The user-specific score normalization in Section 5.5 and user-specific threshold normalization in Sec- tion 5.6 are strongly related. Taking the right-hand sides of (5.4) and (5.5), we have:
Ψj(y) > ∆, (5.12)
y > Ψ′j(∆). (5.13)
Note that the threshold ∆ refers to the threshold found after applying a respective user-specific score normalization procedure and not before (i.e., not directly on the scores prior to normalization).
To show that they are dual, we will re-express (5.13) into the form of (5.12). To do so, it is necessary to assume thatΨ′
j(∆) takes the following form, as a function of ∆:
Ψ′
j(∆) = a∆ + b. (5.14)
Note that all equations in Table 5.1 can be expressed by (5.14) using differenta and b. In particular, for those which do not contain a global threshold,b corresponds to the right hand-sides of the equations. For those using a global threshold, any multiplicative factor to the global threshold will be represented bya and the rest of the terms are represented byb. Replacing (5.14) into (5.13), and after rearrangement, we obtain:
y− b
a > ∆ (5.15)
From (5.12) and (5.15), we see that:
Ψj(y) =
y− b
5.8. SUMMARY 75
For equations whosea = 0, we have:
Ψj(y) = y− b, (5.17)
As a result, manipulating the threshold or the scorey has exactly the same effect. Hence, the threshold refinement procedure (row thee of Table 5.1) is just another score normalization technique. The additional advantage of score normalization over threshold normalization is the additional flexibility provided by the global threshold which can still be adjusted to different operating costs of false acceptance and false rejection.
5.8
Summary
In this chapter, we survey user-specific processing, i.e., a family of techniques that considers the user claimed user index. These techniques can be categorized into three types, according to the level of in- formation dealt with, i.e., feature level, model level, and score level. User-specific score-level processing can further be divided into three types: user-specific fusion, user-specific score normalization and user- specific threshold procedure. Although user-specific processing is extremely useful and has been shown by numerous authors, this is the first survey written on the subject.
There are two somewhat original ideas in this chapter. Firstly, by analyzing the decision function using LLR, we unify the three types of user-specific score-level processing in a single framework. Thanks to the framework, user-specific score normalization can be seen as a special case of user-specific fusion having only a single system. This observation has a significant influence in our work because user-specific fusion techniques can suddenly be used as user-specific score normalization techniques, e.g., Chapter 6, and vice- versa, e.g., Chapter 7.
Secondly, we show that, in theory, user-specific score normalization and user-specific threshold pro- cedure are equivalent. In practice, however, one may not obtain exactly the same result depending on the optimization criterion used and on whether or not the global threshold is considered for decision making. Between these two, user-specific score normalization is more advantageous due to an added degree of flex- ibility – the global threshold which can still be tuned after the normalization. We will therefore focus only on user-specific score normalization. This survey has not been published yet.
Thanks to the survey, we identify our contributions in user-specific processing as follows:
• An original compensation scheme that combines both user-specific and user-independent fusion clas- sifiers consisting ofN participating systems (Chapter 6). This framework generalizes to the case of N = 1 which can be considered as a novel user-specific score normalization.
• A user-specific score normalization called the “F-norm” and a user-specific fusion classifier called the “OR-switcher”. (Chapter 7).
Chapter 6
Compensating User-Specific with
User-Independent Information
6.1
Introduction
While prior works on user-specific fusion require many user-specific genuine samples (apart from those used to train the base-systems) in order to outperform the conventional fusion classifiers, e.g., as many as ten in [139] and six in [41], our goal in this chapter is to reduce the number of required user-specific genuine training samples to one or two.
This chapter contains two original ideas. The first idea is on the design of a user-specific fusion classifier that is in fact a Gaussian classifier with highly constrained Bayesian adaptation. Our novelty lies on the introduction of a set of useful constraints representing the domain knowledge. The second idea is referred to as a compensation scheme since one combines both the outputs of a user-specific fusion classifier (based on the first idea) and a user-independent (conventional) fusion classifier. The scheme is advantageous for three reasons. Firstly, it compensates for the possibly unreliable (due to lack of training data) but useful user-specific fusion classifier. Secondly, both the underlying fusion classifiers can be trained independently of each other. Thirdly, both the fusion classifiers are likely to be independent of each other thanks to the “phenomenon of large number of users”. This phenomenon is based on our observation that when the number of users is large, the class-conditional score likelihood of a population is independent of that of a given user (who can be a member of the population). The scheme is in fact very general because it extends to the case where only a single system is involved; hence resulting in a compensated user-specific score normalization procedure.
Chapter Organization
Section 6.2 analyzes the effect of large number of users. The two original ideas – a compensation scheme and a user-specific classifier – are discussed in Section 6.3. The scheme is then empirically evaluated in Section 6.4. Finally, Section 6.5 draws the conclusions.