  Distance function is a main metrics of measuring the affinity between two
data points in machine learning. Extant distance functions often provide
unreachable distance values in real applications. This can lead to incorrect
measure of the affinity between data points. This paper proposes a reachable
distance function for KNN classification. The reachable distance function is
not a geometric direct-line distance between two data points. It gives a
consideration to the class attribute of a training dataset when measuring the
affinity between data points. Concretely speaking, the reachable distance
between data points includes their class center distance and real distance. Its
shape looks like "Z", and we also call it a Z distance function. In this way,
the affinity between data points in the same class is always stronger than that
in different classes. Or, the intraclass data points are always closer than
those interclass data points. We evaluated the reachable distance with
experiments, and demonstrated that the proposed distance function achieved
better performance in KNN classification.
