A note on terminology.

An alternative definition of hard clustering is that a document can be a full member of more than one cluster. Partitional clustering always refers to a clustering where each document belongs to exactly one cluster. (But in a partitional hierarchical clustering (Chapter 17 ) all members of a cluster are of course also members of its parent.) On the definition of hard clustering that permits multiple membership, the difference between soft clustering and hard clustering is that membership values in hard clustering are either 0 or 1, whereas they can take on any non-negative value in soft clustering.

Some researchers distinguish between exhaustive clusterings that assign each document to a cluster and non-exhaustive clusterings, in which some documents will be assigned to no cluster. Non-exhaustive clusterings in which each document is a member of either no cluster or one cluster are called exclusive . We define clustering to be exhaustive in this book.