Cluster Exploration using Informative Manifold Projections
Stavros Gerolymatos Xenophon Evangelopoulos Vladimir Gusev John Y. Goulermas
Dimensionality reduction (DR) is one of the key tools for the visual
exploration of high-dimensional data and uncovering its cluster structure in
two- or three-dimensional spaces. The vast majority of DR methods in the
literature do not take into account any prior knowledge a practitioner may have
regarding the dataset under consideration. We propose a novel method to
generate informative embeddings which not only factor out the structure
associated with different kinds of prior knowledge but also aim to reveal any
remaining underlying structure. To achieve this, we employ a linear combination
of two objectives: firstly, contrastive PCA that discounts the structure
associated with the prior information, and secondly, kurtosis projection
pursuit which ensures meaningful data separation in the obtained embeddings. We
formulate this task as a manifold optimization problem and validate it
empirically across a variety of datasets considering three distinct types of
prior knowledge. Lastly, we provide an automated framework to perform iterative
visual exploration of high-dimensional data.