Finding a good neighbor, near and fast

You haven't read it yet, but you can already tell this article is going to be one long jumble of words, numbers, and punctuation marks. Indeed, but look at it differently, as a text classifier would, and you will see a single point in high dimension, with word frequencies acting as coordinates. Or take the background on your flat panel display: a million colorful pixels teaming up to make quite a striking picture. Yes, but also one single point in 106-dimensional space - that is, if you think of each pixel's RGB intensity as a separate coordinate. In fact, you don't need to look hard to find complex, heterogeneous data encoded as clouds of points in high dimension. They routinely surface in applications as diverse as medical imaging, bioinformatics, astrophysics, and finance.