Circular Coordinates for Visual Machine Learning

Visually representing multidimensional vectors in spaces above $\mathbb{R}^{3}$ for analyzing correlations and statistical traits remains a significant challenge, particularly within machine learning applications such as clustering analysis. While Inselberg's Parallel Coordinates (1997) set a foundation, the CWU Visual Knowledge Discovery and Imaging Lab expanded on this with Generalized Line Coordinates (Kovalerchuk, 2018). Building on this, we present a system starting from Static Circular Coordinates plotting connected points along a circumference sectioned by n-D vector components $x_1, x_2, \ldots, x_n$. Instead of static sectioning of the circumference, vectors can be plotted as subsequent sections building Dynamic Circular Coordinates. Then, Linear Discriminant Analysis optimizes the coefficients of plotted linear functions. Lastly, computer-aided visually navigated multidimensional scaling can further tune the model. This system allows for analytical prediction of previously unseen vectors using rule-based classification chaining determined from previous vector data from the same domain. By including proportional axes as needed both dual and multi-class comparisons can be made.