  This paper is concerned with nearest neighbor search in distributional
semantic models. A normal nearest neighbor search only returns a ranked list of
neighbors, with no information about the structure or topology of the local
neighborhood. This is a potentially serious shortcoming of the mode of querying
a distributional semantic model, since a ranked list of neighbors may conflate
several different senses. We argue that the topology of neighborhoods in
semantic space provides important information about the different senses of
terms, and that such topological structures can be used for word-sense
induction. We also argue that the topology of the neighborhoods in semantic
space can be used to determine the semantic horizon of a point, which we define
as the set of neighbors that have a direct connection to the point. We
introduce relative neighborhood graphs as method to uncover the topological
properties of neighborhoods in semantic models. We also provide examples of
relative neighborhood graphs for three well-known semantic models; the PMI
model, the GloVe model, and the skipgram model.
