A Markov chain-based ranking-level fusion method for multiple biometric features

Abstract

The present invention discloses a multi-biometric feature ranking-level fusion method based on a Markov chain, which comprises: S1: comparing the corresponding biometric features of a user to be tested through various single-biometric feature recognition algorithms to obtain an initial ranking list of each algorithm for the user; S2: using the set of user identities obtained by comparing the initial ranking lists of all algorithms as a state space, and constructing a Markov chain according to a state transition rule agreement that satisfies the Condorcet standard; S3: checking the number of user identities in the initial ranking list of each algorithm, and if there are unlisted user identities, filling the unlisted user identities in the corresponding list; S4: performing ranking-level fusion on all the filled initial ranking lists to calculate a state transition matrix; S5: obtaining a consensus ranking list according to the state transition matrix.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-biometric recognition result fusion processing, and in particular to a multi-biometric ranking-level fusion method based on a Markov chain. Background Art

[0002] When the output of a single algorithm is sorted in descending order of matching scores (or ascending order of distance scores), the multi-biometric recognition system can use a sorting-level fusion method. Currently, the commonly used sorting-level fusion methods include the highest sequence number fusion method, the Borda count sorting fusion method, and the logistic regression sorting fusion method. To facilitate the introduction of these methods, assume that N users’ biometric information is registered to form various feature template libraries, and there are K algorithms for identification and comparison. Each user has the required biometrics and is registered under the corresponding algorithm to form a feature template library. For a certain user to be tested, their biometrics are collected and identified and compared using various algorithms to obtain the corresponding initial sorting list to form a sorting matrix. Among them, r nk ,n=1,2,…,N;k=1,2,…,K represents the ranking of the registered user n in the ranking list output by the kth algorithm. The processing methods of different ranking level fusion are as follows:

[0003] (1) Highest sequence number fusion method: This method sorts the identities according to the highest sequence number of the user in each sorting list (i.e., the smallest sequence number or the highest ranking), and obtains a consensus ranking table. The consensus ranking score R n Calculated as: Ranking score R n The smaller it is, the higher the consensus ranking list is. This method can take advantage of the strengths of each algorithm. Even if only one algorithm assigns the highest sequence number to the correct user, the correct user is still very likely to get the highest sequence number after re-ranking. However, there may be many ties in the final ranking. When the tie is broken randomly, it is possible to accept the incorrect decision of the weakest algorithm. Another disadvantage is that only the top position of any initial sort list is considered, which may cause the multi-biometric recognition system to make unreliable decisions. Therefore, this method is not safe and reliable. It is usually necessary to introduce a disturbance factor to try to break the tie problem and correct the formula to: in, Here M is a large value used to generate a small perturbation term ε(n), and ε(n) combines all the initial ranking information associated with a specific user n.

[0004] (2) Borda Count Sorting Fusion Method: This method assumes that the initial sorting lists are independent of each other and the performance of the algorithms is similar. This method does not require a training phase and is easy to implement, but it does not consider the differences in recognition performance of individual algorithms. The assumption that all algorithms perform equally well is usually harsh, which makes the Borda Count Sorting Fusion Method extremely susceptible to the influence of weak algorithms. This method calculates the Borda total score B based on the user's serial number in each sorting list. n , in ascending order n Sort by consensus to get the sorting table, B n The smaller the value, the higher the consensus ranking. The formula for calculating the total score of each identity is: The performance of this method can also be improved by discarding the worst ranking among all algorithm outputs, that is,

[0005] (3) Logistic regression sorting fusion method: Logistic regression is a generalization of the Borda counting method. By calculating the weighted sum of the sorting of each sorting table, the consensus sorting table is obtained according to the weighted sum in ascending order. The smaller the weighted sum, the higher the ranking. The weighted sum L is calculated. n The formula for (ω) is: in, Here ω k is the weight of the kth algorithm. During the training phase, continuous optimization is required through multiple system trials and application trials. A logistic regression model is used to understand the recognition performance of each algorithm and assign corresponding weights. The smaller the weight, the better the algorithm's recognition performance. Different algorithms generally have significant differences in recognition accuracy, making this method more practical. However, because the performance of a single biometric recognition algorithm varies with the input sample sets of varying quality, the weight assignment process is more challenging and time-consuming. Improper weight assignment can reduce the overall recognition performance of a multi-biometric recognition system. Therefore, in some cases, this method is not well suited for ranking-level fusion.

