Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a \"digitization\" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the \"shape\" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics.

Rich sources of obesity-related data arising from sensors, smartphone apps, electronic medical health records and insurance data can bring new insights for understanding, preventing and treating obesity. For such large datasets, machine learning provides sophisticated and elegant tools to describe, classify and predict obesity-related risks and outcomes. Here, we review machine learning methods that predict and/or classify such as linear and logistic regression, artificial neural networks, deep learning and decision tree analysis. We also review methods that describe and characterize data such as cluster analysis, principal component analysis, network science and topological data analysis. We introduce each method with a high-level overview followed by examples of successful applications. The algorithms were then applied to National Health and Nutrition Examination Survey to demonstrate methodology, utility and outcomes. The strengths and limitations of each method were also evaluated. This summary of machine learning algorithms provides a unique overview of the state of data analysis applied specifically to obesity.