Data Structure Description

Streaming algorithms aim to summarize a large volume of data into a compact summary, by maintaining a data structure that can be incrementally modified as updates are observed. They allow the approximation of particular quantities. The AMS Sketch is focused on approximating the sum of squared entries of a vector defined by a stream of updates. This quantity is naturally related to the Euclidean norm of the vector, and so has many applications in high-dimensional geometry, and in data mining and machine learning settings that use vector representations of data. The data structure maintains a linear projection of the stream (modeled as a vector) with a number of randomly chosen vectors. These random vectors are defined implicitly by simple hash functions, and so do not have to be stored explicitly. Varying the size of the sketch changes the accuracy guarantees on the resulting estimation. The fact that the summary is a linear projection means that it can be updated flexibly, and sketches can be combined by addition or subtraction, yielding sketches corresponding to the addition and subtraction of the underlying vectors.