Banded structure in binary matrices

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.inria.fr/hal-00658836
Contributor : Gemma C Garriga <>
Submitted on : Tuesday, April 17, 2012 - 6:32:20 PM
Last modification on : Thursday, February 21, 2019 - 10:52:49 AM
Long-term archiving on : Wednesday, July 18, 2012 - 2:20:31 AM

File

bands_revised-v2.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Gemma Garriga, Esa Junttila, Heikki Mannila. Banded structure in binary matrices. Knowledge and Information Systems (KAIS), Springer, 2011, 28 (1), pp.197-226. ⟨10.1007/s10115-010-0319-7⟩. ⟨hal-00658836⟩

Share

Metrics

Record views

542

Files downloads

574