Abstract: Based on analysis on the characteristics of the topic information and according to principles of statistics, the paper puts forwards a mathematical model for space of intelligence topic information by means of the constructive theories of vector space and random event space; strategy of retrieving components from topic information is proposed and design rule of constructing a maximum approximate space of topic information is given. The paper also raises a concrete method to extract the keywords from topic information. The method consists of 3 parts with 9 steps, can extract the keywords with maximal common views in topic information that is built from samples of with universality and representativeness. In the end, the paper presents an example that mines the key elements for a topic of scientific research from the topic information of choosing a scientific subject.

Key words: data mining, intelligence analysis, topic information, mathematical model, keywords