Pattern Recognition as a Human Centered non-Euclidean Problem

Regularities in the world are human defined. Patterns in the observed phenomena are there because we define and recognize them as such. Automatic pattern recognition tries to bridge the gap between human judgment and measurements made by artificial sensors. This is done in two steps: representation and generalization. Traditional representations of real world objects to be recognized, like features and pixels, either neglect possibly significant aspects of the objects, or neglect their dependencies. We therefor reconsider human recognition and observe that it is based on our direct experience of similarity or dissimilarity of objects. Using these concepts, a pattern recognition system can be defined in a natural way by a pairwise comparison of objects. This results in the dissimilarity representation for pattern recognition. An analysis of dissimilarity measures optimized for performance shows that they tend to be non-Euclidean. The Euclidean vector spaces, traditionally used in pattern recognition and machine learning may thereby be suboptimal. The causes and consequences of the use of non-Euclidean representations will be discussed. It is conjectured that human judgment of object differences result in these non-Euclidean representations as object structure is taken into account.