Learning Similarity with Fuzzy Functions of Adaptable Complexity

A common approach in database queries involves the multi-dimensional representation of objects by a set of features. These features are compared to the query representation and then combined together to produce a total similarity metric. In this paper we introduce a novel technique for similarity learning within features (attributes) by manipulating fuzzy membership functions (FMFs) of different complexity. Our approach is based on a gradual complexity increase adaptable to problem requirements. The underlying idea is that less adaptable functions will act as approximations for more complex ones. We begin by interpolating a set of planes in the training dataset and due to linearity we get a fast first impression of the underlying complexity. We proceed to interpolate two asymmetrical sigmoidal functions whose initial approximations are calculated from the plane properties. If satisfactory accuracy is not achieved we provide advanced modeling capabilities by investigating FMFs parameters and convolving their output with additional functions.