calcContinuityFromRank: Calculate continuity based on sample rankings

In csoneson/dreval: Evaluate Reduced Dimension Representations

Calculate continuity based on sample rankings

Description

The continuity was proposed by Venna and Kaski, as a local quality measure of a low-dimensional representation. The metric focuses on the preservation of local neighborhoods, and compares the neighborhoods of points in the low-dimensional representation to those in the reference data. Hence, the continuity measure indicates to which degree we can trust that the points closest to a given sample in the reference data set are placed close to the sample also in the low-dimensional representation. The kTM parameter defines the size of the neighborhoods to consider.

Usage

calcContinuityFromRank(rankReference, rankLowDim, kTM)

Arguments

rankReference	N x N matrix, each row/column corresponding to one sample. The value of entry (i, j) represents the position of sample i in the ranking of all samples with respect to their distance from sample j, based on the reference (high-dimensional) observed values. The sample itself has rank 0.
rankLowDim	N x N matrix, each row/column corresponding to one sample. The value of entry (i, j) represents the position of sample i in the ranking of all samples with respect to their distance from sample j, based on the low-dimensional representation. The sample itself has rank 0.
kTM	The number of nearest neighbors.

Value

The continuity value.

Author(s)

Charlotte Soneson

References

Venna J., Kaski S. (2001). Neighborhood preservation in nonlinear projection methods: An experimental study. In Dorffner G., Bischof H., Hornik K., editors, Proceedings of ICANN 2001, pp 485–491. Springer, Berlin.

csoneson/dreval documentation built on Jan. 26, 2024, 6:32 p.m.