Component Analysis methods (e.g. Kernel Principal Component Analysis, Independent Component Analysis, Tensor factorization) have been successfully applied to modeling, classification and clustering in numerous visual, graphics and signal processing tasks over the last four decades. CA techniques are especially appealing because many can be solved as generalized eigenvalue problems or alternated least squares procedures, for which there exist extremely efficiently and numerically stable algorithms. These spectral approaches offer a potential for solving linear and non-linear estimation/learning problems efficiently and without local minima. In this project, we develop a framework for energy-based learning of component analysis methods and apply it to improve state-of-the-art methods for classification (e.g. support vector machines), clustering (e.g. normalized cuts) or face tracking algorithms (e.g. active appearance models).