Improving the Nonparametric Weighted Feature Extraction Method by Using Training Sample's Linear Combination in Hyperspectral Images

In order to enhance the available methods of feature extraction through non-parametric weighting procedure, an optimization method is introduced in this work. This method can be applied to the problems involving pattern recognition in high dimensional spaces. The method is based on the expansion of non-parametric scattering matrices where their average parameters are calculated for each sample separately using sum of the weighted samples of the other classes. The weight of each of the samples is calculated based on their Euclidean distance from the sample under the study. However, it is not possible to only express the scatteredness of the samples by this parameter alone haply the locations of these samples are important too. That is, it is possible sometimes to have two samples having equal Euclidean distance from the main sample while their degrees of dependences to this main sample are not the same. For instance, it is possible that one of these samples be completely dependent while the other is totally independent of the main sample. On the other hand, the degree of dependence is linearly related to the main sample and hence the linear combination of samples is important in determination of the scattering degree. Using these important parameters, the results of non-parametric weighted feature extraction shows some improvement. In the present work, using this important factor (Linear Combination), the method of non-parametric weighted feature extraction is enhanced and named Linear Combination Non-parametric Weighted Feature Extraction (LC-NWFE). The results show that the suggested method in most of the classes especially in the critical classes where their spectral similarities are high, works much better than NWFE method. The best result achieved was better than 82% for overall accuracy with a kappa accuracy of better than 80%.