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Big Data: Applying Geometry to Understand Data Sets
Think data and you think about statistics and numerical algorithms that process and squeeze data for information. Computer scientists and number crunchers reign in this world while advanced mathematical techniques are often sidelined.
One area of mathematics, topology and advanced geometry, is attracting attention as a possible way to study large data sets.
Topological Data Analysis (TDA) is the name being given to a branch of statistics that is focused on addressing the challenges of analyzing large data sets from a geometric perspective. The field tries to develop tools that can identify and classify geometric characteristics of data sets. TDA attempts to recognize “shapes” in the data that can give overall insight into the science or process that is creating the data.
Topological Data Analysis (TDA) is the name being given to a branch of statistics that is focused on addressing the challenges of analyzing large data sets from a geometric perspective. The field tries to develop tools that can identify and classify geometric characteristics of data sets. TDA attempts to recognize “shapes” in the data that can give overall insight into the science or process that is creating the data.
TDA is being applied to Big Data problems like fraud detection, pharmaceutical development and understanding diseases like cancer.
Noah Giansiracusa, Algebraic Geometer, TDA researcher, said that “over the past few years I think the biggest strides TDA has made have been in terms of better interweaving it with other methods and disciplines—so big topics with lots of progress but still room for more have included confidence intervals, distributions of barcodes, feature selection and kernel methods in persistent homology. These are all exciting topics and healthy for the long-term development of TDA.”
