Summarizing data succinctly with the most informative itemsets
ACM Transactions on Knowledge Discovery from Data (TKDD) - Special Issue on the Best of SIGKDD 2011
Summarizing categorical data by clustering attributes
Data Mining and Knowledge Discovery
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A binary matrix has a banded structure if both rows and columns can be permuted so that the non-zero entries exhibit a staircase pattern of overlapping rows. The concept of banded matrices has its origins in numerical analysis, where entries can be viewed as descriptions between the problem variables; the bandedness corresponds to variables that are coupled over short distances. Banded data occurs also in other applications, for example in the physical mapping problem of the human genome, in paleontological data, in network data and in the discovery of overlapping communities without cycles. We study the banded structure of binary matrices, give a formal definition of the concept and discuss its theoretical properties. We consider the algorithmic problems of computing how far a matrix is from being banded, and of finding a good submatrix of the original data that exhibits approximate bandedness. Finally, we show by experiments on real data from ecology and other applications the usefulness of the concept. Our results reveal that bands exist in real datasets and that the final obtained orderings of rows and columns have natural interpretations.