Skip to main content

Barycentric Discriminant Analysis

  • Living reference work entry
  • Latest version View entry history
  • First Online:
Encyclopedia of Social Network Analysis and Mining

Synonyms

Intraclass analysis; Mean-centered partial least square correlation

Glossary

Barycenter:

The mean of the observations from a given category (also called center of gravity, center of mass, mean vector, or centroid)

Confidence interval:

An interval encompassing a given proportion (e.g., 95%) of an estimate of a parameter (e.g., a mean)

Discriminant analysis:

A technique whose goal is to assign observations to some predetermined categories

Discriminant factor scores:

A linear combination of the variables of a data matrix. Used to assign observations to categories

Design matrix (aka group matrix):

In a group matrix, the rows represent observations and the columns represent a set of exclusive groups (i.e., an observation belongs to one and only one group). A value of 1 at the intersection of a row and a column indicates that the observation represented by the row belongs to the group represented by the column. A value of 0 at the intersection of a row and a column indicates that...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • Abdi H (2003) Multivariate analysis. In: Lewis-Beck M, Bryman A, Futing T (eds) Encyclopedia for research methods for the social sciences. Sage, Thousand Oaks, pp 699–702

    Google Scholar 

  • Abdi H (2007a) Singular value decomposition (SVD) and generalized singular value decomposition (GSVD). In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 907–912

    Google Scholar 

  • Abdi H (2007b) Discriminant correspondence analysis (dica). In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 270–275

    Google Scholar 

  • Abdi H, Williams LJ (2010a) Jackknife. In: Salkind NJ (ed) Encyclopedia of research design. Sage, Thousand Oaks

    Google Scholar 

  • Abdi H, Williams LJ (2010b) Principal component analysis. Wiley Interdiscip Rev: Comput Stat 2:433–459

    Article  Google Scholar 

  • Abdi H, Williams LJ (2010c) Barycentric discriminant analysis (BADIA). In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 64–65

    Google Scholar 

  • Abdi H, Dunlop JP, Williams LJ (2009) How to compute reliability estimates and display confidence and tolerance intervals for pattern classifiers using the bootstrap and 3-way multidimensional scaling (DISTATIS). NeuroImage 45:89–95

    Article  Google Scholar 

  • Abdi H, Williams LJ, Beaton D, Posamentier M, Harris TS, Krishnan A, Devous MD (2012a) Analysis of regional cerebral blood flow data to discriminate among Alzheimer’s disease, fronto-temporal dementia, and elderly controls: a multi-block barycentric discriminant analysis (MUBADA) methodology. J Alzheimer Dis 31:s189–s201

    Google Scholar 

  • Abdi H, Williams LJ, Connolly AC, Gobbini MI, Dunlop JP, Haxby JV (2012b) Multiple subject Barycentric discriminant analysis (MUSUBADA): how to assign scans to categories without using spatial normalization. Comput Math Methods Med 2012:1–15. https://doi.org/10.1155/2012/634165

    MathSciNet  MATH  Google Scholar 

  • Abdi H, Williams LJ, Valentin D, Bennani-Dosse M (2012c) STATIS and DISTATIS: optimum multi-table principal component analysis and three way metric multidimensional scaling. Wiley Interdiscip Rev: Comput Stat 4:124–167

    Article  Google Scholar 

  • Abdi H, Williams LJ, Valentin D (2013) Multiple factor analysis: principal component analysis for multi-table and multi-block data sets. Wiley Interdiscip Rev: Comput Stat 5:149–179

    Article  Google Scholar 

  • Bastin C, Benzécri JP, Bourgarit C, Caze P (1982) Pratique de l’Analyse des Données. Dunod, Paris, pp 102–104

    Google Scholar 

  • Beaton D, Chin Fatt CR, Abdi H (2014) An ExPosition of multivariate analysis with the singular value decomposition in R. Comput Stat & Data Anal 72:176–189

    Article  MathSciNet  Google Scholar 

  • Benzécri J-P (1977) Analyse discriminante et analyse factorielle. Les Cahiers de l’Analyse des Données 2:369–406

    Google Scholar 

  • Bergougnan D, Couraud C (1982) Pratique de la discrimination barycentrique. Les Cahiers de l’Analyse des Données 7:341–354

    Google Scholar 

  • Celeux P, Nakache JP (1994) Analyse discriminante sur variables qualitatives. Polytechnica, Paris

    MATH  Google Scholar 

  • Chessel D, Mercier P (1993) Couplage de triplet statistiques et liaisons espèce-environnement. In: Lebreton JD, Asselain B (eds) Biométrie et Environnement. Dunod, Paris, pp 15–43

