Fig. 2: Results from simulation studies.
From: A spectral method for assessing and combining multiple data visualizations
a Boxplots (center line, median; box limits, upper and lower quartiles; points, outliers) of the mean concordance with the underlying true pattern for 15 candidate visualizations (HLLE omittted due to very low concordance) and the two meta-distance matrices under each simulation setting (Left: n = 900 independent samples generated from the Gaussian mixture model; Middle: n = 500 independent samples generated from the smiley face model; Right: n = 500 independent samples generated from the mammoth model) across various values of the SNR value θ. See Supplementary Fig. 2 for complete plots. b Results for n = 900 independent samples generated under the Gaussian mixture model. Top: examples of candidate visualizations along with their sample-wise concordance \({\{{({\bar{{{{{{{{\bf{P}}}}}}}}}}_{i.}^{(k)})}^{\top }{\bar{{{{{{{{\bf{P}}}}}}}}}}_{i.}^{*}\}}_{1\le i\le n}\) with the structure of noiseless samples, and the proposed meta-visualization using UMAP and the concordance \({\{{({\bar{{{{{{{{\bf{P}}}}}}}}}}_{i.}^{m})}^{\top }{\bar{{{{{{{{\bf{P}}}}}}}}}}_{i.}^{*}\}}_{1\le i\le n}\) for the proposed meta-distance. Bottom: boxplots (center line, median; box limits, upper and lower quartiles; points, outliers) of concordance measures as grouped by the true clusters. See Supplementary Fig. 3 for more examples.
