The rapid development of information technology is making it possible to collect massive amounts of multidimensional, multimodal data with high dimensionality in diverse fields of science and engineering. New statistical learning and data mining methods have been developing in parallel to solve challenging problems arising out of these complex systems. In this talk we will discuss a specific type of statistical learning, namely the problem of feature selection and classification when the features are multidimensional. More specifically they are spatio-temporal in nature. Various machine learning techniques are suitable for this type of problems, but the underlying statistical theories are not well established. We will discuss linear discriminant analysis based technique under spatially dependent feature vector and talk about their theoretical and numerical performances in the context of brain imaging.