Open AccessCurrently, issues on processing of large data volumes are of great importance. Initially, the Andrews plots have been proposed to show multidimensional statistics on the plane. But as the Andrews plots retain information on the average values of the represented values, distances, and dispersion, the distances between the plots linearly indicate distances between the data points, and it becomes possible to use the plots under consideration for the graphical representation of multi-dimensional data of various kinds. The paper analyses a diversity of various mathematical apparatus for Andrews plotting to visualize multi-dimensional data.
The first section provides basic information about the Andrews plots, as well as about a test set of multidimensional data in Iris Fischer’s literature. Analysis of the Andrews plot properties shows that they provide a limitlessly many one-dimensional projections on the vectors and, furthermore, the plots, which are nearer to each other, correspond to nearly points. All this makes it possible to use the plots under consideration for multi-dimensional data representation. The paper considers the Andrews plot formation based on Fourier transform functions, and from the analysis results of plotting based on a set of the test, it draws a conclusion that in this way it is possible to provide clustering of multidimensional data.
The second section of the work deals with research of different ways to modify the Andrews plots in order to improve the perception of the graphical representation of multidimensional data. Different variants of the Andrews plot projections on the coordinate planes and arbitrary subspaces are considered. In addition, the paper studies an effect of the Andrews plot scaling on the visual perception of multidimensional data.
The paper’s third section describes Andrews plotting based on different polynomials, in particular, Chebyshev and Legendre polynomials. It is shown that the resulting image is well correlated with the original point diagram and the Andrews plots based on the Fourier transform. This allows us to draw a conclusion that the Andrews plots based on the polynomial functions can be used for multidimensional data analysis.
The fourth section studies wavelets as a basis for Andrews plotting. It is noted that wavelets have some advantages as compared to the Fourier series. In many areas of the signal analysis a Fourier transform is used for measuring the frequency characteristics of the signal over the entire area. The wavelet transform, on the contrary, is used when it is necessary to measure frequency characteristics in time-localized clusters. Fourier and wavelet transforms are complementary. Fourier transform yields an average frequency with respect to time, and the wavelet transform provides the signal frequency values at any time interval. Based on wavelets Andrews plotting through a set of test data, has shown that it is possible to apply this approach to the graphical representation of multidimensional data.