[0006] Ranking-level fusion in a multi-biometric recognition system is similar to a voting mechanism. Each individual algorithm is considered an independent voter, and the initial ranking list is the result of each vote. The most important factor in a voting system is fairness, and the Condorcet criterion can ensure this fairness. Therefore, when designing a ranking-level fusion system for multi-biometric information, it is important to find a suitable method that meets the Condorcet criterion for a fair ranking process. However, the consensus rankings obtained by the aforementioned existing methods may violate the Condorcet criterion. Therefore, a method that meets the Condorcet criterion and improves the accuracy of the consensus ranking is needed. Summary of the Invention

[0007] The present invention provides a Markov chain-based multi-biometric feature ranking-level fusion method, which uses a Markov chain calculation consensus ranking list constructed according to the state transition rules that meet the Condorcet standard to perform ranking-level fusion on the multi-biometric feature recognition and comparison results. This method can not only meet the Condorcet standard, but also has higher recognition accuracy than a single algorithm or other ranking-level fusion methods.

[0008] To achieve the above objectives, the present invention provides a Markov chain-based multi-biometric feature ranking-level fusion method, which is applied to a multi-biometric feature recognition system and includes:

[0009] Step S1: Input the corresponding biometric information of the user to be tested into different single biometric recognition algorithms to obtain the initial ranking list of each algorithm for the user;

[0010] Step S2: The set of user identities obtained from the initial sorting list of all algorithms is used as the state space S. According to the state transition rule agreement that meets the Condorcet standard, a Markov chain {X n |n=0,1,2,…};

[0011] Step S3: Check the number of user identities in the initial sorting list of each algorithm. If there are any unlisted user identities, fill in the unlisted user identities in the corresponding list;

[0012] Step S4: All the completed initial sorted lists are fused at the sorting level to calculate the state transition matrix P;

[0013] Step S5: Obtain a consensus ranking list according to the state transition matrix P.

[0014] In one embodiment of the present invention, the specific process of obtaining the initial sorted list of single biometric features by each single biometric feature recognition algorithm in step S1 is as follows:

[0015] Step S11: extracting the biometric information of the user to be tested by using a corresponding algorithm;

[0016] Step S12: Match the extracted features with the template library and output the matching results;

[0017] Step S13: Obtain an initial sorted list of corresponding biometric features according to the output matching results.

[0018] In one embodiment of the present invention, the corresponding state transition rule in step S2 is specifically agreed to be:

[0019] Step S21: Assume that the current state is i, i∈S, and randomly select identity j with equal probability, where j∈S, S is the state space;

[0020] Step S22: If more than half of the initial sorted lists output by each algorithm have j ranked higher than i, that is, j is ranked higher than i, then the next state jumps to j; otherwise, the next state remains at i;

[0021] At the same time, suppose the user identity is randomly selected in the state space S, and it is assumed that the identity state changes only at time n, and the user identity selection is performed according to the above state transition rules. If X n represents the user identity selection at time n, then {X n |n=0,1,2,…} is a Markov chain.

[0022] In one embodiment of the present invention, the method for completing the unlisted user identities in the corresponding list in step S3 is any one of the following:

[0023] Use random insertion to randomly insert unlisted user identities at the end of the corresponding initial sorted list; or

[0024] The position insertion method is used to insert the corresponding user identity at the relative position of the unlisted user identity to form a complete sorted list.

[0025] In one embodiment of the present invention, the specific process of step S4 is as follows:

[0026] Step S41: For any state i in the state space S, i∈S, obtain the set J(i) of all states that meet the state transition rule except state i itself according to the state transition rule;

[0027] Step S42: Solve p using the following formula based on equal probability randomness: ij :

[0028] ∑ j∈S p ij =1

[0029]

[0030]

[0031] Among them, p ij is the probability that the next state is j when the current state is i, p ii is the probability that the next state will still be i when the current state is i;

[0032] Further

[0033] Step S43: Repeat steps S41 to S42 for all states in the state space S to obtain the entire state transfer matrix P.

[0034] In one embodiment of the present invention, the first method of calculating the consensus ranking list in step S5 is specifically:

[0035] Step S511: For any state j, j∈S, the consensus ranking list score s is obtained by the difference between the sum of the j-th column elements and the sum of the j-th row elements of the state transition matrix P. j , or the consensus ranking list score s is obtained by calculating the difference between the in-degree and out-degree of the j-th node in the transition graph corresponding to the state transition matrix P j , the specific calculation formula is:

[0036] s j =∑ i∈S p ij -∑ i∈S p ji =∑ i∈S p ij -1;

[0037] Step S512: Calculate all states j and score all the consensus ranking lists obtained s j Arrange them in descending order to get a consensus sorted list.

