# Probability estimation of a distances between samples and references - a classification problem

Background

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).

Problem

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?

• What exactly do you mean by 'distance'? Have you defined some norm and are you only comparing the resulting values to each other, or are you trying to match faces by distances (e.g. eye-distance) ? Commented Dec 5, 2012 at 14:27
• I would presume this would be one of the standard similarity/dissimilarity matrices used for comparing data of this kind. Would be good if the OP could clarify which one. Commented Dec 5, 2012 at 14:36
• Edited my question. In my case I use Local Binary Pattern Historgram to calculate the coordinates for each face. I talk about the distances between points in the coordinate space, that belong to training faces and the coordinate point that belongs to the tested face. Commented Dec 5, 2012 at 14:49