Fisher kernel

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In mathematics, the Fisher kernel, named in honour of Sir Ronald Fisher, is a kernel useful in information retrieval. It was introduced in 1998 by Tommi Jaakola ^[1].

The Fisher kernel is the kernel for a generative probabilistic model. As such, it constitutes a bridge between generative and probabilistic models of documents^[2]. Fisher kernels exist for numerous models, notably tf–idf ^[3], Naive Bayes and PLSI.

1 Fisher score
2 Fisher kernel
3 See also
4 Notes and references

[edit] Fisher score

The Fisher kernel makes use of the Fisher score, defined as

$U_X = \nabla_{\theta} \log P(X|\theta)$

with $θ$ begin a set (vector) of parameters. $log P (X | θ)$ is the log-likelihood of the probabilistic model.

[edit] Fisher kernel

The Fisher kernel is defined as

$K(X_i, X_j) = U_{X_{i}}^T I^{-1} U_{X_{j}}$

with I the Fisher information matrix

[edit] See also

Fisher information metric

[edit] Notes and references

^ Exploiting Generative Models in Discriminative Classifiers (1998) PS, Citeseer
^ Generative vs Discriminative Approaches to Entity Recognition from Label-Deficient Data (2003) PDF, Citeseer
^ Deriving TF-IDF as a fisher kernel (2005) PDF [1]