Topological data analysis (TDA) is a recent approach for analyzing and interpreting complex data sets, based on ideas a branch of mathematics called algebraic topology. TDA has proven useful to disentangle non-trivial data structure in a broad range of data analytics problems including the study of cardiovascular signals. This review aims to provide an overview of the application of TDA to cardiovascular signals and its potential to enhance the understanding of cardiovascular diseases and their treatment. We first introduce the concept of TDA and its key techniques, including persistent homology, Mapper, and multidimensional scaling. We then discuss the use of TDA in analyzing various cardiovascular signals, including electrocardiography, photoplethysmography, and arterial stiffness. We also discuss the potential of TDA to improve the diagnosis and prognosis of cardiovascular diseases, as well as its limitations and challenges. Finally, we outline future directions for the use of TDA in cardiovascular signal analysis and its potential impact on clinical practice. Overall, TDA has shown great promise as a powerful tool for the analysis of complex cardiovascular signals and may offer significant insights into the understanding and management of cardiovascular diseases.

Metabolic Syndrome (MetS) is a serious condition that significantly increases the risk of cardiovascular diseases and the severity of type 2 diabetes, also impacting on the development and evolution of other chronic diseases. Predicting metabolic syndrome is a complex task due to the multifactorial nature of this condition, which involves a combination of various risk factors such as abdominal obesity, insulin resistance, dyslipidemia, and hypertension. The complex interplay of these factors makes it challenging to predict the syndrome. Both genetic predisposition and environmental factors also contribute to the development of metabolic syndrome. Metabolic syndrome affects diverse populations with different ethnicities, lifestyles, and socioeconomic backgrounds. Prediction models, in addition, need to account for population heterogeneity and consider variations in risk factors across different groups. The present study analyzed data from participants in a cohort from Mexico City to identify key risk factors in men and women, addressing the presence of unbalanced data. In order to tackle the issues posed by data imbalance data, SMOTE and ADASYN were applied to assess significant differences in the selection of risk factors for MetS prediction. Random Forest and RPART models using ADASYN and SMOTE demonstrated better performance, achieving a balanced accuracy of approximately 87%. In women, they highlighted sleep quality, anxiety factors, tobacco consumption, and nutritional components. In the case of men, stronger associations were identified with the social development index and factors related to gout in parents.