On Fuzzy vs. Metric Similarity Search in Complex Databases

The task of similarity search is widely used in various areas of computing, including multimedia databases, data mining, bioinformatics, social networks, etc. For a long time, the database-oriented applications of similarity search employed the definition of similarity restricted to metric distances. Due to the metric postulates (reflexivity, non-negativity, symmetry and triangle inequality), a metric similarity allows to build a metric index above the database which can be subsequently used for efficient (fast) similarity search. On the other hand, the metric postulates limit the domain experts (providers of the similarity measure) in similarity modeling. In this paper we propose an alternative non-metric method of indexing for efficient similarity search. The requirement on metric is replaced by the requirement on fuzzy similarity satisfying the transitivity property with a tuneable fuzzy conjunctor. We also show a duality between the fuzzy approach and the metric one.