On classification: simultaneously reducing dimensionality and finding automatic representation using canonical correlation

This report describes an idea based on the work in [1], where an algorithm for learning automatic representation of visual operators is presented. The algorithm in [1] uses canonical correlation to find a suitable subspace in which the signal is invariant to some desired properties. This report presents a related approach specially designed for classification problems. The goal is to find a subspace in which the signal is invariant within each class, and at the same time compute the class representation in that subspace. This algorithm is closely related to the one in [1], but less computationally demanding, and it is shown that the two algorithms are equivalent if we have equal number of training samples for each class. Even though the new algorithm is designed for pure classification problems it can still be used to learn visual operators as will be shown in the experiment section