Browsing by Author "Rodwell, David Timothy"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
- ItemCategorical CVA biplots(Stellenbosch : Stellenbosch University, 2020-12) Rodwell, David Timothy; Van der Merwe, Carel Johannes; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.ENGLISH ABSTRACT: In the modern era a great amount of emphasis is placed on data visualisation, especially in cases where a large amount of data is present. Usually, in these instances, the data is of a high-dimensional nature which cannot be visualised using conventional means. Fortunately, there has been a recent surge in using biplots to visualise multivariate data, where biplots can be described as a generalisation of a scatterplot. Moreover, these biplots use dimension reduction techniques to construct a two-dimensional representation of the data with non-orthogonal axes. However, at present, an effective biplot construction technique which adequately separates classes, in cases where categorical data is present does not exist. Hence, this research builds upon an existing biplot construction technique by using elements from Canonical Variate Analysis (CVA) and non-linear Principal Component Analysis (PCA) to develop a technique that can perform class separation in cases where numerical and categorical data is present. This novel biplot construction methodology forms the crux of this research assignment. Subsequently, the feasibility of this method was explored by considering the well-known Iris data set where two variables are binned to form categorical variables. It is shown that this novel method improves upon existing biplot construction in terms of classification accuracy and class separation. However, it is noted this method can be extended by incorporating CVA in the iterative algorithm which solves the optimal categorical level scores. A web-based Shiny application was built as supplement to this paper, and can be found at https://davidrodwell:shinyapps:io/CategoricalCVABiplotApp/. Here the user can interact with the data sets, proposed methodology, and functionalities presented in this research.