String Kernels, Fisher Kernels and Finite State Automata

In this paper we show how the generation of documents can be thought of as a k-stage Markov process, which leads to a Fisher kernel fromwhich the n-gram and string kernels can be reconstructed. The Fisher kernel view gives a more flexible insight into the string kernel and suggests how it can be parametrised in a way that reflects thestatistics of the training corpus. Furthermore, the probabilistic modellingapproach suggests extending the Markov process to consider subsequences of varying length, rather than the standard fixed-length approach used in the string kernel. We give a procedure for determining which subsequences are informative features and hence generate a Finite State Machine model, which can again be used to obtain a Fisher kernel. By adjusting the parametrisation we can also influence the weighting received by the features. In this way we are able to obtain a logarithmic weighting in a Fisher kernel. Finally, experiments are reported comparing the different kernels using the standard Bag of Words kernel as a baseline.