I have a distance matrix with some noise (e.g. obtained by asking people how similar two objects from a set of objects are). I am interesting in finding the (best guess for the) dimensionality of the feature space for the objects (i.e. how many features of the objects people are presumably taking into account when rating similarity).
I know of algorithms that reduce the dimension to a given (e.g. multidimensional scaling) but I don't know how to guess the number of dimensions given that there is some noise.