I am using the dot product as a way to measure the similarly of two facial-model vectors extracted by a ML algorithm (OpenFace in fact).
I would like to convert the L2 norm to a probability U[0,1] in order to compare with other solutions from other providers that map directly to probabilities but in a blackbox fashion.
By probability I mean the probability that the two vectors represent the same person. So an identical image would give a probability of 1; images of the same person would give a high probability; and orthogonal images (different people, or some suitable toy case) would in the limit have such a probability of zero.
I'd like a uniform distribution for comparison with other providers, but this boils down to knowing what the underlying probability distribution of the feature vectors is.
How do I do this?
- Rayleigh distribution CDF
- Cosine similarity
- (1) is the same as (2)
- Draw from a simulated distribution
- Arbitrarily scale to U[0,1]
- Train into the comparison probability space directly (skipping the feature-vector step)
- None of the above
- Something else?
Some useful links are: