Visualizing and Interacting with Kernelized Data

Author(s)

Barbosa, A. ^[1] ; Paulovich, F. V. ^[1] ; Paiva, A. ^[1] ; Goldenstein, S. ^[2] ; Petronetto, F. ^[3] ; Nonato, L. G. ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Comp & Matemat Computac, Sao Carlos, SP - Brazil

^[2] Univ Estadual Campinas, Inst Comp, Campinas, SP - Brazil

^[3] Univ Fed Espirito Santo, Dept Matemat, Vitoria, ES - Spain

• Document type: Journal article
• Source: IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS; v. 22, n. 3, p. 1314-1325, MAR 2016.
• Web of Science Citations: 8

Abstract

Kernel-based methods have experienced a substantial progress in the last years, tuning out an essential mechanism for data classification, clustering and pattern recognition. The effectiveness of kernel-based techniques, though, depends largely on the capability of the underlying kernel to properly embed data in the feature space associated to the kernel. However, visualizing how a kernel embeds the data in a feature space is not so straightforward, as the embedding map and the feature space are implicitly defined by the kernel. In this work, we present a novel technique to visualize the action of a kernel, that is, how the kernel embeds data into a high-dimensional feature space. The proposed methodology relies on a solid mathematical formulation to map kernelized data onto a visual space. Our approach is faster and more accurate than most existing methods while still allowing interactive manipulation of the projection layout, a game-changing trait that other kernel-based projection techniques do not have. (AU)

• FAPESP's process: 11/22749-8 - Challenges in exploratory visualization of multidimensional data: paradigms, scalability and applications
• Grantee: Luis Gustavo Nonato
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 14/09546-9 - Applications of SPH in geometry processing and fluid flow animation
• Grantee: Afonso Paiva Neto
• Support Opportunities: Regular Research Grants