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SAIEE Africa Research Journal

On-line version ISSN 1991-1696
Print version ISSN 0038-2221

SAIEE ARJ vol.112 n.2 Observatory, Johannesburg Jun. 2021




Optimal human-machine collaboration for enhanced cost-sensitive biometric authentication



Johannes CoetzerI; Jacques P. SwanepoelII; Robert SabourinIII

IDepartment of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa (
IIFlightscope, Stellenbosch, South Africa (email:
IIIEcole de Technologie Supérieure, University of Quebec, Montreal, Canada (email:




Despite growing interest in human-machine collaboration for enhanced decision-making, little work has been done on the optimal fusion of human and machine decisions for cost-sensitive biometric authentication. An elegant and robust protocol for achieving this objective is proposed. The merits of the protocol is illustrated by simulating a scenario where a workforce of human experts and a score-generating machine are available for the authentication of handwritten signatures on, for example, bank cheques. The authentication of each transaction is determined by its monetary value and the quality of the claimed author's signature. A database with 765 signatures is considered, and an experiment that involves 24 human volunteers and two different machines is conducted. When a reasonable number of experts are kept in the loop, the average expected cost associated with the workforce-machine hybrid is invariably lower than that of the unaided workforce and that of the unaided machine.

Index-Terms: human-machine collaboration, dynamic classifier fusion, cost-sensitive biometric authentication




Pattern recognition protocols that produce multiple candidate classifiers, and then combine their output, are popular and well-established [1]-[3]. Each candidate classifier can either be a continuous classifier that generates a score, or a discrete classifier that outputs a decision. Furthermore, by imposing different thresholds on a machine-generated score, different discrete classifiers can be obtained. Multiple candidate classifiers can be generated by extracting different features [4] or by utilising different modelling techniques [5].

By considering optimisation data, an optimal candidate classifier, or group of classifiers (e.g. a maximum attainable receiver operating characteristic (MAROC) curve) can be selected and then implemented on different data [6]. The selected classifiers are referred to as maximum attainable classifiers. When the cost associated with the misclassification of an instance (e.g. a handwritten signature), varies from one instance to another, a second optimisation stage is possible [7]. In these scenarios an optimal candidate classifier, or group of classifiers, that minimizes the expected cost, can be dynamically selected from the available maximum attainable classifiers during system implementation.

The candidate classifiers are traditionally machines (so-called hard sensors). More recently, researchers started to investigate the advantages of keeping humans (so-called soft sensors) in the loop [8]-[10]. Human-machine collaboration allows pattern recognition protocols to exploit the unique capabilities of both humans and machines. Humans are proficient at integrating information and incorporating context, while machines are adept at making fast, consistent and objective decisions. With the advent of the internet, collaboration among human experts is becoming increasingly viable [11].

Depending on the application, human involvement may occur at various stages in the decision-making process. Four possible stages are specified in [12], i.e. the (1) information acquisition, (2) information analysis, (3) decision and action selection, and (4) action implementation stage. During the information acquisition and analysis stages, humans may for example assist machines in extracting suitable features [13]. During the decision and action selection stage, humans may select an appropriate action among a machine-generated list of options [14], or submit a decision, which is then combined with those of one or more machines and/or other humans, in order to reach a final decision [15].

The level of automation (human involvement in the decision-making process) may also vary from one application to another. In [12] a ten-point scale is proposed that varies from level one, where the machine offers no assistance to the human to level ten, where the machine determines everything and the human is ignored. In [16] and [17], for example, the feasibility of adapting the level of automation within a human-robot collaborative system is investigated.

In this paper the feasibility of using a score-generating machine and a workforce of human experts is investigated for the purpose of biometric authentication in a cost-sensitive environment. This investigation considers handwritten signatures on, for example, bank cheques, where authentication relies on both the transaction's monetary value and the quality of the client's signature. For example, the cost associated with the acceptance of a large fraudulent transaction may be high due to the possibility of having to reimburse the client. The cost associated with the rejection of a small legitimate transaction may also be high due to the possibility of unnecessary administrative expenses. The protocol should therefore lean towards rejecting large transactions with low-quality signatures, and accepting small transactions with high-quality signatures. Furthermore, the average expected cost associated with an expert-machine hybrid, should be lower than that of the unaided human workforce, and lower than that of the unaided machine.

