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Data Structures and Algorithms to support the identification of banded

patterns in Zero-One data

By Fatimah Abdullahi

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Related work• The work of Junttila and Mannila on Banded

structures in Binary matrices.• Banded pattern as ordering the rows and

columns so the non zero entries shows staircase pattern of overlapping rows

d e a c bA 0 1 1 0 0B 0 0 0 1 1C 1 1 0 0 0D 0 0 1 1 0

d e a c bC 1 1 0 0 0A 0 1 1 0 0D 0 0 1 1 0B 0 0 0 1 1

d e a c bA 0 1 1 0 0B 0 0 0 1 1C 1 1 0 0 0D 0 0 1 1 0

Nested Pattern

C1P (Consecutive one property)

a b c d e fA 1 0 0 1 1 0B 1 0 0 1 1 0C 0 0 0 0 1 0D 1 1 1 1 1 1E 1 1 0 1 1 0

e a d b c fD 1 1 1 1 1 1E 1 1 1 1 0 0A 1 1 1 0 0 0B 1 1 1 0 0 0C 1 0 0 0 0 0

e a d b c fA 1 1 1 0 0 0B 1 1 1 0 0 0C 1 0 0 0 0 0D 1 1 1 1 1 1E 1 1 1 1 0 0

a b c d e

1 1 1 1 1 0

2 1 1 1 0 0

3 1 0 1 0 0

4 1 0 0 0 1

d b c a e

1 1 1 1 1 0

2 0 1 1 1 0

3 0 0 1 1 0

4 0 0 0 1 1

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Banded pattern is the rearrangement of the columns so that the nonzero entries forms a stair case pattern of overlapping rows. An example is presented in Table 1

A B C D1 0 1 0 12 1 1 0 03 1 0 0 04 1 0 1 05 0 0 1 0

Is it possible to find banded patterns in 3-D data?

D B A C

1 1 1 0 0

2 0 1 1 0

3 0 0 1 0

4 0 0 1 1

5 0 0 0 1

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Different views of 3-D data

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Applications

• Paleontological Data (Fossil species and sites)• Physical Mapping Problems of Genome

(Clones and probe)• DNA Amplification data set (DNA amplification

record and chromosomal location). etc.

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Categorization of Research

AGENT GROUP

DATA MINING AND ITS APPLICATIONS

PATTERN FINDINGS

ALGORITHMS

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Thank you