**POINT CLUSTER GENERALIZATION EVALUATION: AN INFORMATION
THEORETIC APPROACH**

Z.
Wang^{1}, L.X. Li^{2}, Z.H. Wu^{3}, J. Xiao^{1}

*1 - The School of Resource and Environment Science,Wuhan University,
*

*2 - The School of Science, Wuhan University of Technology,
Wuhan, *

*3 - LIESMARS, Wuhan University, *

*wangzhao8734@163.com*

The prime problem in the automatic map generalization is quantifying the efficiency. With the development of algorithms for Point of Interest (PoI) generalization, this paper attempts to evaluate the efficiency of them in an information theoretic approach.

In order to evaluate the result of Point Cluster generalization with reason, a hierarchical model of
map linguistics is proposed as basis referencing to the mature** **method of Semiotic Linguistics, which includes
three levels: syntactic level, semantic level, pragmatic level. Furthermore,
these three levels are step-up, namely a higher level should be established on
the basis of the lower-level and in turn guide the lower-level’s generalization.
It should be noted that the model of Semiotic Linguistics and
McMaster&Shea’s division Model are independent with each other, and should
be used synthetically.

This paper mainly focuses on the syntactic level. In this level, the
entropy of metric information defined by Li&Huang is employed as an evaluating indicator, which is computed via Voronoi
diagram whose attributes of ‘region influence’ for geographical entities
manifest the content of syntactic level information precisely. Then, a quantitative
changing rule when Point Cluster is generalized under the ‘typification’
generalization constraint can be concluded via mathematical theory. (For Point
Cluster, ‘typification’ means preserving spatial distribution
properties, scilicet, preserving the density contrast of the different region correctly
which is the most important and comprehensive request for generalizing Point
Cluster, but is rarely considered actually in the existing automatic generalization
methods.) The rule will be expressed as follows: on the syntactic level
generalization, considering typification model, generalization will reduce
metric information, and the reductions relate to generalization degree (selection
ratio). Further, the greater the generalized degree is (the smaller the
selection ratio is), the more information will be lost, and the amount of
changing between the information of raw map and generalized map will follow the
rule of_{}. Based on this rule, an instance of evaluation is showed,
which proves that the rule meets the practice of map generalization and is
useful to evaluate effective transmission of maps.