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To adapt linear discriminant analysis (LDA) to real-world applications, there is a pressing need to equip it with an incremental learning ability to integrate knowledge presented by one-pass data streams, a functionality to join multiple LDA models to make the knowledge sharing between independent learning agents more efficient, and a forgetting functionality to avoid reconstruction of the overall discriminant eigenspace caused by some irregular changes. To this end, we introduce two adaptive LDA learning methods: LDA merging and LDA splitting. These provide the benefits of ability of online learning with one-pass data streams, retained class separability identical to the batch learning method, high efficiency for knowledge sharing due to condensed knowledge representation by the eigenspace model, and more preferable time and storage costs than traditional approaches under common application conditions. These properties are validated by experiments on a benchmark face image data set. By a case study on the application of the proposed method to multiagent cooperative learning and system alternation of a face recognition system, we further clarified the adaptability of the proposed methods to complex dynamic learning tasks.