1A Systematic Framework for Combination ofBiometric Matchers in Identification SystemsSergey Tulyakov and Venu Govindaraju, Fellow, IEEEAbstract—Combination functions typically used in biometricidentification systems consider as input parameters only thematching scores related to a single person in order to derivea combined score for that person. We present a systematicframework to use all scores received by all persons as inputto a single combination function when sufficient training datais available. More fundamentally, we identify four types ofclassifier combination methods determined by number of com-bining functions that must be trained and the number of inputparameters. We investigate in detail combination methods, whichconsider all available matching scores as input parameters toa single trainable combination function. We describe how suchmethods account for dependencies between scores output by anysingle participating classifier. Our experiments demonstrate theadvantage of using such combination methods when dealing withlarge number of classes, as in the case with biometric personidentification systems.Index Terms— Combination of classifiers, biometric identifica-tion systems.I. INTRODUCTIONBIOMETRIC applications operate in two modes: verifica-tion (1:1) mode and identification (1:N) mode. Commonapproaches to combining biometrics for (1:N) identificationapplications are usually a simple iterative use of the (1:1) ver-ification system. The combined score assigned to a particularenrolled person is obtained as a function of the scores assignedto that person by all the biometric matchers in either modesof operation. However, in the identification mode additionalinformation is available for deriving the combined scorefor any person in the database of enrollees. This additionalinformation is available from the matching scores returned forthe enrollees other than the target person.We consider M multiple biometric matchers used to pro-duce M N matching scores (Figure 1), where N is the numberof enrolled persons. We assume that M is small and N is large.Each biometric matcher in such a setting is equivalent to aclassifier assigning matching scores to each of the N classesor persons. And the combination of biometric matchers canbe viewed as a classifier combination problem with a largenumber of classes.In Figure 1, the combination function usually only considersthe scores s1i, . . . , sMito compute the integrated score ofperson i (column i), and combination methods with suchfunctions are referred to as local methods. In this paperwe explore global methods whose combination functions usethe additional information (all columns) when computing theintegrated score for each person.Both authors are with the State University of New York at Buffalo.Fig. 1. The set of scores available for combinations in identification systemsincludes all MN matching scores from M matchers and assigned to all Npersons. The combination functions f usually only utilize the set of scoresrelated to one person i in order to calculate the combined matching score forthis person.Combination methods can be also categorized based onthe construction properties of the combination functions f.When methods use a single common combination function,they are called class generic methods. When each class hasits own combination function, so that the combined scoresare calculated differently for different classes, the methods arecalled class specific.Local methods take as parameters only the M matchscores related to a particular class (single column in Figure1) whereas the global methods consider the whole set ofMN match scores (all columns in Figure 1) to derive thecombined score for any one class. When classifiers dealwith a small number of classes, the dependencies betweenthe scores assigned to different classes can be learned andused for combination purposes. For example, Xu et al. [1]used class confusion matrices for deriving belief values andintegrated these values into combination algorithms in the digitclassification problem. This algorithm has class specific andglobal combination functions. It is the most general type ofcombination method allowing optimal performance. However,learning class dependencies requires significant number oftraining samples for each class. Such data is usually notavailable for 1:N identification mode systems, where usuallya single template is enrolled for each person. In addition,the database of enrolled persons can be frequently changedmaking learning class relationships infeasible.As a consequence, combination approaches in 1:N identifi-cation systems have considered only the local methods evenwhen all the MN scores are available. In this paper weinvestigate the question of whether it is possible to improve2the performance of the identification system by using all theMN matching scores for deriving the combined score foreach person. We show that the combination methods usingclass generic and global combination functions are both wellsuited for combination of multiple biometric matchers inidentification systems [2], [3].II. PREVIOUS WORK IN IDENTIFICATION SYSTEMCOMBINATIONSTraditionally, two types of biometric person authenticationsystems are defined - verification (1:1) and identification(1:N) systems. It is usually implied that verification systemshave only the matching scores related to one enrolled personavailable to the combination method. However, it is possiblethat a verification system additionally uses matching scoresrelated to other persons. For example, in [4] authors performed’identification based verification’ by utilizing matching scoresof other enrolled peoples while making verification decisionon a particular person.In order to avoid confusion, we define an identificationsystem as a system which provides matching scores for allN enrolled persons. We define an identification system asoperating in identification mode if its purpose is to classify aninput as belonging to any of N classes or persons. We assumethat the classification decision is performed by applying thearg max operator to the N combined scores:C = arg max1≤i≤NSiThe correct identification rate, that is the frequency of correctlyfinding the true class of the input, is the natural measure ofperformance in this case, and we will use it in our experiments.Note, that there could be other performance measures foridentification mode operation, such as Rank Probability Mass,Cumulative Match Curve,