Automatic classification of complex data is an area of great interest as it allows to make efficient use of the increasingly data intensive environment that characterizes our modern world. This thesis presents to two contributions to this research area. Firstly, the problem of discriminative feature extraction for data organized in multidimensional arrays. In machine learning, Linear Discriminant Analysis (LDA) is a popular discriminative feature extraction method based on optimizing a Fisher type criterion to find the most discriminative data projection. Various extension of LDA to high-order tensor data have been developed. The method proposed is called the Efficient Greedy Feature Extraction method (EGFE). This method avoids solving optimization problems of very high dimension. Also, it can be stopped when the extracted features are deemed to be sufficient for a proper discrimination of the classes. Secondly, an application of EGFE methods to early detection of dementia disease. For the early detection task, four cognitive scores are used as the original data while we employ our greedy feature extraction method to derive discriminative privileged information feature from fMRI data. The results from the experiments presented in this thesis demonstrate the advantage of using privileged information for the early detection task.