Ayasdi: Topology & Topological Data Analysis

Topology is the branch of pure mathematics that studies the notion of shape. Topology takes on two main tasks, namely the measurement of shape and the representation of shape. Both tasks are meaningful in the context of large, complex, and high dimensional data sets. They permit one to measure shape related properties within the data, such as the presence of loops, and they provide methods for creating compressed representations of data sets that retain features, and which reflect the