Application of Hypercorrelated Matrices in Ecological Research

Branko Karadžić; Snežana Jarić; Pavle Pavlović; Saša Marinković; Miroslava Mitrović

doi:doi:10.11648/j.cbb.20140204.12

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Application of Hypercorrelated Matrices in Ecological Research

Branko Karadžić, Snežana Jarić, Pavle Pavlović, Saša Marinković, Miroslava Mitrović

Published in Computational Biology and Bioinformatics (Volume 2, Issue 4)

Received: 18 August 2014 Accepted: 11 September 2014 Published: 30 September 2014

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Abstract

Ecological data matrices often require some form of pre-processing so that any undesirable effects (e.g. the variable size effect) may be removed from multivariate analyses. This paper describes hypercorrelation, a simple data transformation that improves ordination methods significantly. Hypercorrelated matrices efficiently eliminate the ‘arch’ (or Guttman) effect, a spurious polynomial relation between ordination axes. These matrices reduce the sensitivity of correspondence analysis to outliers. Canonical analyses (canonical correspondence analysis and redundancy analysis) of hypercorrelated matrices are resistant to undesirable effects of missing data. Finally, the hypercorrelation extends applicability of “linear ordination method” (principal components analysis and redundancy analysis) to sparse (high beta diversity) matrices.

Published in	Computational Biology and Bioinformatics (Volume 2, Issue 4)
DOI	10.11648/j.cbb.20140204.12
Page(s)	57-62
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Arch Effect, Beta Diversity, (Canonical) Correspondence Analysis, Hypercorrelation, Missing Data, Outliers, Principal Components Analysis, Redundancy Analysis

References

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APA Style

Branko Karadžić, Snežana Jarić, Pavle Pavlović, Saša Marinković, Miroslava Mitrović. (2014). Application of Hypercorrelated Matrices in Ecological Research. Computational Biology and Bioinformatics, 2(4), 57-62. https://doi.org/10.11648/j.cbb.20140204.12

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ACS Style

Branko Karadžić; Snežana Jarić; Pavle Pavlović; Saša Marinković; Miroslava Mitrović. Application of Hypercorrelated Matrices in Ecological Research. Comput. Biol. Bioinform. 2014, 2(4), 57-62. doi: 10.11648/j.cbb.20140204.12

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AMA Style

Branko Karadžić, Snežana Jarić, Pavle Pavlović, Saša Marinković, Miroslava Mitrović. Application of Hypercorrelated Matrices in Ecological Research. Comput Biol Bioinform. 2014;2(4):57-62. doi: 10.11648/j.cbb.20140204.12

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@article{10.11648/j.cbb.20140204.12,
  author = {Branko Karadžić and Snežana Jarić and Pavle Pavlović and Saša Marinković and Miroslava Mitrović},
  title = {Application of Hypercorrelated Matrices in Ecological Research},
  journal = {Computational Biology and Bioinformatics},
  volume = {2},
  number = {4},
  pages = {57-62},
  doi = {10.11648/j.cbb.20140204.12},
  url = {https://doi.org/10.11648/j.cbb.20140204.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbb.20140204.12},
  abstract = {Ecological data matrices often require some form of pre-processing so that any undesirable effects (e.g. the variable size effect) may be removed from multivariate analyses. This paper describes hypercorrelation, a simple data transformation that improves ordination methods significantly. Hypercorrelated matrices efficiently eliminate the ‘arch’ (or Guttman) effect, a spurious polynomial relation between ordination axes. These matrices reduce the sensitivity of correspondence analysis to outliers. Canonical analyses (canonical correspondence analysis and redundancy analysis) of hypercorrelated matrices are resistant to undesirable effects of missing data. Finally, the hypercorrelation extends applicability of “linear ordination method” (principal components analysis and  redundancy analysis) to sparse (high beta diversity) matrices.},
 year = {2014}
}

