Electrocardiograms (ECGs) provide non-invasive measurements of heart activity and are established tools for detecting cardiac arrhythmias. Although supervised machine learning has emerged as a promising approach for automated heartbeat classification, substantial variations in ECG signals across individuals and leads, combined with inconsistent labeling standards and dataset biases, make it difficult to develop generalizable models. Dimensionality reduction maps high-dimensional data into a lower-dimensional space while preserving the underlying structure, enabling visualization and pattern discovery. Conventional methods, e.g., principal component analysis, prioritize large variances and typically overlook subtle yet clinically relevant patterns. Here, we show that nonlinear dimensionality reduction (NLDR) algorithms, e.g., t-SNE and UMAP, can identify medically relevant features in ECG signals without pretraining or prior information. Using the MIT-BIH Arrhythmia Database, we show that: a) applying NLDR to a mixed population of heartbeats reveals inter-individual morphological differences, as signals from the same person cluster together in latent spaces; and b) applying NLDR to heartbeats of a single individual separates normal beats from arrhythmias into distinct clusters, identifiable in an unsupervised manner. To our knowledge, this is the first systematic evaluation of NLDR for unsupervised arrhythmia detection. Both UMAP and t-SNE achieved trustworthiness scores >=0.95, indicating that local neighborhoods are well preserved in the embedding. Classification on 2D embeddings outperforms the original high-dimensional space, with a k-NN classifier discriminating individual recordings with >=80% accuracy and identifying arrhythmias with median accuracy >=98% and median F1-score >=85%. These results show that NLDR holds much promise for cardiac monitoring and personalized healthcare.