Multidimensional Projection with Radial Basis Function and Control Points Selection

Multidimensional projection techniques provide an appealing ap-proach for multivariate data analysis, for their ability to translate high-dimensional data into a low-dimensional representation that preserves neighborhood information. In recent years, pushed by the ever increasing data complexity in many areas, numerous ad-vances in such techniques have been observed, primarily in terms of computational efficiency and support for interactive applications. Both these achievements were made possible due to the introduc-tion of the concept of control points, which are used in many differ-ent multidimensional projection techniques. However, little atten-tion has been drawn towards the process of control points selection. In this work we propose a novel multidimensional projection tech-nique based on radial basis functions (RBF). Our method uses RBF to create a function that maps the data into a low-dimensional space by interpolating the previously calculated position of control points. We also present a built-in method for the control points selection based on “forward-selection ” and “Orthogonal Least Squares ” tech-niques. We demonstrate that the proposed selection process allows our technique to work with only a few control points while retaining the projection quality and avoiding redundant control points