The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

We study a model of unsupervised learning where the real-valued data vectors are isotropically distributed, except for a single symmetry-breaking binary direction Bin¿-1,+1¿(N), onto which the projections have a Gaussian distribution. We show that a candidate vector J undergoing Gibbs learning in this discrete space, approaches the perfect match J=B exponentially. In addition to the second-orde...