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TY  - JOUR
T1  - Application of Hypercorrelated Matrices in Ecological Research
AU  - Branko Karadžić
AU  - Snežana Jarić
AU  - Pavle Pavlović
AU  - Saša Marinković
AU  - Miroslava Mitrović
Y1  - 2014/09/30
PY  - 2014
N1  - https://doi.org/10.11648/j.cbb.20140204.12
DO  - 10.11648/j.cbb.20140204.12
T2  - Computational Biology and Bioinformatics
JF  - Computational Biology and Bioinformatics
JO  - Computational Biology and Bioinformatics
SP  - 57
EP  - 62
PB  - Science Publishing Group
SN  - 2330-8281
UR  - https://doi.org/10.11648/j.cbb.20140204.12
AB  - Ecological data matrices often require some form of pre-processing so that any undesirable effects (e.g. the variable size effect) may be removed from multivariate analyses. This paper describes hypercorrelation, a simple data transformation that improves ordination methods significantly. Hypercorrelated matrices efficiently eliminate the ‘arch’ (or Guttman) effect, a spurious polynomial relation between ordination axes. These matrices reduce the sensitivity of correspondence analysis to outliers. Canonical analyses (canonical correspondence analysis and redundancy analysis) of hypercorrelated matrices are resistant to undesirable effects of missing data. Finally, the hypercorrelation extends applicability of “linear ordination method” (principal components analysis and  redundancy analysis) to sparse (high beta diversity) matrices.
VL  - 2
IS  - 4
ER  -

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Author Information

Branko Karadžić
Snežana Jarić
Pavle Pavlović
Saša Marinković
Miroslava Mitrović

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Plain Text BibTeX RIS

APA Style

Branko Karadžić, Snežana Jarić, Pavle Pavlović, Saša Marinković, Miroslava Mitrović. (2014). Application of Hypercorrelated Matrices in Ecological Research. Computational Biology and Bioinformatics, 2(4), 57-62. https://doi.org/10.11648/j.cbb.20140204.12

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ACS Style

Branko Karadžić; Snežana Jarić; Pavle Pavlović; Saša Marinković; Miroslava Mitrović. Application of Hypercorrelated Matrices in Ecological Research. Comput. Biol. Bioinform. 2014, 2(4), 57-62. doi: 10.11648/j.cbb.20140204.12

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AMA Style

Branko Karadžić, Snežana Jarić, Pavle Pavlović, Saša Marinković, Miroslava Mitrović. Application of Hypercorrelated Matrices in Ecological Research. Comput Biol Bioinform. 2014;2(4):57-62. doi: 10.11648/j.cbb.20140204.12

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@article{10.11648/j.cbb.20140204.12,
  author = {Branko Karadžić and Snežana Jarić and Pavle Pavlović and Saša Marinković and Miroslava Mitrović},
  title = {Application of Hypercorrelated Matrices in Ecological Research},
  journal = {Computational Biology and Bioinformatics},
  volume = {2},
  number = {4},
  pages = {57-62},
  doi = {10.11648/j.cbb.20140204.12},
  url = {https://doi.org/10.11648/j.cbb.20140204.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbb.20140204.12},
  abstract = {Ecological data matrices often require some form of pre-processing so that any undesirable effects (e.g. the variable size effect) may be removed from multivariate analyses. This paper describes hypercorrelation, a simple data transformation that improves ordination methods significantly. Hypercorrelated matrices efficiently eliminate the ‘arch’ (or Guttman) effect, a spurious polynomial relation between ordination axes. These matrices reduce the sensitivity of correspondence analysis to outliers. Canonical analyses (canonical correspondence analysis and redundancy analysis) of hypercorrelated matrices are resistant to undesirable effects of missing data. Finally, the hypercorrelation extends applicability of “linear ordination method” (principal components analysis and  redundancy analysis) to sparse (high beta diversity) matrices.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Application of Hypercorrelated Matrices in Ecological Research
AU  - Branko Karadžić
AU  - Snežana Jarić
AU  - Pavle Pavlović
AU  - Saša Marinković
AU  - Miroslava Mitrović
Y1  - 2014/09/30
PY  - 2014
N1  - https://doi.org/10.11648/j.cbb.20140204.12
DO  - 10.11648/j.cbb.20140204.12
T2  - Computational Biology and Bioinformatics
JF  - Computational Biology and Bioinformatics
JO  - Computational Biology and Bioinformatics
SP  - 57
EP  - 62
PB  - Science Publishing Group
SN  - 2330-8281
UR  - https://doi.org/10.11648/j.cbb.20140204.12
AB  - Ecological data matrices often require some form of pre-processing so that any undesirable effects (e.g. the variable size effect) may be removed from multivariate analyses. This paper describes hypercorrelation, a simple data transformation that improves ordination methods significantly. Hypercorrelated matrices efficiently eliminate the ‘arch’ (or Guttman) effect, a spurious polynomial relation between ordination axes. These matrices reduce the sensitivity of correspondence analysis to outliers. Canonical analyses (canonical correspondence analysis and redundancy analysis) of hypercorrelated matrices are resistant to undesirable effects of missing data. Finally, the hypercorrelation extends applicability of “linear ordination method” (principal components analysis and  redundancy analysis) to sparse (high beta diversity) matrices.
VL  - 2
IS  - 4
ER  -

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