# Geometric Stream Mining

**DOI:**https://doi.org/10.1007/978-1-4899-7993-3_180-2

## Definition

Let *P* = {*p*_{1}, *p*_{2}, …}be a stream of points in the metric space (*X*, *L*_{q}). Usually, *X* = *ℝ*^{d} or *X* = {1, … , *U*}^{d} (discrete case), and *L*_{q} = *L*_{2} is the Euclidean distance. The set *P* is called a *spatial data stream*. Geometric stream mining algorithms compute the (approximate) answer to a geometric question over the subset of *P* seen so far. For example, the *diameter* problem asks to maintain the pair of points that are farthest away in the current stream. A more comprehensive list of problems is presented later.

## Historical Background

Geometric algorithms in the offline setting have been extensively studied over the past decades. Their applications encompass many fields, such as image processing, robotics, data mining, or VLSI design. For an introduction to computational geometry, refer to the book [8]. On the other hand, research on spatial data streams is a recent development. Shortly after the first results on numeric data streams appeared, a slew of papers argued that in many...

## Keywords

Query Point Minimum Span Tree Problem Range Counting Offline Algorithm Spatial Stream## Recommended Reading

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