Interactive visual data categorization systems and methods

The present disclosure provides interactive visual data labeling systems and methods that improve upon power-diagram Voronoi Treemaps by supporting interactive arranging and grouping of objects represented by thumbnail images. The provided interactive visual data labeling system enables new and innovative fluid interactions and direct manipulation of treemap cells to arrange objects and groups of objects, and create, merge, expand, or collapse groups. In effect, these enabled fluid interactions and direct manipulation provide an intuitive, stable, and predictable Voronoi treemap for users. In at least some aspects, the provided visual data labeling system uses a force-directed power diagram technique, which enables controlling the stability of the Voronoi treemap layout and updating it smoothly when dragging a cell across a parent cell. In effect, the predictability and stability enables the Voronoi treemap to react as a user expects during the user's interaction with the treemap.