Digital Signal Processing Reference
In-Depth Information
Since is usually difficult to compute, one can rewrite (1) in
terms of class-conditional probabilities. Using Bayes Rule, we have
Since P(
f
) is class independent and assuming equally likely class
distribution,
Eq. (1) is equivalent to
Computation of class-conditional probabilities needs a prior
modeling step, through which a probability density function of feature
vectors is estimated for each class by using available training data. This
modeling step is also referred to as training phase.
In a speaker identification scheme, a reject mechanism is also required
due to possible impostor identity claims. A possible reject strategy is thus to
refer a reject (imposter) class
so that a likelihood ratio
in
logarithmic domain is used for accept or reject decision:
Ideally, the imposter class model should be constructed by using all
possible imposter observations for class
n
, which is practically unfeasible to
achieve. In this work we use the universal background model, which is
estimated, by using all available training data regardless of which class they
belong to. The final decision strategy can be stated as follows:
where is the optimal threshold which is usually determined experimentally
to achieve the desired false accept or false reject rate.
When two or more modalities exist, the selection of the appropriate
fusion technique, whether data or decision fusion, should take into account
how these modalities are correlated to each other. In the case of decision
