6.2
Fusion Methods
There are two ways to consider biometric fusion [57]. First, a single biometric type (e.g., fingerprint) may be classified using several classifiers, then the individual results combined to create a single probability. The second way, the one that is adopted in this study, is to use two or more different biometrics (e.g., keystroke dynamics and speaker verification), classify them individually, and combine the results of these two biometric modalities into a single probability. In this latter case, each biometric modality may be presented to a different pattern classifier depending on which one provides the best results for the data presented to it. While this is the approach taken for testing the efficacy of the two methods proposed in this chapter, these methods may also be used with multiple values from the same type of biometric.
Fusion methods for multiple biometric measurements include feature-level, decision-level and score-level fusion [57, 123], as discussed in Chapter 2. Feature-level fusion techniques were excluded because the two biometrics do not have features in common, which means that combining the feature vectors may be more likely to produce higher error rates [57]. Decision-level fusion is also unsuitable because it can result in a multimodal biometric that produces worse error rates than the individual biometrics. This is because it only has access to the decision and not the granularity thereof. Thus, a decision could be made to reject based on a borderline case (i.e., one very close to the threshold), which favors false rejections rather than false positives.
Score-level fusion has been chosen for combining the keystroke dynamics and speaker ver- ification patterns for this research because the two pattern classifiers output a score that is interpreted as a probability that the gathered feature belongs to the device owner. This method does not rely on pattern independence, which is important as some implementations of the Transparent Authentication Framework may use different dependent biometrics.
6.2.1
Score-Level Fusion Techniques
Score-level fusion is a technique in which the scores or probabilities of several biometrics may be combined. The biometric decision has not been made at this point, but the feature vectors have been presented to a classifier that outputs either a probability or a score-match matrix. Many of these methods require normalization to ensure that the different classifier outputs are within the same range.
6.2. Fusion Methods 109
Score Normalization
The scores to be combined are normalized to ensure that the value they represent comes from the same distribution, say between 0 and 1 [127]. Normalization reduces the effect of differing distributions. For instance, if one classifier outputs a score between 0 and 100 and another classifier outputs a score between 1000 and 2000, the first biometric will have little effect on the fusion result since its scores seem much lower than the second biometric. With- out the normalization step, the biometric with the higher range of scores will eliminate the contribution of the biometric with the lower range of scores. Furthermore, score normaliza- tion allows the addition or substitution of other biometrics as they become available without considering whether the scores will complement each other.
Common normalization techniques include Min-Max, Z-Score, and TANH, among oth- ers [122, 166]. These methods, in general, involve combining the median, maximum and minimum values, and standard deviations of several scores to ensure they fall within the same ranges. The interested reader is directed to the sources cited previously for a detailed discussion of normalization techniques.
Score-Match Matrix Methods
Many studies into multimodal biometrics use well-known score-level fusion methods that are based on a score-match matrix [122, 166, 167]. Score-match matrix creation begins with pattern classification. When classifying a particular test feature vector, the new input data is compared to each feature vector in the training set. The comparison results in a distance that represents how different (i.e., how far) the new data is from the training data. For each pair of training and testing data, these distances are put into an n x n score-match matrix, where n is the size of the training set. At the end of this process (i.e., the end of the classifier’s testing phase), there is a score-match matrix for every feature vector in the test set.
The score-level fusion techniques that are common in the literature are summarized in Ta- ble 6.1. These techniques are presented here to give a sense of the state-of-the-art, and to justify the choice of the Na¨ıve and Posterior Probability Methods for this research. The im- plementations in Table 6.1 assume that Mi is the score-match matrix from classifier i, and
that there are K classifiers in total.
Once all score-match matrices have been created, the fusion methods must normalize and then combine them using the formulae shown in Table 6.1. For instance, the Simple Sum method adds all elements of the matrices together, and the Minimum and Maximum Score methods choose the smallest and largest scores, respectively, resulting in a new score-match matrix that represents all input matrices [168]. These methods imply processing possibly
6.2. Fusion Methods 110 Name Formula Description
Simple Sum PK
i=1Mi
The score-match matrix values for each biometric are summed to provide a new score-match matrix.
Min Score min(M1, M2, . . . , MK)
The smallest score for each element in all score-match matrices is selected, creating a combined score-match matrix.
Max Score max(M1, M2, . . . , MK)
The largest score for each element in all score-match matrices is selected, creating a combined score-match matrix.
Table 6.1: Summary of score-level biometric fusion methods that use score-match matrices. large and complex data structures. This represents a potentially significant amount of pro- cessor and memory use, both of which are constrained on mobile devices. For these reasons, fusion methods that rely on score-match matrices are discounted from use in this research. Instead, fusion methods that take probabilities as input were used rather than those that use score-match matrices.
Sum and Product of Probabilities
Two common score-level fusion techniques that use output probabilities, Sum of Probabili- ties and Product of Probabilities, were considered for this study [166, 168]. These methods, summarized in Table 6.2, calculate the sum and product of the posterior probabilities of a class given the input data. While these methods seem ideal for this work, the literature does not provide adequate information to recreate such methods. When using the sum method, for instance, there is no discussion of normalization techniques except to state that they are “implied in the algorithm” [166]. Due to the lack of implementation details, these methods were discounted from use in this study.
Name Formula Description Sum of Probabilities PK
i=1P (Owner | Mi)
Probabilities for all biometrics are summed to create a single,
combined probability. Product of Probabilities QK
i=1P (Owner | Mi)
Probabilities for all biometrics are multiplied to create a single, combined probability.