[0038] In one embodiment of the present invention, the second method of calculating the consensus ranking list in step S5 is specifically:

[0039] Step S521: For any state j, j∈S, the consensus ranking list score s is obtained by calculating the difference between the sum of the elements in the jth column and the sum of the elements in the jth row of the matrix W, that is, the difference between the number of edges with the jth node as the end point and the number of edges with the jth node as the starting point in the transition graph corresponding to the state transition matrix P. j , the specific calculation formula is:

[0040] s j =∑ i∈S ω ij -∑ i∈S ω ji ,

[0041] Among them, any element Denoted as a matrix

[0042] Step S522: Calculate all states j and score all the consensus ranking lists obtained s j Arrange in descending order to obtain a consensus sorted list.

[0043] Compared with the existing sorting-level fusion method, the Markov chain-based multi-biometric sorting-level fusion method of the present invention can well handle the situation where the initial sorting list is a small part of the registered users in the registration template library, provide a more comprehensive comparison between candidate users, and can also process and compare when the results of the initial sorting lists are very different, with higher accuracy. Therefore, it has a wider range of application scenarios in the sorting-level fusion of multi-biometric recognition systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0045] Figure 1 A schematic diagram of a process for performing sorted set fusion according to an embodiment of the present invention;

[0046] Figure 2 The figure is a comparison of the CMC curves of the method of the present invention and three single biometric recognition algorithms;

[0047] Figure 3 This is a CMC curve comparison diagram of the method of the present invention and other sorting-level fusion algorithms. DETAILED DESCRIPTION

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0049] In order to clearly illustrate the present invention, several basic principles involved in the present invention are described below:

[0050] (1) Markov chain:

[0051] Assume that the discrete random process is {X n |n=0,1,2,…}, its discrete state space is S={s1,s2,…}, if for any integer n and any state i0,i1,…,i n-1 ∈S, and the conditional probability satisfies: P{X n+1 =i n+1 |X0=i0,X1=i1,…,X n =i n}=P{Xn+1 =i n+1 |X n =i n}, then {X n |n=0,1,2,…} is a Markov chain.

[0052] (2) Condorcet Criteria:

[0053] The Condorcet criterion states that if there is an option that can win in a pair of votes against each other, it is considered the winner of the election and is called the Condorcet winner. The specific process can be summarized as follows: all alternatives are compared in pairs. The decision-making group first randomly selects two options for voting. The option that receives a majority of votes is then compared in pairs with all remaining options, and voting continues until the Condorcet winner is selected.

[0054] Figure 1 FIG. 1 is a flow chart of sorted set fusion according to an embodiment of the present invention. Figure 1 As shown, the present invention provides a Markov chain-based multi-biometric feature sorting level fusion method, which is applied to a multi-biometric feature recognition system, and includes:

[0055] Step S1: The corresponding biometric information of the user to be tested is input into different single biometric identification algorithms to obtain an initial sorting list of each algorithm for the user; wherein, the single biometric identification algorithm can adopt the algorithm for identifying each biometric in the prior art, which is not limited by the present invention.

[0056] Figure 1 This embodiment assumes that different biometric features or algorithms are independent of each other. To ensure data security and privacy, experimental data was constructed. Three biometric features were selected, each with a one-to-one correspondence, to construct a virtual user sample, serving as the test user set for this experiment. The number of biometric features in this embodiment (three) is used solely for experimental purposes and is not intended to limit the number of biometric features in the user sample of this invention.

[0057] Figure 1 The user test sample is input into three algorithms for recognizing the first biometric feature, the second biometric feature, and the third biometric feature, namely, Algorithm 1, Algorithm 2, and Algorithm 3. In one embodiment of the present invention, the specific process of obtaining the initial sorted list of single biometric features by each single biometric feature recognition algorithm in step S1 is as follows:

[0058] Step S11: extracting the biometric information of the user to be tested by using a corresponding algorithm;

[0059] Step S12: Match the extracted features with the template library and output the matching results;

[0060] Step S13: Obtain an initial sorted list of corresponding biometric features according to the output matching results.

[0061] See also Figure 1 , through the first biometric matching result output by algorithm 1, we get the initial sorted list 1; through the second biometric matching result output by algorithm 2, we get the initial sorted list 2; through the third biometric matching result output by algorithm 3, we get the initial sorted list 3.

[0062] Step S2: The set of user identities obtained from the initial sorting list of all algorithms is used as the state space S. According to the state transition rule agreement that meets the Condorcet standard, a Markov chain {X n |n=0,1,2,…}; In this embodiment, in order to compare the recognition performance differences between the fusion algorithm and the individual algorithms, the three initial sorting lists of the selected test samples have certain differences in the corresponding comparison results, and at least one algorithm can be compared in its initial sorting list.

