Craig Saunders, Alexei Vinokourov, John Shawe-taylor
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 ker(cid:173) nel from which the n-gram and string kernels can be re-constructed. The Fisher kernel view gives a more flexible insight into the string kernel and suggests how it can be parametrised in a way that re(cid:173) flects the statistics of the training corpus. Furthermore, the prob(cid:173) abilistic modelling approach suggests extending the Markov pro(cid:173) cess to consider sub-sequences of varying length, rather than the standard fixed-length approach used in the string kernel. We give a procedure for determining which sub-sequences 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.