Since the performance of humans are often comparable to that of machines in authenticating handwritten signature images [18], it is reasonable to investigate human-machine collaboration within the context of the decision and action selection stage as proposed in this paper. The empirical findings in [19] confirm that human team members are extremely sensitive to their workload in pressured, high-tempo situations and when supported by machines, perform better by maintaining team performance at acceptable levels.

It is concluded in [15] that, with all the human experts in the loop, the inclusion of an HMM-based machine simplifies cost-sensitive authentication and decreases the expected cost for all operating conditions. This self-contained paper improves on [15] in several ways: (1) a more detailed motivation, description and analysis of the dynamic classifier selection strategy is presented; (2) a more proficient classifier fusion protocol is proposed; and (3) the efficacy of the improved protocol is demonstrated (for two different machines) in scenarios where only a subset of the human workforce is available.

In Sections II and III recent work that relates to the proposed protocol is discussed and relevant ROC-based strategies for classifier fusion are introduced. This is followed by a discussion on ROC-based classification in a cost-sensitive environment (Section IV). In Sections V and VI the proposed strategy for human-machine collaboration is introduced, followed by an analysis of the relevant handwritten signature data, the experimental protocol, and results.



Human-machine collaboration at automation stages, other than the decision and action selection stage, has been widely investigated in the fields of aviation [20] and medicine [21]. However, due to the difficulty of quantifying the inherent uncertainty of human data, very little work has been done on combining human and machine decisions [8]. Furthermore, research on human-machine collaboration, for the specific purpose of biometric authentication, is still in its infancy. The aforementioned scenario is only investigated in [13], which focusses on the recognition of flowers and faces. In this paper human-machine collaboration facilitates feature extraction during the information acquisition and analysis stages. A computer-generated impression of the target image is first superimposed onto the object to be recognised. A human expert then assists the machine in extracting suitable features by appropriately modifying the computer-generated impression. The authors demonstrate that the collaborative recognition protocol outperforms unaided machine classification, is more efficient than unaided human classification, and that the proficiency of both the human experts and the machine increases after system implementation.

Classifier selection strategies in scenarios where the mis-classification cost varies from one instance to another have only been investigated on a few previous occasions. The construction of so-called cost curves is proposed in [7], where the 'normalized expected cost' is plotted against the 'probability cost' for different operating conditions-an operating condition is obtained by imposing a specific threshold on a machine-generated score. The authors show that cost curves are superior to ROC curves for visualising classifier performance in most scenarios. The reader is referred to [7] for detailed definitions of the above-mentioned parameters. The protocol proposed in this paper employs several other parameters also discussed in [7], for which detailed definitions are given in Section IV.

As an alternative to cost curves, so-called AUCIV curves are proposed in [22]. AUCIV curves are obtained by adapting conventional ROC curves in such a way that they allow for instance-varying costs.



The proposed protocol for human-machine collaboration is based upon performance evaluation in receiver operating characteristic (ROC) space. In order to standardise the terminology and notation, key concepts in ROC analysis are first reviewed.

The true positive rate (TPR) for classifier CA, i.e. t+, approximates the probability that it will correctly classify a positive instance (authentic signature), while its false positive rate (FPR), i.e. f+A, approximates the probability that it will erroneously classify a negative instance (fraudulent signature).

In ROC space, the TPR and FPR represent the vertical and horizontal axes respectively. The performance of a discrete classifier (e.g. a human expert that provides a decision of either 'true' or 'false') can therefore be represented by a single point in ROC space. When two discrete classifiers are compared, the superior classifier's performance is represented by the more 'northwesterly' point in ROC space. The two machines considered in this paper are both examples of continuous classifiers, since they both output scores to which different decision thresholds can be applied to determine class membership. The performance of a continuous classifier is represented by an ROC curve. An ROC curve therefore consists of a number of FPR-TPR pairs, where each pair is associated with a specific threshold value and constitutes a discrete classifier. When two continuous classifiers are compared, the superior classifier has a larger area under its corresponding ROC curve (AUC).

