Design of knowledge-based kernels by t-equivalences

• Bernhard Moser

The motivation for this proposal is based on a recently revealed interrelationship between kernels as used in machine learning and fuzzy equivalence relations. This result shows that normalized kernels can be represented as fuzzy equivalence relations in a way that is commonly used in fuzzy systems for representing fuzzy relations and fuzzy rule bases. Driven by the same geometric imagination which led to this insight new mathematical conjectures are stated whose verification would be of fundamental interest concerning questions of optimization and determining estimates and bounds in the context of kernel-based methods. In addition to this basic and fundamental theoretical point of view the revealed relationship also opens up a new way of looking at the problem of incorporating prior knowledge for the design of kernel-based methods. The novel aspect is that by this it becomes possible to take advantage from knowledge in terms of fuzzy sets and relations when designing a kernel. The goal is to explore thoroughly this relationship and its impact on the design of kernel-based methods from a mathematical as well as from a machine learning point of view.