A theory of learning with similarity functions

Kernel functions have become an extremely popular tool in machine learning, with an attractive theory as well. This theory views a kernel as implicitly mapping data points into a possibly very high dimensional space, and describes a kernel function as being good for a given learning problem if data is separable by a large margin in that implicit space. However, while quite elegant, this theory does not directly correspond to one's intuition of a good kernel as a good similarity function. Furthermore, it may be difficult for a domain expert to use the theory to help design an appropriate kernel for the learning task at hand since the implicit mapping may not be easy to calculate. Finally, the requirement of positive semi-definiteness may rule out the most natural pairwise similarity functions for the given problem domain. In this work we develop an alternative, more general theory of learning with similarity functions (i.e., sufficient conditions for a similarity function to allow...

• Type: Journal
• Year: 2008
• Where: ML
• Authors: Maria-Florina Balcan, Avrim Blum, Nathan Srebro
• Keywords: Kernel Function, Machine Learning, ML 2008, Similarity Function, Theory