Neural Networks from Similarity Based Perspective

A framework for Similarity-Based Methods (SBMs) includes many neural network models as special cases. Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons, combining soft hyperplanes to provide decision borders. Scalar product is replaced by a distance function between the inputs and the weights, offering a natural generalization of the standard MLP model to the distance-based multilayer perceptron (D-MLP) model. D-MLPs evaluate similarity of inputs to weights making the interpretation of their mappings easier. Cluster-based initialization procedure determining architecture and values of all adaptive parameters is described. D-MLP networks are useful not only for classification and approximation, but also as associative memories, in problems requiring pattern completion, offering an efficient way to deal with missing values. Non-Euclidean distance functions may also be introduced by normalization of the input vectors in an extended feature space. Both approaches influence the shapes of decision borders dramatically. An illustrative example showing these changes is provided.