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{
"protocol": "Each geometry is applied to each modality independently, so no transform crosses the gauge or uses the pairing. The bound is the anchor upper bound; the last column re-computes it with a rank comparison operator instead of a linear one.",
"label": "natural-best",
"rows": [
{
"geometry": "euclidean (current)",
"correlation": 0.7157944505313568,
"anchor_bound": 0.3359375,
"anchor_bound_rank_operator": 0.1453125
},
{
"geometry": "global rank (copula)",
"correlation": 0.6453667782045476,
"anchor_bound": 0.171875,
"anchor_bound_rank_operator": 0.1453125
},
{
"geometry": "row rank",
"correlation": 0.6374571651517471,
"anchor_bound": 0.165625,
"anchor_bound_rank_operator": 0.1484375
},
{
"geometry": "local scaling",
"correlation": 0.7162509779848556,
"anchor_bound": 0.3625,
"anchor_bound_rank_operator": 0.1703125
},
{
"geometry": "diffusion t=3",
"correlation": 0.5659469014331384,
"anchor_bound": 0.0546875,
"anchor_bound_rank_operator": 0.0453125
},
{
"geometry": "heat kernel",
"correlation": 0.7381033036202107,
"anchor_bound": 0.31875,
"anchor_bound_rank_operator": 0.1546875
},
{
"geometry": "hyperbolic d=16",
"correlation": 0.7135662664726405,
"anchor_bound": 0.246875,
"anchor_bound_rank_operator": 0.1703125
}
],
"best": {
"geometry": "local scaling",
"correlation": 0.7162509779848556,
"anchor_bound": 0.3625,
"anchor_bound_rank_operator": 0.1703125
}
}
|