    Google Scholar 

  • Cioli C, Abdi H, Beaton D, Burnod Y, Mesmoudi S (2014) Human cortical gene expression and properties of functional networks. PLoS One 9(12):1–28

    Article  Google Scholar 

  • Diaconis P, Efron B (1983) Computer-intensive methods in statistics. Scientific American 248:116–130

    Article  Google Scholar 

  • Doledec S, Chessel D (1994) Co-inertia analysis: an alternative method for studying species- environment relationships. Freshw Biol 31:277–294

    Article  Google Scholar 

  • Dray S, Dufour AB (2007) The ade4 package: implementing the duality diagram for ecologists. J Stat Softw 22(4):1–20

    Article  Google Scholar 

  • Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman & Hall, New York

    Book  MATH  Google Scholar 

  • El Behi M, Sanson C, Bachelin C, Guillot-Noel L, Fransson J, Stankoff B, Maillart E, Sarrazin N, Guillemot V, Abdi H, Rebeix I, Fontaine B, Zujovic V (2017) Adaptive human immunity drives remyelination in a mouse model of demyelination. Brain 140(4):967–980

    Article  Google Scholar 

  • Gittins R (1980) Canonical analysis: a review with applications in ecology. Springer Verlag, New York

    MATH  Google Scholar 

  • Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, London

    MATH  Google Scholar 

  • Horst P (1961) Relations among m sets of measures. Psychometrika 26:129–149

    Article  MathSciNet  MATH  Google Scholar 

  • Krishnan A, Williams LJ, McIntosh AR, Abdi H (2010) Partial least squares (PLS) methods for neuroimaging: a tutorial and review. NeuroImage 56:455–475

    Article  Google Scholar 

  • Krzanowski WJ, Radley D (1989) Nonparametric confidence and tolerance regions in canonical variate analysis. Biometrics 45:1163–1173

    Article  MathSciNet  MATH  Google Scholar 

  • Leclerc A (1976) Une etude de la relation entre une variable qualitative et un groupe de variables qualitatives. Int Stat Rev 44:241–248

    Article  MATH  Google Scholar 

  • Manly BFJ (1997) Randomization, bootstrap, and Monte Carlo methods in biology, 2nd edn. Chapman & Hall, New York

    MATH  Google Scholar 

  • Nakache J-P, Lorente P, Benzcri J-P, Chastang J-F (1977) Aspects pronostiques et therapeutiques de l’infarctus myocardique aigu compliqu d’une dfaillance sévère de la pompe cardiaque. Application des methodes de discrimination Les Cahiers de l’Analyse des Données 2:415–434

    Google Scholar 

  • Perriere G, Lobry JR, Thioulouse J (1996) Correspondence discriminant analysis: a multivariate method for comparing classes of protein and nucleic acid sequences. CABIOS 12:519–524

    Google Scholar 

  • Saporta G, Niang N (2006) Correspondence analysis and classification. In: Greenacre M, Blasius J (eds) Multiple correspondence analysis and related methods. Boca Raton, Chapman & Hall/CRC, pp 371–392

    Chapter  Google Scholar 

  • St. Laurent M, Abdi H, Burianová H, Grady GL (2011) Influence of aging on the neural correlates of autobiographical, episodic, and semantic memory retrieval. J Cogn Neurosci 23:4150–4163

    Article  Google Scholar 

  • Takane Y (2013) Constrained principal component analysis and related techniques. CRC Press, Boca Raton

    MATH  Google Scholar 

  • Tucker LR (1958) An inter-battery method of factor analysis. Psychometrika 23:111–136

    Article  MathSciNet  MATH  Google Scholar 

  • Williams LJ, Abdi H, French R, Orange JB (2010) A tutorial on multi-block discriminant correspondence analysis (MUDICA): a new method for analyzing discourse data from clinical populations. J Speech Lang Hear Res 53:1372–1393

    Article  Google Scholar 

  • Witten DM, Tibshirani R, Hastie T (2009) A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10:515–534

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hervé Abdi .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Science+Business Media LLC

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Abdi, H., Williams, L.J., Béra, M. (2018). Barycentric Discriminant Analysis. In: Alhajj, R., Rokne, J. (eds) Encyclopedia of Social Network Analysis and Mining. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7163-9_110192-2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-7163-9_110192-2

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-7163-9

  • Online ISBN: 978-1-4614-7163-9

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Barycentric Discriminant Analysis
    Published:
    15 December 2017

    DOI: https://doi.org/10.1007/978-1-4614-7163-9_110192-2

  2. Original

    Barycentric Discriminant Analysis
    Published:
    09 June 2017

    DOI: https://doi.org/10.1007/978-1-4614-7163-9_110192-1