Explanation of shape descriptors to characterize the point clouds shown in Fig. 1.

<p>All examples come from the <i>Conference</i> data set. Panel A describes Kendall’s τ—a correlation coefficient based on the counting of discordant pairs (pairs of points connected by a line of negative slope). Panels B and C show the maximal separation of discordant pairs. In B, the measures focus on the pair with the largest separation in the <i>R</i>₀ direction. Δ_<i>R</i>0 denotes the maximum separation; ρ_<i>R</i>0 is the mean <i>R</i>₀ value for the maximally discordant pair. Panel C shows the similar quantities, Δ_Ω and ρ_Ω, defined along the Ω direction. Panels D, E, and F illustrate the measurement of λδ-balance via τ_αΩ. This descriptor captures the tendency of some data sets to have high-λ, low-δ points above high-δ, low-λ points, while for other data sets, the situation is reversed. Panel D illustrates how the <i>R</i>₀ axis is segmented into bins. Panel E shows how we assign a (λ,δ)-plane angle, α, to all points in the bin. Panel F shows how we measure the correlation between α and Ω, which is very weak in this particular case.