Characterizing inherent image ordinality to improve multiclass classification

Many medical diagnostic tasks have outcomes that are ordinal in nature and the features associated with these ordinal outcomes are often also ordinal. For example, cancer grades often follow a grading system from 0 to 4 and many patient characteristics, such as size of lesion, increase with cancer grade. Despite this reality, most classification models that learn mappings from features to class do not explicitly model the ordinality of the data. This work seeks to develop methods to quantify the inherent ordinality in data in the interest of improving classification performance. We build on prior work that proposed summarizing feature ordinality with a pairwise separability matrix (PSM). We propose new distance measures to calculate the PSM and to summarize the apparent ordinality of the entire PSM into a new single number reflective of the overall ordinality present in data. We validate these methods with 1) multiple variations of simulated data for a four-class ordinal task and with 2) radiomics features extracted from a multi-institutional set of N=660 chest x-ray radiographs acquired to identify four grades of pneumoconeosis. Results demonstrate that PSM’s can be reliably calculated based on separation of features in the original feature space using conventional distance measures (discriminant ratio or Frechet distance). Likewise, we show that our proposed summary measure estimates overall ordinality that correlates well with known levels of ordinality in both the simulated and real data. These promising results suggest that the overall ordinality measure could be used to a) determine if a classification task would benefit from an ordinal-aware loss function and b) set optimal weights for ordinal-aware loss functions.