MystiQ is a system that uses probabilistic query semantics [3] to find answers in large numbers of data sources of less than perfect quality. There are many reasons why the data originating from many different sources may be of poor quality, and therefore difficult to query: the same data item may have different representation in different sources; the schema alignments needed by a query system are imperfect and noisy; different sources may contain contradictory information, and, in particular, their combined data may violate some global integrity constraints; fuzzy matches between objects from different sources may return false positives or negatives. Even in such environment, users some-times want to ask complex, structurally rich queries, using query constructs typically found in SQL queries: joins, subqueries, existential/universal quantifiers, aggregate and group-by queries: for example scientists may use such queries to query multiple scientific data sources, or a law enforcement agency may use it in order to find rare associations from multiple data sources. If standard query semantics were applied to such queries, all but the most trivial queries will return an empty answer.

This paper proposes an algorithm to hierarchically cluster documents. Each cluster is actually a cluster of documents and an associated cluster of words, thus a document-word co-cluster. Note that, the vector model for documents creates the document-word matrix, of which every co-cluster is a submatrix. One would intuitively expect a submatrix made up of high values to be a good document cluster, with the corresponding word cluster containing its most distinctive features. Our algorithm looks to exploit this. We have defined matrix density, and our algorithm basically uses matrix density considerations in its working.The algorithm is a partitional-agglomerative algorithm. The partitioning step involves the identification of dense submatrices so that the respective row sets partition the row set of the complete matrix. The hierarchical agglomerative step involves merging the most similar submatrices until we are down to the required number of clusters (if we want a flat clustering) or until we have just the single complete matrix left (if we are interested in a hierarchical arrangement of documents). It also generates apt labels for each cluster or hierarchy node. The similarity measure between clusters that we use here for the merging cleverly uses the fact that the clusters here are co-clusters, and is a key point of difference from existing agglomerative algorithms. We will refer to the proposed algorithm as RPSA (Rowset Partitioning and Submatrix Agglomeration). We have compared it as a clustering algorithm with Spherical K-Means and Spectral Graph Partitioning. We have also evaluated some hierarchies generated by the algorithm.