The Shape of Data

5 Geometry in Data Science

In this chapter, we’ll explore several tools from geometry: we’ll look at distance metrics and their use in k-nearest neighbor algorithms; we’ll discuss manifold learning algorithms that map high-dimensional data to potentially curved lower-dimensional manifolds; and we’ll see how to apply fractal geometry to stock market data. The motivation for this chapter follows, among other things, from the manifold hypothesis, which posits that real-world data often has a natural dimensionality lower than the dimensionality of the dataset collected. In other words, a dataset that has 20 variables (that is, a dimensionality ...