allow for signed distances

[maxheld83]

so then the cell entries are not a distance metric, technically speaking.

[maxheld83]

non-metric distance matrices may serve to represent this; perhaps by modelling this is a directed graph with (negative) weights. https://en.wikipedia.org/wiki/Distance_matrix

[maxheld83]

or maybe a similarity matrix might do the trick, because it allows negative values for very dissimilar objects (which is kinda sorta what we're after here?) https://en.wikipedia.org/wiki/Similarity_measure

[maxheld83]

or maybe non-metric multidimensional scaling? nMDS? https://en.wikipedia.org/wiki/Multidimensional_scaling

[maxheld83]

apparently nonmetric mds also deals with ordinal data, so maybe just -1, 1, 0

[maxheld83]

this is also known as an oriented distance function https://en.wikipedia.org/wiki/Signed_distance_function