Supplementary Figure 9: PHATE preserves separations and cluster structure in addition to continuum structure.
From: Visualizing structure and transitions in high-dimensional biological data
To quantify the ability of PHATE to preserve cluster structure, we generated 30 random datasets with cluster structure using the Splatter package (Zappia et al., Genome Biology, vol. 18, no. 1, p. 174, 2017). Each dataset has \(n = 2000\) cells and between 7 and 14 clusters. We then computed the Adjusted Rand Index (Rand, Journal of the American Statistical Association, vol. 66, no. 336, pp. 846-850, 1971) (ARI, y-axis) between the ground truth clusters and clusters obtained by running k-means clustering on the embeddings. An ARI of 1 means perfect recovery of the clusters. We performed this analysis on Splatter data with increasing amounts of noise added during generation. For each noise level we compare clustering on the raw data, on 2-dimensional PCA, 2D t-SNE, 2D UMAP, and 2D PHATE. On average, PHATE preserves local cluster structure as well or better than the other methods. In the boxplots, the box limits indicate the lower and upper quartile values with a line at the median while the whiskers show the range of the data.
