You want to assign things to a set of clusters so that things that share similar properties are grouped closely together. But, we also want those clusters to be as big as possible. We don't want to leave little islands that only have a few things in them.

Take, for example, classification of email messages. Let's say you have a billion email messages and you want to find a way to cluster them automatically into 10 categories. You don't know what the categories are ahead of time. You just have a way of making sure that an email can be represented by a vector of numbers such that two emails that are close together in their meaning and characteristics will have similar numbers.

K-Means clustering solves that problem but is intractable to calculate for large datasets having high dimensionality (such as the email example). My understanding is that E-Means is away to achieve this spectacularly more efficiently than the best alternative previously known.

Impressive results ...