Sensible functional linear discriminant analysis

Fisher's linear discriminant analysis (LDA) is extended to both densely recorded functional data and sparsely observed longitudinal data for general c-category classification problems. An efficient approach is proposed to identify the optimal LDA projections in addition to managing the noninvertibility issue of the covariance operator emerging from this extension. To tackle the challenge of projecting sparse data to the LDA directions, a conditional expectation technique is employed. The asymptotic properties of the proposed estimators are investigated and asymptotically perfect classification is shown to be achievable in certain circumstances. The performance of this new approach is further demonstrated with both simulated data and real examples.