Concise and Accessible Representations for Multidimensional Datasets: Introducing a Framework Based on the nD-EVM and Kohonen Networks

Joint Authors

Ruiz-Rodríguez, Ricardo
Pérez-Aguila, Ricardo

Source

Applied Computational Intelligence and Soft Computing

Issue

Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-21, 21 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2015-03-01

Country of Publication

Egypt

No. of Pages

21

Main Subjects

Information Technology and Computer Science

Abstract EN

A new framework intended for representing and segmenting multidimensional datasets resulting in low spatial complexity requirements and with appropriate access to their contained information is described.

Two steps are going to be taken in account.

The first step is to specify (n-1)D hypervoxelizations, n≥2, as Orthogonal Polytopes whose nth dimension corresponds to color intensity.

Then, the nD representation is concisely expressed via the Extreme Vertices Model in the n-Dimensional Space (nD-EVM).

Some examples are presented, which, under our methodology, have storing requirements minor than those demanded by their original hypervoxelizations.

In the second step, 1-Dimensional Kohonen Networks (1D-KNs) are applied in order to segment datasets taking in account their geometrical and topological properties providing a non-supervised way to compact even more the proposed n-Dimensional representations.

The application of our framework shares compression ratios, for our set of study cases, in the range 5.6496 to 32.4311.

Summarizing, the contribution combines the power of the nD-EVM and 1D-KNs by producing very concise datasets’ representations.

We argue that the new representations also provide appropriate segmentations by introducing some error functions such that our 1D-KNs classifications are compared against classifications based only in color intensities.

Along the work, main properties and algorithms behind the nD-EVM are introduced for the purpose of interrogating the final representations in such a way that it efficiently obtains useful geometrical and topological information.

American Psychological Association (APA)

Pérez-Aguila, Ricardo& Ruiz-Rodríguez, Ricardo. 2015. Concise and Accessible Representations for Multidimensional Datasets: Introducing a Framework Based on the nD-EVM and Kohonen Networks. Applied Computational Intelligence and Soft Computing،Vol. 2015, no. 2015, pp.1-21.
https://search.emarefa.net/detail/BIM-1052218

Modern Language Association (MLA)

Pérez-Aguila, Ricardo& Ruiz-Rodríguez, Ricardo. Concise and Accessible Representations for Multidimensional Datasets: Introducing a Framework Based on the nD-EVM and Kohonen Networks. Applied Computational Intelligence and Soft Computing No. 2015 (2015), pp.1-21.
https://search.emarefa.net/detail/BIM-1052218

American Medical Association (AMA)

Pérez-Aguila, Ricardo& Ruiz-Rodríguez, Ricardo. Concise and Accessible Representations for Multidimensional Datasets: Introducing a Framework Based on the nD-EVM and Kohonen Networks. Applied Computational Intelligence and Soft Computing. 2015. Vol. 2015, no. 2015, pp.1-21.
https://search.emarefa.net/detail/BIM-1052218

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-1052218