A Minimally Constrained Optimization Algorithm for Table Cartograms

Abstract

Table cartograms are a recent type of data visualization that encodes numerical tabular data as a grid of quadrilaterals whose area are brought into correspondence with the input data. The overall effect is similar to that of a heat map that has been ‘area-ed‘ rather than shaded. There exist several algorithms for creating these structures—variously utilizing techniques such as computational geometry and numerical optimization —yet each of them impose aesthetically-motivated conditions that impede fine tuning or manipulation of the visual aesthetic of the output. In this work we contribute an optimization algorithm for creating table cartograms that is able to compute a variety of table cartograms layouts for a single dataset. We make our web-ready implementation available as table-cartogram.ts.

What are Table Cartograms Good for Anyway? An Algebraic Analysis

“…The visual effect is that of a shaded matrix that has been "area-ed" rather than colored. They can be characterized as having Planar Grid Topology (none of the cells overlap) and an Accurate Data Embedding (data is represented accurately as area) [MK20]. While color is a consonant secondary encoding, its use is not definitionally required.…”

“…They use a computational geometry-based algorithm to constructively demonstrate that all tables of positive numbers admit a TACO. Subsequent work [LI19, IL20,MK20] found that more expressive graphics could be produced with optimization-based techniques, utilizing the fact the problem is under-constrained [IL20]. This allows for multiple outputs for a single input, as in Fig.…”

“…Fig. 1 shows an example, garnered from changing algorithms, however significant variance can result from seeminglyinnocuous parameter changes [MK20]. This multiplicity is a Hallucinator.…”

“…A possible factor for the current rarity of TACOs is a lack of easily accessible implementations. At the time of this writing there are two known publicly available implementations, both of which utilize optimization-based schemes for computation [Has21,MK20]. There are several more known versions, which are not available publicly, including Inoue and Li's [IL20] optimizationbased approach, and Evans et al's [EFK * 13] geometry-based and optimization-based approaches.…”

“…We demonstrate the potential of such an analysis by investigating the properties of an uncommon visualization-the table cartogram (TACO)-through a lens informed by Kindlmann and Scheidegger's Algebraic Visualization Design (AVD) [KS14]. We study TACOs because, despite having existed for several years [EFK * 13], appropriate usage is still unknown [MK20]. We focus on AVD because-in contrast to other frameworks-it provides concrete assertions about visualization quality which are human-operable and interpretable.…”