Q-metrics: An efficient formulation of normalized distance functions

A generalized class of normalized distance functions called Q-metrics is described in this paper. The Q-metrics approach relies on a unique functional, using a single bounded parameter lambda, which characterizes the conventional distance functions in a normalized per-unit metric space. In addition to this coverage property of the proposed model, a distinguishing and extremely attractive characteristic of the Q-metric function is its low computational complexity. We present a formal mathematical proof that Q-metrics satisfy the standard metric axioms. A novel artificial neural network is completely defined and constructed using Q-metrics. This new network is shown to outperform a conventional feed forward back propagation network with the same size when tested on real data sets.