title: Visualizing and Interacting with Kernelized Data.
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.
authors.forename: A
authors.initials: A
authors.lastname: Barbosa
authors.forename: F V
authors.initials: FV
authors.lastname: Paulovich
authors.forename: A
authors.initials: A
authors.lastname: Paiva
authors.forename: S
authors.initials: S
authors.lastname: Goldenstein
authors.forename: F
authors.initials: F
authors.lastname: Petronetto
authors.forename: L G
authors.initials: LG
authors.lastname: Nonato