# Comparison of Dimensionality Reduction Approaches and Logistic Regression for ECG Classification
## 1 Introduction  
Cardiac arrhythmias are electrical disorders of the heart rhythm and are a leading cause of morbidity and mortality worldwide [1, 2]. Common arrhythmias include sinus bradycardia (SB), atrial fibrillation (AFIB), supraventricular tachycardia (SVT), and sinus tachycardia (ST), each exhibiting distinct electrocardiographic signatures. The electrocardiogram (ECG) remains the gold standard for the non-invasive detection of such abnormalities, capturing key waveform elements such as the P wave, QRS complex, and T wave [3, 4].  
To enable automated and accurate ECG interpretation, the availability of robust, well-annotated databases is crucial, especially for training supervised machine learning (ML) models. Datasets such as the 2020 SPH ECG dataset [5] provide a large volume of labeled signals covering a broad spectrum of arrhythmias. Compared to the historically significant MIT-BIH Arrhythmia Database, SPH offers a considerably larger sample size and a wider diversity of rhythm classes, making it particularly suitable for modern classification pipelines. However, SPH remains less studied than MIT-BIH in classical ML settings, offering an opportunity to investigate lightweight alternatives to deep learning.  
Over the past decade, several machine learning techniques--including support vector machines, decision trees, and deep learning models such as convolutional neural networks(CNNs) and recurrent neural networks (RNNs)--have been explored for arrhythmia classification [6; 7; 8]. While deep learning models often achieve high classification accuracy, they require substantial computational resources, large volumes of raw data, and are typically difficult to interpret, challenges that limit their immediate applicability in clinical practice. In contrast, interpretable models such as logistic regression (LR) and K-Nearest Neighbors (KNNs), when coupled with dimensionality reduction techniques, can offer comparable performance with significantly lower complexity and enhanced transparency. This study investigates the classification of five clinically important heart rhythms: SB, SR (considered normal), AFIB, ST, and SVT. While some of these have been addressed independently in the literature, to our knowledge, their combined classification using low-dimensional models has not been extensively studied. Our work bridges this gap by comparing the performance of interpretable models under both classical and Bayesian frameworks.  
Specifically, we evaluate two dimensionality reduction techniques--Principal Component Analysis (PCA) and Uniform Manifold Approximation and Projection (UMAP)--in combination with the KNN classifier. These are contrasted with logistic regression models implemented using both maximum likelihood estimation and Bayesian inference (with informative and non-informative priors). The choice of these methods is motivated by their computational efficiency, interpretability, and suitability for deployment in constrained environments such as point-of-care devices. We assess all models using common classification metrics, including positive predictive value (PPV), negative predictive value (NPV), sensitivity, specificity, accuracy, and F1-score.