Chapter 4 Clustering - Definitions and Basic Algorithms

x Do not read this story; turn the page quickly. The story may upset you. Anyhow, you probably know it already. It is a very disturbing story. Everyone knows it. The glory and the crime of Commander Suzdal have been told in a thousand different ways. Don't let yourself realize that the story is the truth. It isn't. not at all. There's not a bit of truth to it. There is no such planet as Arachosia, no such people as klopts, no such world as Catland. These are all just imaginary, they didn't happen, forget about it, go away and read something else. In this chapter, we will initiate our discussion of clustering. Clustering is one of the most fundamental computational tasks, but frustratingly, one of the fuzziest. It can be stated informally as: " Given data, find interesting structure in the data. Go! " The fuzziness arise naturally from the requirement that it would be " interesting " , as this is not well defined and depends on human perception which is sometime impossible to quantify clearly. Similarly, what is " structure " is also open to debate. Nevertheless, clustering is inherent to many computational tasks like learning, searching and data-mining. Empirical study of clustering concentrates on trying various measures for the clustering, and trying out various algorithms and heuristics to compute these clusterings. See bibliographical notes for some relevant references. Here, we will concentrate on some well defined clustering tasks, including k-center clustering, k-median clustering, and k-means clustering, and some basic algorithms for these problems. A clustering problem is usually defined by a set of items, and a distance function defined between these items. While these items might be points in IR d and the distance function is just the regular x This work is licensed under the Creative Commons Attribution-Noncommercial 3.0 License. To view a copy of this license, visit