An improved manifold learning method, called enhanced semi-supervised local fisher discriminant analysis (ESELF), for gene expression data classification is proposed. Motivated by the fact that semi-supervised and parameter-free are two desirable and promising characteristics for dimension reduction, a new difference-based optimization objective function with unlabeled samples has been designed. The proposed method preserves the global structure of unlabeled samples in addition to separating labeled samples in different classes from each other. The semi-supervised method has an analytic form of the globally optimal solution and it can be computed based on eigen decompositions. The experimental results and comparisons on synthetic data and two DNA micro array datasets demonstrate the effectiveness of the proposed method.
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