Proximity visualization via Common Fate luminance changes

We introduce a new design for visualizing high dimensional data. Points in high dimensional space are often illustrated through 2D or 3D embeddings, which are often cluttered and may-be unaccessible to non-scientific audience. In our design, instead of representing data points as 2D/3D vectors, each data point is represented by a smoothly varying function of time. These smooth functions are used to control the luminance of iconic representations of the data points, where the value of each such function determines the luminance of one icon that is associated with the underlying data point. The resulting display has a high capacity and is intuitively clear to the viewer. Perceptually, it is based on a fundamental psychophysical principle, namely the Gestalt law of Common Fate. Algorithmically, we present two methods designed to meet the demands of the visualization: a new non-negative matrix factorization method, and a partition-based grid embedding technique.