cPro: Circular Projections Using Gradient Descent

Abstract

Typical projection methods such as PCA or MDS rely on mapping data onto an Euclidean space, limiting the design of resulting visualizations to lines, planes, or cubes and thus may fail to capture the intrinsic non-linear relationships within data, resulting in inefficient use of two-dimensional space. We introduce the novel projection technique -cPro-, which aligns high-dimensional data onto a circular layout. We apply gradient descent, an adaptable optimization technique to efficiently reduce a customized loss function. We use selected distance measures to reduce high data dimensionality and reveal patterns on a two-dimensional ring layout. We evaluate our approach compared to 1D and 2D MDS and discuss further use cases and potential extensions. cPro enables the design of novel visualization techniques that employ semantic distances on a circular layout.