  This paper presents an extension and an elaboration of the theory of
differential similarity, which was originally proposed in arXiv:1401.2411
[cs.LG]. The goal is to develop an algorithm for clustering and coding that
combines a geometric model with a probabilistic model in a principled way. For
simplicity, the geometric model in the earlier paper was restricted to the
three-dimensional case. The present paper removes this restriction, and
considers the full $n$-dimensional case. Although the mathematical model is the
same, the strategies for computing solutions in the $n$-dimensional case are
different, and one of the main purposes of this paper is to develop and analyze
these strategies. Another main purpose is to devise techniques for estimating
the parameters of the model from sample data, again in $n$ dimensions. We
evaluate the solution strategies and the estimation techniques by applying them
to two familiar real-world examples: the classical MNIST dataset and the
CIFAR-10 dataset.
