Granular Description of Data: A Comparative Study Regarding to Different Distance Measures

In data science, how to depict data in the concise and comprehensive way is an important issue. To address the issue, the key is to construct descriptors that are highly interpretable and can be used to reveal the data structure. Information granules, as one important role in the field of granular computing, are entities that can be easily represented and abstracted from data. Therefore, by constructing a series of information granules, the characteristics of data can be captured and described, and the granular description of data is realized. A key part of the granular description of data is to explore the geometric characteristics (locations and shapes) of information granules used to describe data. Since distance measures directly affect the geometric characteristics of the constructed information granules, a comparative study based on three different distance measures is conducted in this paper. From the experimental results based on both synthetic and UCI repository datasets, it can be seen that the information granules constructed in the case where three different distance measures are used show different geometrical shapes, and can describe the data in a concise way. Furthermore, the data structure can be explored more comprehensively by using three distance measures.