A monitoring display of multivariate outliers

Caussinus, Henri; Fekri, M.; Hakam, Sayful; Ruiz‐Gazen, Anne

doi:10.1016/s0167-9473(03)00059-8

Cited by 16 publications

(7 citation statements)

References 13 publications

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“…However, in other cases of interest, our practice and some limited unpublished results lead to different values, e.g. 2, the value which appears in Caussinus et al (2003a). We hope that the authors will be interested in further investigating these various issues.…”

Section: Discussion On the Paper By Tyler Critchley Dümbgen And Ojamentioning

confidence: 95%

“…The answer to this practical question rests on the distribution of eigenvalues of the matrix product involved. We gave very preliminary theoretical results for specific scatter matrices in Caussinus et al (2003a) for the detection of outliers and in Caussinus et al (2003b) for the detection of groups. Another issue is the complementary use of invariant co‐ordinate selection and classification.…”

Section: Discussion On the Paper By Tyler Critchley Dümbgen And Ojamentioning

confidence: 96%

“…Less attention has been given to the comparison of different estimates of scatter for a single set of variables from a single population. Some work in this direction, though, can be found in Art et al (1982), Caussinus and Ruiz‐Gazen (1990, 1993, 1995), Caussinus et al (2003) and Ruiz‐Gazen (1993), which will be discussed in later sections.…”

Section: Comparing Scatter Matricesmentioning

confidence: 99%

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Invariant Co-Ordinate Selection

Tyler

Critchley

Dümbgen

et al. 2009

Journal of the Royal Statistical Society Series B: Statistical Methodology

111

132

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Summary.A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue-eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection. By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant coordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given.

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Section: Discussion On the Paper By Tyler Critchley Dümbgen And Ojamentioning

confidence: 95%

Section: Discussion On the Paper By Tyler Critchley Dümbgen And Ojamentioning

confidence: 96%

Section: Comparing Scatter Matricesmentioning

confidence: 99%

See 1 more Smart Citation

Invariant Co-Ordinate Selection

Tyler

Critchley

Dümbgen

et al. 2009

Journal of the Royal Statistical Society Series B: Statistical Methodology

111

132

View full text Add to dashboard Cite

show abstract

“…Among the unsupervised dimension reduction methods, one can quote exploratory projection pursuit (EPP) with principal component analysis (PCA) as a special case, the projection index being the variance. More recently, the invariant coordinate selection (ICS) method has been proposed by and studied in . The PCA and ICS methods are based on a spectral decomposition and lead to some orthogonal projection matrices that define nested vector subspaces.…”

Section: High Dimensionmentioning

confidence: 99%

Beyond multidimensional data in model visualization: High‐dimensional and complex nonnumeric data

Villa-Vialaneix¹,

Ruiz‐Gazen

2015

Statistical Analysis

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“…The multivariate functions are called clustermap and pcamap. The function pcamap implements the generalized principal components analysis (PCA) as it is described in Caussinus, Fekri, Hakam, and Ruiz-Gazen (2003). Note that using the link between map and scatterplot, users can rapidly customize GeoXp to any other dimension reduction method.…”

Section: Multivariate Functionsmentioning

confidence: 99%

GeoXp: AnRPackage for Exploratory Spatial Data Analysis

Laurent¹,

Ruiz‐Gazen²,

Thomas‐Agnan³

2012

J. Stat. Soft.

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We present GeoXp, an R package implementing interactive graphics for exploratory spatial data analysis. We use a data set concerning public schools of the French MidiPyrénées region to illustrate the use of these exploratory techniques based on the coupling between a statistical graph and a map. Besides elementary plots like boxplots, histograms or simple scatterplots, GeoXp also couples maps with Moran scatterplots, variogram clouds, Lorenz curves and other graphical tools. In order to make the most of the multidimensionality of the data, GeoXp includes dimension reduction techniques such as principal components analysis and cluster analysis whose results are also linked to the map.

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A monitoring display of multivariate outliers

Cited by 16 publications

References 13 publications

Invariant Co-Ordinate Selection

Invariant Co-Ordinate Selection

Beyond multidimensional data in model visualization: High‐dimensional and complex nonnumeric data

GeoXp: AnRPackage for Exploratory Spatial Data Analysis

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