DimFlux: Force-Directed Additive Line Diagrams

Abstract

The visualization of concept lattices is a central problem in the field of Formal Concept Analysis. Force-directed algorithms, as popular in graph drawing, are a promising approach, treating lattice diagrams as physical models, optimizing node positions based on forces derived from the lattice structure. We build on the work of Zschalig, who, however, limited himself to attribute-additive diagrams. We use a more general additivity, in which both the attributes and the objects contribute to the positions of the concept nodes. We replace the planarity enhancer used by Zschalig to obtain a starting diagram for force-directed optimization with the DimDraw algorithm, which generates structured order diagrams on its own. The combination results in DimFlux, an algorithm that leverages the advantages of DimDraw but generates additive diagrams in which readability is increased by maximizing the conflict distance between nodes and non-incident edges.

Figures (15)

• Figure 1: A small formal context of the five dwarf planets and a poorly designed diagram of its concept lattice.
• Figure 2: The set representation matrix SRM for Figure \ref{['fig:bungled']} (doubly-additive). The rows are labeled by the eleven formal concepts (in lectic order of their intents) and the columns are labeled by the objects and attributes.
• Figure 3: Additive diagram that has been obtained as an orthogonal projection from the non-additive diagram in Figure \ref{['fig:bungled']}.
• Figure 4: The middle atom is dragged to the right.
• Figure 5: Possible positions of a concept $v$ relative to a non-incident edge $v_1 v_2$

Theorems & Definitions (4)

• Theorem 1
• proof : Proof of Theorem \ref{['thm:additive_extension']}
• Theorem 2
• proof : Proof of Theorem \ref{['thm:additive_realizer_rd']}