Browsing by Subject "Biplots"

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    Open Access
    Biplots based on principal surfaces
    (2019) Ganey, Raeesa; Er, Sebnem; Lubbe, Sugnet
    Principal surfaces are smooth two-dimensional surfaces that pass through the middle of a p-dimensional data set. They minimise the distance from the data points, and provide a nonlinear summary of the data. The surfaces are nonparametric and their shape is suggested by the data. The formation of a surface is found using an iterative procedure which starts with a linear summary, typically with a principal component plane. Each successive iteration is a local average of the p-dimensional points, where an average is based on a projection of a point onto the nonlinear surface of the previous iteration. Biplots are considered as extensions of the ordinary scatterplot by providing for more than three variables. When the difference between data points are measured using a Euclidean embeddable dissimilarity function, observations and the associated variables can be displayed on a nonlinear biplot. A nonlinear biplot is predictive if information on variables is added in such a way that it allows the values of the variables to be estimated for points in the biplot. Prediction trajectories, which tend to be nonlinear are created on the biplot to allow information about variables to be estimated. The goal is to extend the idea of nonlinear biplot methodology onto principal surfaces. The ultimate emphasis is on high dimensional data where the nonlinear biplot based on a principal surface allows for visualisation of samples, variable trajectories and predictive sets of contour lines. The proposed biplot provides more accurate predictions, with an additional feature of visualising the extent of nonlinearity that exists in the data.
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    Open Access
    Visualisation of quadratic discriminant analysis and its application in exploration of microbial interactions
    (BioMed Central, 2015-02-25) Gardner-Lubbe, Sugnet; Dube, Felix S
    Background: When comparing diseased and non-diseased patients in order to discriminate between the aspects associated with the specific disease, it is often observed that the diseased patients have more variability than the non-diseased patients. In such cases Quadratic discriminant analysis is required which is based on the estimation of different covariance structures for the different groups. Having different covariance matrices means the Canonical variate transformation cannot be used to obtain a visual representation of the discrimination and group separation. Results: In this paper an alternative method is proposed: combining the different transformations for the different groups into a single representation of the sample points with classification regions. In order to associate the differences in variables with group discrimination, a biplot is produced which include information on the variables, samples and their relationship.