Large-Scale Mining of Co-occurrences: Challenges and Solutions

The ability to extract frequent pairs from a set of baskets (or frequent word co-occurrences from a set of documents) is one of the fundamental building blocks of data mining. When the number of items in a given basket is relatively small the problem is trivial. Even when dealing with millions of baskets it is still trivial providing that the number of unique items in the basket set is small. The problem becomes much more challenging when we deal with millions of baskets, each containing hundreds of items that are part of a set of millions of potential items. Especially when we are looking for highly correlated results at extremely low support levels. A particularly difficult case is when "items" are words and "baskets" are long documents in a very large text corpus. For 17 years the Direct Hashing and Pruning Park Chen Yu (PCY) Algorithm has been the principal technique used when there are billions of potential pairs that need to be counted. In this paper we show new approaches that allow us to take full advantage of both multi-core and multi-CPU setups for cases where PCY fails and Map-Reduce struggles, offering excellent performance scaling when the number of processors, unique items and items per transaction are at their highest. We believe that our approaches have much broader applicability in the field of co-occurrence counting, and can be used to generate much more interesting results when mining very large data sets.