Feature Transformation With Applications To SAR Target Discrimination

In SAR target discrimination, a well-formed feature set is the key to achieve high prediction performance. As a classical and valuable feature transformation tool, Fisher linear discrimination analysis(FLDA) has been widely studied due to its simplicity, robustness, and predictive accuracy. In this thesis, we propose two new algorithms based on Fisher’s discrimination criterion.In chapter 2, we review FLDA, analyze its limitations, and develop an iterative scheme to modify FLDA by combining it with sequential hypothesis testing(SHT). Details are as follows: firstly, the standard FLDA is performed to get the projecting direction; then in the projection space, we estimate the posterior distribution of one single test sample, and use the likelihood ratio test to determine whether or not this transformation space is informative enough to classify the current sample; if the likelihood ratio criterion is satisfied, the test sample will be classified according to its posterior; if not, we will refer to the test sample’s posterior as its prior in FLDA, update the projecting direction, and repeat the steps from the beginning. By making full use of the information of different test data, a particular and more appropriate transformation space is designed for every single test sample. Results on UCI datasets and SAR image measured data show this iteration process is competitive compared with other methods.Although FLDA is great in dimension reduction, its low-dimensional subspace is still trapped by all features, including some overly correlated or irrelevant features. In chapter 3, we add a sparsity-induced penalty term to the regression-formed FLDA problem, in which feature selection and FLDA are built into one optimization formation.The idea relies on the fact that the value of the regression coefficients is an indicator of the relative usefulness of the corresponding features, which means features with zero value coefficients are redundant in the feature set or less important in classification. By treating each row of the matrix of the regression coefficients as a group, the optimization procedure is able to set some rows to exact zero, and thereafter the effect of features with zero coefficients is eliminated from the construction of the projecting space, also from the classification. The real power of the new model is that it realizes feature selection and FLDA simultaneously. Tested on UCI datasets and SAR image measured data, the approach enjoys high accuracy in classification and efficiency in feature selection.