Unsupervised real-time constrained linear discriminant analysis to hyperspectral image classification

We have proposed a constrained linear discriminant analysis (CLDA) approach for classifying the remotely sensed hyperspectral images. Its basic idea is to design an optimal linear transformation operator which can maximize the ratio of inter-class to intra-class distance while satisfying the constraint that the different class centers after transformation are aligned along different directions. Its major advantage over the traditional Fisher's linear discriminant analysis is that the classification can be achieved simultaneously with the transformation. The CLDA is a supervised approach, i.e., the class spectral signatures need to be known a priori. But, in practice, these informations may be difficult or even impossible to obtain. So in this paper we will extend the CLDA algorithm into an unsupervised version, where the class spectral signatures are to be directly generated from an unknown image scene. Computer simulation is used to evaluate how well the algorithm performs in terms of finding the pure signatures. We will also discuss how to implement the unsupervised CLDA algorithm in real-time for resolving the critical situations when the immediate data analysis results are required.