String Kernels , Fisher Kernels

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 from which the n-gram and string kernels can be reconstructed. The Fisher kernel view gives a more exible insight into the string kernel and suggests how it can be parametrised in a way that re-ects the statistics of the training corpus. Furthermore, the prob-abilistic modelling approach suggests extending the Markov process to consider sub-sequences of varying length, rather than the standard xed-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 innuence 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 diierent kernels using the standard Bag of Words kernel as a baseline.