Faithfulness of mapped distances

MappingQuality() calculates the trustworthiness and continuity of mapped distances (Venna and Kaski 2001; Kaski et al. 2003) . Trustworthiness measures, on a scale from 0–1, the degree to which points that are nearby in a mapping are truly close neighbours; continuity, the extent to which points that are truly nearby retain their close spatial proximity in a mapping.

Usage

MappingQuality(original, mapped, neighbours = 10L)

ProjectionQuality(original, mapped, neighbours = 10L)

Arguments

original, mapped

Square matrix or dist object containing original / mapped pairwise distances.

neighbours

Integer specifying number of nearest neighbours to use in calculation. This should typically be small relative to the number of points.

Value

MappingQuality() returns a named vector of length four, containing the entries: Trustworthiness, Continuity, TxC (the product of these values), and sqrtTxC (its square root).

References

Kaski S, Nikkila J, Oja M, Venna J, Toronen P, Castren E (2003). “Trustworthiness and metrics in visualizing similarity of gene expression.” BMC Bioinformatics, 4, 48. doi:10.1186/1471-2105-4-48 .

Venna J, Kaski S (2001). “Neighborhood preservation in nonlinear projection methods: an experimental study.” In Dorffner G, Bischof H, Hornik K (eds.), Artificial Neural Networks — ICANN 2001, Lecture Notes in Computer Science, 485–491. doi:10.1007/3-540-44668-0_68 .

See also

Other tree space functions: Islands(), MSTSegments(), MapTrees(), SpectralEigens(), cluster-statistics, median.multiPhylo()

Author

Martin R. Smith (martin.smith@durham.ac.uk)

Examples

library("TreeTools", quietly = TRUE)
trees <- as.phylo(0:10, nTip = 8)
distances <- ClusteringInfoDistance(trees)
mapping <- cmdscale(distances)
MappingQuality(distances, dist(mapping), 4)
#> Trustworthiness      Continuity             TxC         sqrtTxC 
#>       0.7929293       0.8737374       0.6928120       0.8323533