The problem investigated in this paper is addressed by employing classifier combination at the decision and action selection stage through majority voting and iterative Boolean combination (IBC). Majority voting is the most popular classifier combination strategy when a system has access to the output of three or more discrete classifiers, e.g. human experts, that make conditionally independent errors. It is significant to note that this conditional independence requirement guarantees that the estimated combined performance (when the classifiers in question evaluate signatures produced by a set of representative writers in a controlled environment) is a good predictor of future performance (when the same classifiers evaluate signatures produced by different writers).

The IBC algorithm [23] combines the output of two continuous classifiers-their respective performances are represented by two ROC curves-by fusing the output of every threshold-specific discrete classifier associated with the one ROC curve with the output of every threshold-specific discrete classifier associated with the other ROC curve. The authors emphasise that the IBC algorithm does not require any prior assumptions on the conditional independence of the classifiers or the convexity of their respective ROC curves. Ten Boolean fusion functions are implemented for combining the output of any pair of discrete classifiers, CAand CB, where Λ, V, , and ® denote conjunction, disjunction, negation, and the XOR operator, respectively: (1) CaΛCb, (2) CaΛCb, (3) CaΛCb, (4) (CaΛCb), (5) Ca VCb, (6) Ca VCb, (7) Ca VCb, (8) (Ca V Cb), (9) Ca ® Cb, and (10) (Ca ® Cb). In this way a set of candidate hybrid classifiers are produced of which only the the optimal hybrids, represented by the MAROC curve, are selected.

It is worthwhile to note that the IBC algorithm is also well-suited for combining the output of three or more continuous classifiers by first considering the two least proficient classifiers, after which the output of the resulting optimal hybrids, represented by the MAROC curve, is combined with the output of the third least proficient classifier. This process is repeated until all of the available continuous classifiers have been considered. The authors of the IBC algorithm state that the proficiency of the hybrid system can be further improved by repeating the entire procedure, that involves all of the available continuous classifiers, until no significant gain in proficiency is observed. However, the details of this iterative process are not relevant to the protocol employed in this paper.

The classifier combination protocol proposed in this paper is discussed in detail in Section V and employs the ten Boolean fusion functions utilised in [23] in conjunction with majority voting. We show in Section VI that the proposed protocol is simple, computationally efficient, and robust in the sense that it leads to small generalisation errors. Note, however, that the proposed protocol does not combine MAROC curves in an iterative way as suggested in [23], since the IBC approach is computationally expensive and does not generalise well in this context.



In order to select the specific hybrid classifier on a MAROC curve, which is associated with the lowest expected cost, the use of iso-cost lines with variable gradients is proposed.

It is reasonable to assume that the cost incurred by rejecting a negative instance and the cost incurred by accepting a positive instance both equals zero, i.e. S(-|-) = S(+|+) = 0. Given this assumption, the expected cost associated with a transaction that is authenticated by a classifier Cacan be expressed as follows [7],

where P (+) and P (-) represent the prior probabilities of the questioned instance being positive and negative respectively. The cost incurred by rejecting a positive instance, and the cost incurred by accepting a negative instance, are denoted by S(-|+) and S(+|-) respectively, while the error rates for classifier Caare represented by t+A and f+A.

It can be deduced from (1) that the iso-cost line in ROC space, that depicts the proficiency of all hypothetical classifiers associated with a specific expected cost E, is given by

In Figure 1 (a) the horizontal, vertical and diagonal lines represent parallel iso-cost lines, for the scenarios where S(+|-)P(-) = 0, S(-|+)P(+) = 0, and S(-|+)P(+) = S(+|-)P(-), respectively.

