A framework for developing associative classifiers based on ICA

Connective approaches are useful for developing theoretical tools for classifying, filtering, and modeling raw data. The redundancy of inputs and system states allows the development of approximations for nonlinear problems. One of the most useful connective approaches is the use of associative memory; it creates a relation between data inputs and data outputs through a linear relationship expressed by a matrix. This relation is usually expressed in the binary domain, and the learning process consists of how the linear matrix is built and weighted. Associative memory approaches are founded on the linear independence concept, which defines when a particular mixture of inputs can be associated with a mixture of outputs. The redundancy of states is useful for creating a better approximation when the input and outputs are not strictly linearly related. This work presents a new family of associative memories, expanding the concept of independence to create the relation between inputs and outputs. This approach is founded on two different types of independence: linear independence and probabilistic independence. We present and discuss the foundations and concepts involved. Then, we show the practical results obtained after applying this new framework as a pattern classifier in image analysis tasks.