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In this paper, we present a summary of our ongoing research on the classification of hyperspectral images. We are experimenting with both supervised and unsupervised algorithms. In particular, we have developed an unsupervised classification algorithm based on Independent Component Analysis (ICA). This algorithm is known as the ICA mixture model (ICAMM) algorithm and has shown promising results. In addition, we are investigating the use of Support Vector Machines (SVMs), a supervised approach for the classification of hyperspectral data. We have employed the Lagrangian optimization method and call our classifier the Lagrangian SVM (LSVM) classifier. Classification accuracy of these classifiers has been assessed using an error matrix based overall accuracy measure.