Since the overwhelming majority of questioned signatures on bank cheques are authentic, the pragmatic strategy will be to set the prior probabilities equal to P(+) 1 and P(-) 0. For this scenario, an almost optimal expected cost (E <<. 1) can be attained by accepting all questioned signatures as demonstrated in Figure 1 (b). This strategy will however cause any manual or automated authentication protocol to be redundant. It is more sensible to embark from the assumption that the prior probabilities are equal, i.e. P(+) = P(-) = 0.5. All human experts are therefore directed to be as unbiased as possible. The strategy for selecting an optimal hybrid classifier from a set of candidates is also based on this assumption. As a result (1) simplifies as follows,

When the error costs (S(+|-) and S(-|+)) are kept constant, the line in ROC space represented by t+ = Mf+ + N(E) depicts the proficiency of all hypothetical classifiers that correspond to the specific expected cost E, where M = S(+|-)/S(-|+) and N(E) = 1 - (2E)/S(-|+). By considering different values of E, different parallel iso-cost lines can be obtained for a specific value of M. Note that M therefore denotes both a specific cost ratio, and the cost gradient of the corresponding iso-cost lines-these two terms are henceforth used interchangeably. After a cost-ratio is specified, only one iso-cost line (with gradient M) intersects a linearly interpolated version of a MAROC curve at a single point (see Figure 2 (b)). The aforementioned point is optimal in the sense that it represents the performance of the hybrid classifier that corresponds to the lowest expected cost-this classifier is therefore selected.

It is important to note that, although the above-mentioned geometric interpretation of the proposed classifier selection strategy is informative, classifier selection is in actual fact achieved through a non-geometric approach. This approach entails the calculation of the expected cost for each of the candidate hybrids using (2), after which the hybrid associated with the lowest expected cost is selected.

Figure 2 (b) illustrates the geometric interpretation of the proposed protocol for selecting the hybrid classifier associated with the lowest expected cost, for three different cost scenarios.



The proposed protocol for human-machine collaboration in a cost-sensitive environment is encapsulated in Figure 3



It is assumed that, during an initial enrollment phase, a financial institution requires each new client to produce a number of authentic samples of his/her handwritten signature. The utilisation of these samples for signature modelling is explained in Section VI. This enrollment process is relatively non-intrusive and may be repeated after set time intervals to allow for subtle changes in the client's signature. The proposed protocol is partitioned into an optimisation and implementation stage.

Optimisation. During the optimisation stage both a machine and a workforce of human experts are required to authenticate a compilation of labelled authentic and fraudulent signature samples, in order to assess their proficiency. These samples are produced by representative writers in a controlled setting. The protocol for compiling and presenting these signatures is discussed in detail in Section VI. By considering the representative signatures, an estimate of the combined performance of a specific human expert and each threshold-specific machine-generated classifier is obtained by considering each of the ten Boolean fusion functions defined in Section III. A set of candidate human-machine hybrids is therefore generated for this expert, after which only the MAROC curve is retained. This process is repeated for every expert so that a set of expert-specific MAROC curves is obtained.

The consultant and the client (financial institution) agree on a mapping between the transaction value V є [Vmin,Vmax] (in monetary terms) and a finite set of discrete cost gradients {Mi},i = 1,2,...,K, i.e. V ->{Mi} (see Figure 2 (a)).

For a specific cost gradient, the optimal expert-machine hybrid, i.e. the hybrid that corresponds to the lowest expected cost, is selected for each expert-specific MAROC curve. This process is repeated for every specified cost gradient. After the conclusion of the optimisation stage, only the optimal expert-specific hybrids for every specified cost gradient are stored and the optimisation process is only conducted once. When new experts are added to the human workforce, or when existing experts undergo updated proficiency tests, the optimal hybrid for only the aforementioned experts need to be re-calculated. Figure 2 (b) illustrates three different cost scenarios with the corresponding iso-cost lines, as well as a hypothetical expert-specific MAROC curve. For each of these scenarios, the performance of the optimal hybrid is denoted by a solid marker.

Implementation. During the implementation stage the optimal expert-specific hybrids are efficiently and dynamically selected. When investigating an unlabelled signature, claimed to belong to a specific writer and associated with a certain transaction value, the transaction value is first mapped to the appropriate cost gradient. Subsequently, for the cost-gradient in question, the output from all the optimal expert-specific hybrids are combined through majority voting. In this way all the available experts are included in the decision process.

