In domains where input features are ordered (e.g., images or time series, as opposed to tabular data), we expect relevant information to be located in a smooth and coherent region of the input. This property can be evaluated in two complementary ways.
First, [Fong and Vedaldi (2017)] assess the locality of the explanans: a higher degree of cohesion is achieved when relevant information lies within a small, contiguous region of interest, making the explanans more condensed and easier to interpret. In saliency maps, this can be quantified by computing the area of the smallest bounding box that encloses the thresholded explanans.
Second, [Saifullah et al. (2024)] assess the smoothness of the explanans: a more continuous attribution map is often easier to understand. This can be measured by summing the absolute differences in attribution between neighboring features (e.g., in x- and y-directions for images). A higher score indicates a more fragmented, less interpretable explanans.
Both variants are applicable to data with ordered features and extend naturally to temporal domains. While originally proposed for FAs, these metrics can also be applied to CE when concept-based saliency maps are available (e.g., as presented by [Lucieri et al. (2020)]).