Using Nested Surfaces for Visual Detection of Structures in Databases

We define, compute, and evaluate nested surfaces for the purpose of visual data mining. Nested surfaces enclose the data at various density levels, and make it possible to equalize the more and less pronounced structures in the data. This facilitates the detection of multiple structures, which is important for data mining where the less obvious relationships are often the most interesting ones. The experimental results illustrate that surfaces are fairly robust with respect to the number of observations, easy to perceive, and intuitive to interpret. We give a topology-based definition of nested surfaces and establish a relationship to the density of the data. Several algorithms are given that compute surface grids and surface contours, respectively. DOI: https://doi.org/10.1007/978-3-540-71080-6_7 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-56372 Accepted Version Originally published at: Mazeika, Arturas; Böhlen, Michael Hanspeter; Mylov, Peer (2008). Using Nested Surfaces for Visual Detection of Structures in Databases. In: Simoff, Simeon J; Böhlen, Michael Hanspeter; Mazeika, Arturas. Visual Data Mining: Theory, Techniques and Tools for Visual Analytics. Berlin / Heidelberg: Springer, 91-102. DOI: https://doi.org/10.1007/978-3-540-71080-6_7 Using Nested Surfaces to Detect Structures in Databases Arturas Mazeika Michael Böhlen Peer Mylov [email protected] [email protected] [email protected] 1Department of Computer Science, Aalborg University, Fredrik Bajers Vej 7E, 9220 Aalborg, Denmark 2Institute of Communication, Aalborg University, Niels Jernes Vej 14, 9220 Aalborg, Denmark Abstract. We define, compute, and evaluate nested surfaces for the purpose of visual data mining. Nested surfaces enclose the data at various density levels, and make it possible to equalize the more and less pronounced structures in the data. This facilitates the detection of multiple structures, which is important for data mining where the less obvious relationships are often the most interesting ones. The experimental results illustrate that surfaces are fairly robust with respect to the number of observations, easy to perceive, and intuitive to interpret. We give a topology-based definition of nested surfaces and establish a relationship to the density of the data. Several algorithms are given that compute surface grids and surface contours, respectively. We define, compute, and evaluate nested surfaces for the purpose of visual data mining. Nested surfaces enclose the data at various density levels, and make it possible to equalize the more and less pronounced structures in the data. This facilitates the detection of multiple structures, which is important for data mining where the less obvious relationships are often the most interesting ones. The experimental results illustrate that surfaces are fairly robust with respect to the number of observations, easy to perceive, and intuitive to interpret. We give a topology-based definition of nested surfaces and establish a relationship to the density of the data. Several algorithms are given that compute surface grids and surface contours, respectively.