Abstract
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.
Highlights
Data description [1], [2], which can reveal the nature of data, is playing an increasingly pivotal role in the field of data analysis
Based on the framework of constructing one-dimensional interval information granules proposed by Pedrycz in [10], we introduce the criteria of coverage and specificity as the quantitative standard for constructing multidimensional hypersphere information granules
This study has presented a novel granular description method based hypersphere information granules regarding three different distance measures
Summary
Data description [1], [2], which can reveal the nature of data, is playing an increasingly pivotal role in the field of data analysis. Unlike the ‘‘multiple information granularity’’ in [19] and the ‘‘union information granule’’ in [21], the ultimate objective of this article is focusing on using three different distance measures to generate hypersphere information granules with three different geometric shapes (sphere, cube and diamond) to carry out a comparative study instead of focusing on changing the sizes or quantities of information granules By accomplishing this objective, we can perform granular description of data from three perspectives compared to the methods proposed by the existing papers. Granules proposed by Pedrycz in [10], we introduce the criteria of coverage and specificity as the quantitative standard for constructing multidimensional hypersphere information granules
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