limited GASS sample. These tests demonstrate that whilst a single ANN model could not be found that is a good representation of all of the galaxies in the combined GASS and ALFALFA samples, it is nonetheless possible to post-facto exclude those galaxies for which the ANN is not suitable. For this reason, our approach for the remainder of the paper is to train our networks only using the ALFALFA sample, and then to develop a set of criteria from which we can assess the robustness of the gas fraction estimate. The cuts used in Fig. \[fig-gr-mu\] represent a rather crude approach, and practical here only because we are dealing with a two-dimensional input parameter space. With greater dimensionality (higher number of input parameters for the calibration), such simple cuts are cumbersome and complex, and ultimately subjective with no quantitative assessment of suitability. Therefore, whilst the general approach of limiting the data suitable for the application of a given calibration is desirable, a more sophisticated method is required. We return to this issue in Section \[sec-pr\].

![The same as Figure \[fig-alfa-gass-two-par\], using the same input variables, but now using the matrix representation in Eq. \[eq-basis-function\] with 15 independent coefficients rather than 