The past decade has witnessed developments in the field of biology that have brought about profound changes in understanding the dynamic of disease and of biological systems in general. New technology has given biologists an unprecedented wealth of information, but it has generated data that is difficult to analyze mathematically, thereby making its biological interpretation challenging. Essentially the data lives in extremely high dimensional space, making it so sparce that traditional analysis methods have difficulty identifying meaningful patterns.

These challenges have given rise to a myriad novel exciting mathematical challenges and have provided an impetus to modify and adapt traditional mathematics tools, as well as develop novel techniques to tackle the data analysis problems raised in biology.

I will discuss a general approach to address some of these computational challenges by way of data decompositions that highlight specific biologically driven questions. In conjunction with modern applied topological data analysis tools, these data decompositions have been applied in a wide range of settings, in particular for the study of the biology of disease. I will discuss some of these applications, including the use of data decompositions to discover a new type of breast cancer and the associated biology that drives the disease; identifying the driving mechanisms in acute myeloid leukemia; and network decompositions to understand the intricate interraction between host and pathogen in salmonella infections.

These examples show how data decompositions can help circumvent the “curse of high dimensionality” in understanding data analysis in the context of biological systems as well as a multitude of other data-driven areas of study.

Note: there is no need to understand biology prior to listening to this talk.