Facing a problem of clustering amultimillion-data-point collection, amachine learning practitioner may choose to apply the simplest clustering method possible, because it is hard to believe that fancier methods can be applicable to datasets of such scale. Whoever is about to adopt this approach should first weigh the following considerations:

• Simple clustering methods are rarely effective. Indeed, four decades of research would not have been spent on data clustering if a simple method could solve the problem. Moreover, even the simplest methods may run for long hours on a modern PC, given a large-scale dataset. For example, consider a simple online clustering algorithm (which, we believe, is machine learning folklore): first initialize k clusters with one data point per cluster, then iteratively assign the rest of data points into their closest clusters (in the Euclidean space). If k is small enough, we can run this algorithm on one machine, because it is unnecessary to keep the entire data in RAM. However, besides being slow, it will produce low-quality results, especially when the data is highly multi-dimensional.

• State-of-the-art clustering methods can scale well, which we aim to justify in this chapter.

With the deployment of large computational facilities (such as Amazon.com's EC2, IBM's BlueGene, and HP's XC), the Parallel Computing paradigm is probably the only currently available option for tackling gigantic data processing tasks. Parallel methods are becoming an integral part of any data processing system, and thus getting special attention (e.g., universities introduce parallel methods to their core curricula; see Johnson et al., 2008).