Chapter 30 - Comparing Data Streams Using Hamming Norms (How to Zero In)

Abstract

Data streams are fundamental to many data processing applications. Internet routers produce large-scale diagnostic data streams. Such streams are rarely stored in traditional databases and, instead, must be processed “on the fly” as they are produced. Similarly, sensor networks produce multiple data streams of observations from their sensors. There is growing focus on manipulating data streams, and hence, there is a need to identify basic operations of interest in managing data streams, and to support them efficiently. The chapter proposes computation of the Hamming norm as a basic operation of interest. The Hamming norm formalizes ideas that are used throughout data processing. When applied to a single stream, the Hamming norm gives the number of distinct items that are present in that data stream, which is a statistic of great interest in databases. When applied to a pair of streams, the Hamming norm gives an important measure of (dis)similarity: the number of unequal item counts in the two streams. Hamming norms have many uses in comparing data streams. For many applications that produce data streams, it is useful to visualize the underlying data seen so far or underlying state of the system as a very high dimensional vector.