Analysis on Fisher discriminant criterion and linear separability of feature spac\e

For feature extraction resulted from Fisher discriminant analysis (FDA), it is expected that the optimal feature space is as low-dimensional as possible while its linear separability among different classes is as large as possible. Note that the existing theoretical expectation on the optimal feature dimensionality may contradict with experimental results. Due to this, we address the optimal feature dimensionality problem with this paper. The multi-dimension Fisher criterion is used to measure the linear separability of the feature space obtained using FDA and to analyze the optimal feature dimensionality problem. We also attempt to answer the question "what kind of real-world application is FDA competent for". Theoretical analysis shows that the genuine optimal feature dimensionality should be lower than that presented by Jin et al. A number of experiments illustrate that the proposed optimal feature extraction does have advantages.