Biplots of compositional data

The singular value decomposition and its interpretation as a linear biplot has proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the speciffic case of compositional data consisting of positive vectors each of which is constrained to have unit sum. These relative variation biplots have properties relating to special features of compositional data: the study of ratios, subcompositions and models of compositional relationships. The methodology is demonstrated on a data set consisting of six-part colour compositions in 22 abstract paintings, showing how the singular value decomposition can achieve an accurate biplot of the colour ratios and how possible models interrelating the colours can be diagnosed.Logratio transformation, principal component analysis, relative variation biplot, singular value decomposition, subcomposition

Contribution biplots

In order to interpret the biplot it is necessary to know which points – usually variables – are the ones that are important contributors to the solution, and this information is available separately as part of the biplot’s numerical results. We propose a new scaling of the display, called the contribution biplot, which incorporates this diagnostic directly into the graphical display, showing visually the important contributors and thus facilitating the biplot interpretation and often simplifying the graphical representation considerably. The contribution biplot can be applied to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. In the contribution biplot one set of points, usually the rows of the data matrix, optimally represent the spatial positions of the cases or sample units, according to some distance measure that usually incorporates some form of standardization unless all data are comparable in scale. The other set of points, usually the columns, is represented by vectors that are related to their contributions to the low-dimensional solution. A fringe benefit is that usually only one common scale for row and column points is needed on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot legible. Furthermore, this version of the biplot also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important, when they are in fact contributing minimally to the solution.biplot, contributions, correspondence analysis, discriminant analysis, log-ratio analysis, MANOVA, principal component analysis, scaling, singular value decomposition, weighting.

ANALISIS LAPANGAN PEKERJAAN UTAMA DI JAWA TENGAH BERDASARKAN GRAFIK BIPLOT SQRT (SQUARE ROOT BIPLOT)

Biplot analysis is one of the methods of descriptive statistical analysis that can present data of the n objectswhichp variables into a two-dimensional graph. Biplot has several types according to the scale of α used. There are three scales α which is often used in the biplotanalysis, that are α = 0, α = 0,5 and α = 1. Biplot with α = 1 is called the RMP biplot (Row Matric Preserving). Biplot with α = 0 is called CMP biplot (Column Matric Preserving). While biplot with α = 0,5 called SQRT biplot (Square Root Biplot). Biplot with a scale of α = 0,5 is the best biplot to describe a data, because it make a graph between variable and object spread evenly. This study aims to create a SQRT biplot amount of population aged 15 years and over who worked according to district/city and major employment opportunities in Central Java. Biplot chart shows areas that have similar characteristics with the closest Euclidean distance. The diversity of characteristics is indicated by the length of the vector, the longest vector contained in the agricultural sector. Based on the biplot analysis in this study, it was obtained that the goodness size biplot is equal to 64,19958%. Keywords: Biplot, Singular Value Decomposition, Jobs, SQRT, Square Root Biplo

Interactive Biplot Construction

We analyze and discuss how a generic software to produce biplot graphs should be designed. We describe a data structure appropriate to include the biplot description and we specify the algorithm(s) to be used for several biplot types. We discuss the options the software should offer to the user in two different environments. In a highly interactive environment the user should be able to specify many graphical options and also to change them using the usual interactive tools. The resulting graph needs to be available in several formats, including high quality format for printing. In a web-based environment, the user submits a data file or listing together with some options specified either in a file or using a form. Then the graphic is sent back to the user in one of several possible formats according to the specifications. We review some of the already available software and we present an implementation based in XLISP-STAT. It can be run under Unix or Windows, and it is also part of a service that provides biplot graphs through the web.

Area Biplots

Classical multivariate analysis techniques such as principal components analysis and correspondence analysis use inner products to estimate data values. The results of these techniques may be visualized by representing the row and column points jointly in a biplot where the projection of a row point onto a column point vector followed by a multiplication by the length of the column point vector gives the inner-product that estimates the corresponding data element. In this paper, we propose a newvisualization: after a 90 degrees rotation of the row points, the areas spanned by a triangle of a row point, a column point and the origin estimate the data values. In contrast to the projection biplot, the areas spanned by different row and column points can be compared directly. Areas can only be produced for two dimensions at a time, but higher dimensional solutions can be represented by summing areas over subsequent pairs of dimensions. Here, the area biplot is developed for principal components analysis, correspondence analysis, and for interaction biplots but has general applicability.interaction;correspondence analysis;visualization;principal component analysis;biplot

Biplot and Singular Value Decomposition Macros for Excel©

The biplot display is a graph of row and column markers obtained from data that forms a two-way table. The markers are calculated from the singular value decomposition of the data matrix. The biplot display may be used with many multivariate methods to display relationships between variables and objects. It is commonly used in ecological applications to plot relationships between species and sites. This paper describes a set of Excelé macros that may be used to draw a biplot display based on results from principal components analysis, correspondence analysis, canonical discriminant analysis, metric multidimensional scaling, redundancy analysis, canonical correlation analysis or canonical correspondence analysis. The macros allow for a variety of transformations of the data prior to the singular value decomposition and scaling of the markers following the decomposition.

Biplot dan Implementasinya dengan Pemrograman Fungsional Mathematica

Teknik pemrograman fungsional mathematica digunakan untuk mengimplementasikan metode (Gabriel) biplot. Hasil utarna yang diperoleh berupa suatu perintah/fungsi biplot[data, 0, opsi]. Argumen pertama: data berupa data mentah dalam bentuk matriks dan peubah ganda yang terdiri dari n obyek dan p peubah. Argumen a berupa koefisien a € [0,1] pada penguraian nilai singular rnatriks data X = VA V\u27 = (U Aa)( A I-a V\u27)=GH". Nilai a = 0 menghasilkan biplot korelasi, a = 1 menghasilkan biplot jarak Euclid, 0.= 0.5 menghasilkan biplot antara. Kombinasi a, = 1 untuk G dan 0.2 = 0 untuk H menghasilkan biplot kombinasi. Argumen opsi berupa tambahan untuk label titik-titik obyek dan vektor peubah. Perintah biplot akan menghasilkan sekaligus plot obyek yang dinyatakan dengan tebaran titik koordinatnya, dan plot vektor peubah yang dinyatakan dengan garis. Illustrasi kasus nyata berupa biplot pernanfaatan dan pengembangan Teknologi Informasi (TI) pada beberapa negara diberikan untuk melihat tampilan biplot yang dihasilkan beserta interpretasinya