Topological spatial data can be useful for the classification and analysis of biomedical data. Neural networks have been used previously to make diagnostic classifications of corneal disease using summary statistics as network inputs. This approach neglects global shape features (used by clinicians when they make their diagnosis) and produces results that are difficult to interpret clinically. In this study we propose the use of Zernike polynomials to model the global shape of the cornea and use the polynomial coefficients as features for a decision tree classifier. We use this model to classify a sample of normal patients and patients with corneal distortion caused by keratoconus. Extensive experimental results, including a detailed study on enhancing model performance via adaptive boosting and bootstrap aggregation leads us to conclude that the proposed method can be highly accurate and a useful tool for clinicians. Moreover, the resulting model is easy to interpret using visual cues.