7. Component Analysis methods for pattern recognition

Component analysis (CA) methods (e.g. kernel principal component analysis, linear discriminant analysis, spectral clustering) have been extensively used as a feature extraction step for modeling, classification and clustering in numerous pattern recognition, signal processing or social sciences tasks. The aim of CA is to decompose a signal into relevant components that explicitly or implicitly (e.g. kernel methods) define the representation of the signal. CA techniques are especially appealing because many can be formulated as eigen-problems, offering great potential for efficient learning of linear and non-linear representations of the data without local minima. Although CA methods have been widely used, there is still a need for a better mathematical framework to analyze and extend CA techniques. This tutorial reviews previous work and proposes a unified framework for energy-based learning in CA methods.