Glossary
- Barycenter:
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The mean of the observations from a given category (also called center of gravity, center of mass, mean vector, or centroid)
- Confidence interval:
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An interval encompassing a given proportion (e.g., 95%) of an estimate of a parameter (e.g., a mean)
- Discriminant analysis:
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A technique whose goal is to assign observations to some predetermined categories
- Discriminant factor scores:
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A linear combination of the variables of a data matrix. Used to assign observations to categories
- Design matrix (aka group matrix):
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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...
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
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
Abdi H (2007b) Discriminant correspondence analysis (dica). In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 270–275
Abdi H, Williams LJ (2010a) Jackknife. In: Salkind NJ (ed) Encyclopedia of research design. Sage, Thousand Oaks
Abdi H, Williams LJ (2010b) Principal component analysis. Wiley Interdiscip Rev: Comput Stat 2:433–459
Abdi H, Williams LJ (2010c) Barycentric discriminant analysis (BADIA). In: Salkind NJ (ed) Encyclopedia of measurement and statistics. Sage, Thousand Oaks, pp 64–65
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
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
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
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
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
Bastin C, Benzécri JP, Bourgarit C, Caze P (1982) Pratique de l’Analyse des Données. Dunod, Paris, pp 102–104
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
Benzécri J-P (1977) Analyse discriminante et analyse factorielle. Les Cahiers de l’Analyse des Données 2:369–406
Bergougnan D, Couraud C (1982) Pratique de la discrimination barycentrique. Les Cahiers de l’Analyse des Données 7:341–354
Celeux P, Nakache JP (1994) Analyse discriminante sur variables qualitatives. Polytechnica, Paris
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
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
Diaconis P, Efron B (1983) Computer-intensive methods in statistics. Scientific American 248:116–130
Doledec S, Chessel D (1994) Co-inertia analysis: an alternative method for studying species- environment relationships. Freshw Biol 31:277–294
Dray S, Dufour AB (2007) The ade4 package: implementing the duality diagram for ecologists. J Stat Softw 22(4):1–20
Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman & Hall, New York
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
Gittins R (1980) Canonical analysis: a review with applications in ecology. Springer Verlag, New York
Greenacre MJ (1984) Theory and applications of correspondence analysis. Academic Press, London
Horst P (1961) Relations among m sets of measures. Psychometrika 26:129–149
Krishnan A, Williams LJ, McIntosh AR, Abdi H (2010) Partial least squares (PLS) methods for neuroimaging: a tutorial and review. NeuroImage 56:455–475
Krzanowski WJ, Radley D (1989) Nonparametric confidence and tolerance regions in canonical variate analysis. Biometrics 45:1163–1173
Leclerc A (1976) Une etude de la relation entre une variable qualitative et un groupe de variables qualitatives. Int Stat Rev 44:241–248
Manly BFJ (1997) Randomization, bootstrap, and Monte Carlo methods in biology, 2nd edn. Chapman & Hall, New York
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
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
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
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
Takane Y (2013) Constrained principal component analysis and related techniques. CRC Press, Boca Raton
Tucker LR (1958) An inter-battery method of factor analysis. Psychometrika 23:111–136
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
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
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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
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Barycentric Discriminant Analysis- Published:
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DOI: https://doi.org/10.1007/978-1-4614-7163-9_110192-2
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Barycentric Discriminant Analysis- Published:
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DOI: https://doi.org/10.1007/978-1-4614-7163-9_110192-1