Introduction to algorithms
Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
Indifference Digraphs: A Generalization of Indifference Graphs and Semiorders
SIAM Journal on Discrete Mathematics
A Spectral Algorithm for Seriation and the Consecutive Ones Problem
SIAM Journal on Computing
Modern Information Retrieval
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
ACM '68 Proceedings of the 1968 23rd ACM national conference
PQ-tree algorithms.
A certifying algorithm for the consecutive-ones property
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Permuting Sparse Rectangular Matrices into Block-Diagonal Form
SIAM Journal on Scientific Computing
Model-based overlapping clustering
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
NP-completeness results for edge modification problems
Discrete Applied Mathematics - Special issue: Traces of the Latin American conference on combinatorics, graphs and applications: a selection of papers from LACGA 2004, Santiago, Chile
Nestedness and segmented nestedness
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Using background knowledge to rank itemsets
Data Mining and Knowledge Discovery
Summarising data by clustering items
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part II
Model order selection for boolean matrix factorization
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Tell me what i need to know: succinctly summarizing data with itemsets
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
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A 0--1 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 in this paper 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 ordering of rows and columns have natural interpretations.