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Structured Semi-supervised Discriminant Analysis

Classical Linear Discriminant Analysis(LDA) is an effective dimensionality reduction method which preserve class separabiliy by maximizing the between class covariance and simultaneously minimizing the within class covariance. But, the covariance matrix of each class may not be accurately estimated when the given training samples is not sufficient. To overcome this disadvantage of LDA, a novel Semi-supervised Discriminant Analysis(SDA) was introduced, which can effectively utilize the labeled and unlabeled samples. However, SDA still can not fully use the structure information hidden in data, since the samples in a class may be scattered in several regions. Therefore, in this paper, we introduce a novel approach, called Structured Semi-supervised Discriminant Analysis(SSDA), which exploits the data structures hidden in samples in a class via semi-supervised clustering methods and uses them as “different classes” in calculating the between class covariance, hence it is an extension and improvement of SDA. Experiments on 2 artificial datasets and 8 real-life dataset show the effectiveness of our algorithm.