# Contribution Biplots

@article{Greenacre2013ContributionB, title={Contribution Biplots}, author={Michael J. Greenacre}, journal={Journal of Computational and Graphical Statistics}, year={2013}, volume={22}, pages={107 - 122} }

To interpret the biplot, it is necessary to know which points—usually variables—are the ones that are important contributors to the solution, especially when there are many variables involved. This information can be calculated separately as part of the biplot's numerical results, but this means that a table has to be consulted along with the graphical display. We propose a new scaling of the display, called the contribution biplot, which incorporates this diagnostic information directly into…

## 65 Citations

### Biplots: the joy of singular value decomposition

- Computer Science
- 2012

Biplot geometry underlies many classical multivariate procedures, such as principal component analysis, simple and multiple correspondence analysis, discriminant analysis, and other variants of dimension reduction methods such as log‐ratio analysis.

### Features of the Polynomial Biplot for Ordered Contingency Tables

- MathematicsJournal of Computational and Graphical Statistics
- 2021

Abstract For more than 20 years, variants of correspondence analysis have arisen that accommodate for the structure of ordered categorical variables using orthogonal polynomials. When the visual…

### Principal component analysis

- Computer ScienceNature Reviews Methods Primers
- 2022

This Primer describes how the principal component analysis method can be used for data analysis, explaining the mathematical background, analytical workflows, how to interpret a biplot and variants of the method.

### Weighted Euclidean Biplots

- Computer ScienceJournal of Classification
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A weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix is constructed, inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data.

### Weighted Euclidean Biplots

- Computer ScienceJ. Classif.
- 2016

A weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix is constructed, inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data.

### The contributions of rare objects in correspondence analysis.

- ChemistryEcology
- 2013

An alternative scaling of the correspondence analysis solution, the contribution biplot, is proposed as a way of displaying the results in order to avoid the problem of outlying and low contributing rare objects.

### Local biplots for multidimensional scaling, with application to the microbiome

- MathematicsJournal of Computational and Graphical Statistics
- 2022

Abstract We present local biplots, an extension of the classic principal component biplot to multidimensional scaling. Noticing that principal component biplots have an interpretation as the Jacobian…

### Visualizing Class Specific Heterogeneous Tendencies in Categorical Data

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Abstract In multiple correspondence analysis, both individuals (observations) and categories can be represented in a biplot that jointly depicts the relationships across categories and individuals,…

### Ordination with any dissimilarity measure: a weighted Euclidean solution.

- Environmental ScienceEcology
- 2017

A simple solution is proposed, consisting of the estimation of a weighted Euclidean distance that optimally approximates the dissimilarities, to extend the classical approach to ordination to any non-Euclidean or nonmetric dissimilarity.

### Quantification of intrinsic quality of a principal dimension in correspondence analysis and taxicab correspondence analysis

- Computer Science
- 2021

This essay considers CA and taxicab CA as a stepwise Hotelling/Tucker decomposition of the cross-covariance matrix of the row and column categories into four quadrants and reviews the notion of quality/quantity in multidimensional data analysis as discussed by Benzécri.

## References

SHOWING 1-10 OF 31 REFERENCES

### Biplots in Practice

- Computer Science
- 2009

This book explains the specific application and interpretation of the biplot in many different areas of multivariate analysis, notably regression, generalized linear modelling, principal component analysis, log-ratio analysis, various forms of correspondence analysis and discriminant analysis.

### Biplots in correspondence analysis

- Computer Science
- 1993

It is pointed out that joint correspondence analysis leads to a joint display of several variables which can be calibrated in a similar fashion to recover profile elements of the subtables of the Burt matrix.

### Goodness of fit of biplots and correspondence analysis

- Environmental Science
- 2002

The present paper examines proportional goodness of fit to variables recorded on individuals, the variances and covariances of the variables, and the form and distances between individuals. No single…

### Analysis of Meteorological Data by Means of Canonical Decomposition and Biplots.

- Environmental Science
- 1972

Abstract The biplot is a graphical display of a two-dimensional approximation to a matrix. Its usefulness in the display and analysis of matrices of meteorological data is demonstrated by a detailed…

### The biplot graphic display of matrices with application to principal component analysis

- Mathematics
- 1971

SUMMARY Any matrix of rank two can be displayed as a biplot which consists of a vector for each row and a vector for each column, chosen so that any element of the matrix is exactly the inner product…

### Biplots of Compositional Data

- Geology
- 2002

Summary. The singular value decomposition and its interpretation as a linear biplot have proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology…

### Canonical Correspondence Analysis: A New Eigenvector Technique for Multivariate Direct Gradient Analysis

- Environmental Science
- 1986

A new multivariate analysis technique, developed to relate community composition to known variation in the environment, is described. The technique is an extension of correspondence analysis…

### Correspondence Analysis in R, with Two- and Three-dimensional Graphics: The ca Package

- Business
- 2007

An implementation of simple, multiple and joint correspondence analysis in R with special emphasis on the visualization functions that offer features such as different scaling options for biplots and three-dimensional maps using the rgl package.

### Distributional Equivalence and Subcompositional Coherence in the Analysis of Compositional Data, Contingency Tables and Ratio-Scale Measurements

- MathematicsJ. Classif.
- 2009

The weighted log-ratio methodology is used here to visualize frequency data in linguistics and chemical compositional data in archeology and is theoretically equivalent to “spectral mapping”, a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra.

### Biplots in biomedical research.

- Computer ScienceStatistics in medicine
- 1990

The biplot is a graphical display of multivariate data that allows for inspection of data preliminary to formal analysis, and can follow an analysis by the graphical inspection of residuals.