I am doing face recognition with an algorithm that is comparing a given test face to all other faces in a multidimensional space (face space). Essentially, this means, that the test face is classified as the person with the smallest distance to the test face. In my case I pick the 10 best faces (smallest distances) and I would like to calculate some kind of probability which represents the likelihood of being the same person as on the test image.
The distances between faces are the distances between the respective points in the coordinate system. Each face, which was used for training and each face on which is tested is first transferred in this coordinate space (face space). This can be done by various algorithms (Eigenfaces, Fisherfaces, Liner Binary Pattern Histogram).
Given is a set of distances to a sample and the maximum distance to this sample. As far as I understand, there is no direct relation to a probability. But I think if we assume, that samples of the same person are normally distributed a probability estimate could be calculated. Is it the right way to come up with a solution?