<title>Cognitive distance</title>

Abstract

In geographic space, it is well known that spatial behaviors of humans are directly driven by their spatial cognition, rather than by the physical or geometrical reality. The cognitive distance in spatial cognition is fundamental in intelligent pattern recognition. More precisely, the cognitive distance can be used to measure the similarities (or relevance) of cognized geographic objects. In the past work, the physical or Euclidean distances are used very often. In practice, many inconsistencies are found between the cognitive distance and the physical distance. Usually the physical distance is overestimated or underestimated in the process of human spatial behaviors and pattern recognition. These inconsistencies are termed distance distortions. The aim of this paper is to illustrate the conceptions of cognitive distance and distance distortion. And if the cognitive distance is argued to be two-dimensional, it exists in heterogeneous space and the property of quasi-metric is shown. If the cognitive distance is multi-dimensional, it exists in homogeneous space and the property of metric is shown. We argue that distance distortions arise from the transformation of homogeneous to heterogeneous space and from the transformation of the two-dimensional cognitive distance to the multi-dimensional cognitive distance. In some sense, the physical distance is an instance of cognitive distance.