probabilities are estimated in the training phase using the annotated data sets. Afterwards, using the estimated HMM networks, fQRS locations are detected in the testing phase. To evaluate the proposed technique, the accuracy of the correct detection of QRS complex with respect to the correct annotation of QRS complex location is considered and quantified by the sensitivity, probability of false alarm, and accuracy. Results: The best results that have been achieved using the proposed method are: accuracy – 97.1%, correct detection rate (translated to sensitivity) – 100%, and false alarm rate – 2.89%.
Keywords: fECG | mECG | Machine learning | HMM | Accuracy | Sensitivity
Application of multi-objective optimization to blind source separation
استفاده از بهینه سازی چند هدفه برای جداسازی منبع کور-2019
Several problems in signal processing are addressed by expert systems which take into account a set of priors on the sought signals and systems. For instance, blind source separation is often tackled by means of a mono-objective formulation which relies on a separation criterion associated with a given property of the sought signals (sources). However, in many practical situations, there are more than one property to be exploited and, as a consequence, a set of separation criteria may be used to recover the original signals. In this context, this paper addresses the separation problem by means of an approach based on multi-objective optimization. Differently from the existing methods, which provide only one estimate for the original signals, our proposal leads to a set of solutions that can be utilized by the system user to take his/her decision. Results obtained through numerical experiments over a set of biomedical signals highlight the viability of the proposed approach, which provides estimations closer to the mean squared error solutions compared to the ones achieved via a mono-objective formulation. Moreover, since our proposal is quite general, this work also contributes to encourage future researches to develop expert systems that exploit the multi-objective formulation in different source separation problems.
Keywords: Blind source separation | Multi-objective optimization | Evolutionary algorithms
Geometrical and topological approaches to Big Data
روش هندسی و توپولوژیکی به داده های بزرگ-2017
Modern data science uses topological methods to find the structural features of data sets before further supervised or unsupervised analysis. Geometry and topology are very natural tools for analysing massive amounts of data since geometry can be regarded as the study of distance functions. Mathematical formalism, which has been developed for incorporating geometric and topological techniques, deals with point cloud data sets, i.e. finite sets of points. It then adapts tools from the various branches of geometry and topology for the study of point cloud data sets. The point clouds are finite samples taken from a geometric object, perhaps with noise. Topology provides a formal language for qualitative mathematics, whereas geometry is mainly quantitative. Thus, in topology, we study the relationships of proximity or nearness, without using distances. A map between topological spaces is called continuous if it preserves the nearness structures. Geometrical and topological methods are tools allowing us to analyse highly complex data. These methods create a summary or compressed representation of all of the data features to help to rapidly uncover particular patterns and relationships in data. The idea of constructing summaries of entire domains of attributes involves understanding the relationship between topological and geometric objects constructed from data using various features. A common thread in various approaches for noise removal, model reduction, feasibility reconstruction, and blind source separation, is to replace the original data with a lower dimensional approximate representation obtained via a matrix or multi-directional array factorization or decomposition. Besides those transformations, a significant challenge of feature summarization or subset selection methods for Big Data will be considered by focusing on scalable feature selection. Lower dimensional approximate representation is used for Big Data visualization. The cross-field between topology and Big Data will bring huge opportunities, as well as challenges, to Big Data communities. This survey aims at bringing together state-of-the-art research results on geometrical and topological methods for Big Data.
Keywords:Big Data|Industry 4.0|Topological data analysis|Persistent homology|Dimensionality reduction|Big Data visualization