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Application of Hypercorrelated Matrices in Ecological Research

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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    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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