The protocol presented here differs from the one proposed in [15]. According to the protocol adopted in [15] the output from all of the available human experts (and not the decisions of expert-specific hybrids) is first fused through majority voting-the majority-vote decision of the entire available work-force is then combined with every threshold-specific machine-generated decision. It is shown in Section VI-C that the human-machine collaboration protocol proposed in this paper is superior to and more robust than the one proposed in [15], as long as a significant number of human experts are kept in the loop.



The experimental data is split into an optimisation set (OS) and evaluation set (ES). In order to prevent model over-fitting and biased results, the above-mentioned subsets contain signatures produced by different writers. The OS contains signatures produced by representative writers in a controlled setting, while the ES contains signatures from other writers emulating banking clients. It is reasonable to presume that positive signatures are obtainable for each writer in both the OS and ES. These signatures may be used to train writer-specific HMMs, act as reference signatures for writer-independent LDF-based classifiers, or serve as reference for human experts.

Labelled positive and negative signatures are associated with writers in the OS only. These signatures may be used for estimating the proficiency of the human experts and the machine in question, as well as for selecting the optimal expert-specific hybrids. Unlabelled positive and negative signatures, that belong to writers in the ES, are used to estimate the generalisation capability of the proposed protocol.

A. Data

The efficacy of the proposed protocol is illustrated by considering a selected subset of signatures within a larger database originally captured online [24]. This dataset contains dynamic signatures from 51 different writers. In order to emulate signatures extracted from bank cheques, the dynamic data is transformed into static images by applying a morphological dilation operator to the pixels positioned at the captured pen tip coordinates [25]. Only skilled forgeries are used for experimentation. A skilled forgery is produced by an individual who had ample time to study a set of known (labelled) authentic signatures at his/her leisure. Adopting the terminology laid out in [24], this dataset contains 15 authentic 'training' signatures and 75 'test' signatures for each writer. The 75 'test' signatures consist of 15 authentic samples and 60 skilled forgeries.

B. Experimental protocol

For each writer in the dataset, all of the 15 authentic training signatures are selected for signature modelling. A reduced test set, that consists of only 15 signatures, is now constructed. This new test set is employed during the optimisation and implementation stages of experimentation and contains a randomly selected number (between 0 and 15) of skilled forgeries. The rest of the test signatures are randomly selected from the 15 authentic test signatures for the writer in question. A specific test set may therefore consist of only authentic signatures or only skilled forgeries. Consequently, each classifier (human expert or machine) authenticates 15 x 51 = 765 test signatures in total. Due to the random nature of this selection strategy, the total number of authentic and forged samples in the entire reduced test set is 432 and 333 respectively.

Human experts. The potential actions of a human expert is emulated by presenting each volunteer (a faculty member or a graduate student) with a training set (15 signatures) and corresponding test set (15 signatures) for all 51 writers. Twenty-four volunteers are utilised. Each volunteer is presented with all the writers' training and corresponding test sets on different sheets of paper. The volunteers are instructed to compare every test signature to the corresponding training set, and decide which of the test signatures are fraudulent. Each training set is scrutinised as a whole. These volunteers are also instructed not to mull over each decision, so as to emulate the probable actions of a typical bank employee.

Machines. The signatures presented to the human volunteers, are also presented to two machines, i.e. a writer-dependent hidden Markov model-based (HMM-based) classifier [25] and a writer-independent linear discriminant function-based (LDF-based) classifier [26], as discussed below.

HMM-based classifier. Features based on the computation of the discrete Radon transform (DRT), are extracted from each signature image. These features are employed to train an HMM for each writer in the dataset. A questioned signature is matched with the appropriate HMM through Viterbi-alignment and a score is obtained. This score is then normalised through a strategy based on the z-norm.

