1 Introduction

Dimensionality Reduction methods are either manifold learning approaches or methods of projection. Projection methods should be prefered if the goal is the visualization of cluster structures [Thrun, 2018]. Two-dimensional projections are visualized as scatter plot. The Johnson–Lindenstrauss lemma states that in such a case the low-dimensional similarities does not represent high-dimensional distances coercively (details in [Thrun/Ultsch,2018]). To solve this problem the high-dimensional distances can be visualized in the two-dimensional projection as 3D landscape of a topographic map with hypsometric tints[Thrun, 2018; Ultsch/Thrun, 2017; Thrun et al., 2016, Thrun/Ultsch, 2020].

Exemplary we use the 3D artificial dataset of Chainlink showes below. Other examples can be found in [Ultsch/Thrun, 2017] or [Thrun/Ultsch, 2020].

data(Chainlink)
Data=Chainlink$Data
Cls=Chainlink$Cls
require(DataVisualizations)
DataVisualizations::Plot3D(
  Data,
  Cls,
  type = 's',
  radius = 0.1,
  box = F,
  aspect = T,
  top = T
)
rgl::grid3d(c("x", "y", "z"))