MAD-FC: A fold change visualization with readability, proportionality, and symmetry

We propose a fold change transform that demonstrates a combination of visualization properties exhibited by log and linear plots of fold change. A fold change visualization should ideally exhibit: (1) readability, where fold change values are recoverable from datapoint position; (2) proportionality, where fold change values of the same direction are proportionally distant from the point of no change; (3) symmetry, where positive and negative fold changes of the same magnitude are equidistant to the point of no change; and (4) high dynamic range, where datapoint values are distinguishable across orders of magnitude within a fixed plot area and pixel resolution. A linear visualization has readability and partial proportionality but lacks high dynamic range and symmetry (because negative direction fold changes are bound between [0, 1] while positive are between (1, ∞)). Log plots of fold change have partial readability, high dynamic range, and symmetry, but lack proportionality because of the log transform. We outline a new transform, named mirrored axis distortion of fold change (MAD-FC), that extends a linear visualization of fold change data to exhibit readability, proportionality, and symmetry (but still has the limited dynamic range of linear plots). We illustrate the use of MAD-FC with biomedical data using various fold change plots. We argue that MAD plots may be a more useful visualization than log or linear plots for applications that do not require a high dynamic range (less than 8 units in log2 space).