LDF-based classifier. During signature modelling, a dissimilarity representation is achieved by employing a two-stage process. Binary signature images are first converted into feature sets using the DRT. Using a dynamic time warping algorithm these feature sets are matched to those extracted from writer-specific reference signatures, so that a set of dissimilarity vectors is obtained. The dissimilarity vectors obtained from signatures in the training set are used to train an LDF. During the implementation stage, questioned signatures from the ES are encoded into dissimilarity vectors, by comparing these signatures to the appropriate writer-specific reference signatures. The trained LDF is then used to predict class membership.

Cross-validation with repetition. The experimental protocol employs three-fold cross validation in conjunction with repetitive data randomisation. The experimental protocol is outlined as follows: (1) The dataset is partitioned into three equal subsets, where each subset contains signatures produced by 17 writers; (2) Each subset, in turn, is employed as an ES, that contains signatures produced by 17 writers, while the remaining two subsets constitute the OS, that contains signatures produced by the other 34 writers; (3) The order of the writers is randomly rearranged, and the procedure is repeated 10 times. The results for 30 trials are thus reported.

A set of 19 different cost gradients is specified as follows,

A specific trial is executed by considering all of the cost gradients in (3). For a specific cost gradient, the signatures in the OS are first used to select the optimal expert-machine hybrid (i.e. the hybrid that corresponds to the lowest expected cost) on each expert-specific MAROC curve. The signatures in the ES are then authenticated by combining the decisions of the optimal expert-machine hybrids through majority voting, and the expected cost is estimated. This process is repeated for every cost gradient in (3) so that the average expected cost over all cost gradients is reported for the trial in question.

In order to demonstrate the efficacy of the proposed protocol for randomly selected subgroups of human experts, the empirical protocol outlined in Algorithm 1is adopted.



C. Results

The dataset introduced in Section VI-A is now considered, and the level of experimental complexity is increased in a step-wise fashion. This approach clarifies the methodology and demonstrates the efficacy of the collaboration protocol.

A single human expert is first considered and the OS is employed to illustrate how the optimal expert-machine hybrid, for a specific cost gradient, is selected (see Figure 4. Three human experts are then considered and the ES is employed to show that, when the selected three expert-machine hybrids are again combined through majority voting, the expected cost associated with the combined hybrid classifier is lower than that of the optimal unaided threshold-specific machine for the cost gradient in question (see Figure 5. The expected cost associated with the combined hybrid classifier is also lower than that of the unaided human workforce, when the individual human decisions are combined through majority voting. The results in Figures 4 and 5 are generated for a single cost gradient during a single trial, while only the HMM-based machine is considered.

Since only the cost gradient/ratio M is specified in the remaining experiments, and not the individual error costs (S(+|-) and S(-|+)), the constraint, S(+|-)+S(-|+) = 1, is imposed. Since M = S(+|-)/S(-|+), (2) simplifies to

for an arbitrary classifier CA. This is convenient for plotting the expected cost associated with CAas a function of the cost gradient M. The relaxation of the above-mentioned constraint has no impact on the shape of the EA - M graph. In fact, this relaxation only results in a re-calibration of the EA-axis.

In Figure 6 the average expected cost over all 30 trials is shown as a function of the cost gradient M, with the different values of M specified in (3). The same three human experts that relate to Figure 5 are again considered here. For a specific trial and cost gradient, the OS is used to select the three optimal expert-machine hybrids, while the ES is used to estimate the expected cost when these hybrids are combined through majority voting. The combined hybrid classifier outperforms the optimal unaided HMM-based classifier and the unaided human workforce (when the individual human decisions are combined through majority voting) for all cost gradients.



Figures 7 and 8 show the average expected cost for the unaided human workforce (using majority voting), the optimal unaided threshold-specific machine, the human-machine collaboration strategy proposed in [15], and the human-machine collaboration strategy proposed in this paper, as a function of the number of available experts, by considering the HMM-based and LDF-based machines (described in Section VI-B), respectively. By considering the ES only, the average expected cost is obtained by calculating the mean cost over all 30 trials (and all specified cost gradients). For the HMM-based machine, both of the above-mentioned collaboration strategies outperform the unaided human workforce and the optimal unaided threshold-specific HMM-based classifier when more than two experts are available. For the LDF-based machine, only the collaboration strategy proposed in this paper outperforms the unaided human workforce and the optimal unaided threshold-specific LDF-based classifier when more than five experts are available.





