Figure 1

Three-dimensional Spiral dataset, with \(n=5000\), \({\bar{S}}=1\), \(\sigma ^2_x=\sigma ^2_y=0.5\), and \(\sigma ^2_z=1\). The resulting data points are displayed on the left. On the right, we show how observing the data at different scales can produce different insights regarding the dimensionality of the dataset.