Non-Euclidean Problems in Pattern Recognition Related to Human Expert Knowledge

Abstract

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 human judgment with measurements made by artificial sensors. This is done in two steps: representation and generalization.

Traditional object representations in pattern recognition, 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 dissimilarities between objects. Using these concepts, pattern recognition systems can be defined in a natural way by pairwise object comparisons. 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. We will show this by some examples. Causes and consequences of non-Euclidean representations will be discussed. It is conjectured that human judgment of object differences result in non-Euclidean representations as object structure is taken into account.