Since the human-machine collaboration protocol presented in this paper enhances the performance of both the less proficient HMM-based machine and the more proficient LDF-based machine, when a reasonable number of experts are kept in the loop, the protocol presented here is superior to, and more robust than, the one proposed in [15].



A novel human-machine collaboration protocol for the purpose of biometric authentication in a cost-sensitive environment was proposed. This protocol enables a consultant to provide a client (financial institution) with a customised and intuitively understandable mapping between a finite set of transaction value intervals and corresponding cost gradients. Should the economic climate change, the mapping can be easily adjusted. In order to demonstrate the feasibility of the protocol, twenty-four human volunteers and two different machines were considered for the purpose of detecting skilled forgeries in a dataset that contains 765 static handwritten signatures from fifty-one different writers. It was clearly shown that, when compared to scenarios where either an unaided human workforce or an unaided machine is employed, the utilisation of the proposed collaboration strategy consistently leads to a lower average expected cost. This is invariably the case when a reasonable number of human experts (more than five) are kept in the loop.

Potential future work may involve an investigation into a human-machine collaboration strategy where the Boolean fusion functions detailed in Section III are first utilised to combine the output of a specific human expert with that of every threshold-specific machine-generated classifier, after which the best expert-specific hybrid is selected. This process is then repeated for every available expert, so that a pool of optimal expert-machine hybrids is produced. For each specified ROC-based cost gradient, a genetic search algorithm can subsequently be used to obtain the subset of expert-machine hybrids that minimises the expected cost-fusion is achieved through majority voting. This expert-machine collaboration strategy may potentially be more accurate than the protocol proposed in this paper, but certainly much less efficient. Furthermore, the utilisation of a genetic search algorithm within this context does not guarantee that all the available experts are included in the authentication process. However, the number of experts in the loop may be maximised by using both the cardinality of the hybrid set and the expected cost as objective functions to guide the search.

A protocol may also be investigated for scenarios where each human expert, instead of submitting a decision, assigns a score or confidence value to each questioned biometric instance.



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Based on "Dynamic fusion ofhuman and machine decisions for efficient cost-sensitive biometric authentication", by Johannes Coetzer, Jacques P. Swanepoel, and Robert Sabourin, which was published in the Proceedings of the SAUPEC/RobMech/PRASA 2020 Conference held in Cape Town, South Africa from 29to31 January 2020. ©2020 SAIEE



Johannes Coetzer was born in Bloemfontein, South Africa in 1971. He received an M.Sc. in Applied Mathematics from the University of the Free State in 1996 and a Ph.D. in Applied Mathematics from Stellenbosch University in 2005. From 1997 to 1998, he was a Junior Lecturer, and from 1999 to 2001, a Lecturer in Applied Mathematics at the University of the Free State. From 2002 to 2008, he was a Lecturer, and since 2009, a Senior Lecturer in Applied Mathematics at Stellenbosch University. His research interests include machine learning, biometric authentication and classifier combination.



Jacques P. Swanepoel received an M.Sc. in Applied Mathematics from Stellenbosch University in 2009 and a Ph.D. in Applied Mathematics from Stellenbosch University in 2015. From 2010 to 2015, he was a Junior Lecturer in Computer Science, and in 2016, a Lecturer in Applied Mathematics at Stellenbosch University. From 2016 to 2018 he was an Applied Mathematician, and since 2019, a team leader in signal processing and modelling technology at FlightScope. His research interests include machine learning and biometrics.



Robert Sabourin is a Full Professor at the Department of Automated Production Engineering at Ecole de Technologie Superieure (ETS), University of Quebec, Montreal, Canada. He has authored more than 486 publications and has been a member of the circle of excellence at the University of Quebec since 2012. His research interests include machine learning, neural networks, hidden Markov models, biometrics, genetic algorithms, signal, image and video processing, as well as postal applications.

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