Ridge regression-based feature extraction for hyperspectral data

Feature extraction based on ridge regression (FERR) is proposed in this article. In FERR, a feature vector is defined in each spectral band using the mean of all classes in that dimension. Then, it is modelled using a linear combination of its farthest neighbours from among other defined feature vectors. The representation coefficients obtained by solving the ridge regression model compose the projection matrix for feature extraction. FERR can extract each desired number of features while the other methods such as linear discriminant analysis (LDA) and generalized discriminant analysis (GDA) have limitations in the number of extracted features. Experimental results on four popular real hyperspectral images show that the efficiency of FERR is superior to those of other supervised feature extraction methods in small sample-size situations. For example, for the Indian Pines dataset, the comparison between the highest average classification accuracies achieved by different feature extraction methods using a support vector machine (SVM) classifier and 16 training samples per class shows that FERR is 7% more accurate than nonparametric weighted feature extraction and is also 9% better than GDA. LDA, having the singularity problem in the small sample-size situations, has 40% less accuracy than FERR. The experiments show that generally the performance of FERR using the SVM classifier is better than when using the maximum likelihood classifier.