[0063] In one embodiment of the present invention, the corresponding state transition rule in step S2 is specifically agreed to be:

[0064] Step S21: Assume that the current state is i, i∈S, and randomly select identity j with equal probability, where j∈S, S is the state space;

[0065] Step S22: If more than half of the initial sorted lists output by each algorithm have j ranked higher than i, that is, j is ranked higher than i, then the next state jumps to j; otherwise, the next state remains at i;

[0066] At the same time, suppose the user identity is randomly selected in the state space S, and it is assumed that the identity state changes only at time n, and the user identity selection is performed according to the above state transition rules. If X n represents the user identity selection at time n, then {X n |n=0,1,2,…} is a Markov chain.

[0067] Step S3: Check the number of user identities in the initial sorting list of each algorithm. If there are any unlisted user identities, fill in the unlisted user identities in the corresponding list. Since the length of the final consensus sorting list is the number of user identities compared in all initial sorting lists, it is necessary to fill in the unlisted user identities here.

[0068] In one embodiment of the present invention, the method for completing the unlisted user identities in the corresponding list in step S3 is any one of the following:

[0069] Use random insertion to randomly insert unlisted user identities at the end of the corresponding initial sorted list; or

[0070] Using the position insertion method, the corresponding user identity is inserted at the relative position of the unlisted user identity (for example, a method such as Borda score sorting can be used) to form a complete sorted list. In this embodiment, the position insertion method can be used first. When a tie occurs in the comparison, the random insertion method is used for random insertion.

[0071] In this embodiment, when completing the initial sorting list of one algorithm for user test samples, the comparison results of the other two algorithms are inserted at the end of the list in sequence. For the same comparison result, only the one with the smallest sequence number is selected. In this way, each of the completed initial sorting lists will match the user test samples. Therefore, in this experiment, the virtual user test samples are all positive samples.

[0072] Step S4: All the completed initial sorted lists are fused at the sorting level to calculate the state transition matrix P;

[0073] In one embodiment of the present invention, the specific process of step S4 is as follows:

[0074] Step S41: For any state i in the state space S, i∈S, obtain the set J(i) of all states that meet the state transition rule except state i itself according to the state transition rule;

[0075] Step S42: Solve p using the following formula based on equal probability randomness: ij :

[0076] ∑ j∈S p ij =1

[0077]

[0078]

[0079] Among them, p ij is the probability that the next state is j when the current state is i, p ii is the probability that the next state will still be i when the current state is i;

[0080] Further

[0081] Step S43: Repeat steps S41 to S42 for all states in the state space S to obtain the entire state transfer matrix P.

[0082] Step S5: Obtain a consensus ranking list according to the state transition matrix P.

[0083] In one embodiment of the present invention, the first method of calculating the consensus ranking list in step S5 is specifically:

[0084] Step S511: For any state j, j∈S, the consensus ranking list score s is obtained by the difference between the sum of the j-th column elements and the sum of the j-th row elements of the state transition matrix P. j , or the consensus ranking list score s is obtained by calculating the difference between the in-degree and out-degree of the j-th node in the transition graph corresponding to the state transition matrix P j , the specific calculation formula is:

[0085] s j =∑ i∈S p ij -∑ i∈S p ji =∑ i∈S p ij -1;

[0086] Step S512: Calculate all states j and score all the consensus ranking lists obtained s j Arrange them in descending order to get a consensus sorted list.

[0087] In one embodiment of the present invention, the second method of calculating the consensus ranking list in step S5 is specifically:

[0088] Step S521: For any state j, j∈S, the consensus ranking list score s is obtained by calculating the difference between the sum of the elements in the jth column and the sum of the elements in the jth row of the matrix W, that is, the difference between the number of edges with the jth node as the end point and the number of edges with the jth node as the starting point in the transition graph corresponding to the state transition matrix P. j , the specific calculation formula is:

[0089] s j =∑ i∈S ω ij -∑ i∈S ω ji ,

[0090] Among them, any element Denoted as a matrix

[0091] Step S522: Calculate all states j and score all the consensus ranking lists obtained s j Arrange in descending order to obtain a consensus ranking list. In this embodiment, steps S511-S512 and steps S521-S522 are two different calculation methods for obtaining a consensus ranking list.

[0092] Figure 2The CMC curve (Cumulative Match Characteristic, cumulative matching curve) comparison diagram of the method of the present invention and three single biometric feature recognition algorithms is shown in the figure. Figure 2 As shown, Algorithms 1, 2, and 3 are Figure 1 In Algorithms 1, 2, and 3, Markov method 1 corresponds to the method of obtaining the consensus ranking list through steps S511 to S512, and Markov method 2 corresponds to the method of obtaining the consensus ranking list through steps S521 to S522. Figure 2 As shown, this embodiment uses the top k hit rate top(k) as the evaluation indicator for each algorithm. According to the CMC curve drawn based on the initial sorted list after the test sample set is completed and the consensus sorted list obtained by each algorithm, it can be seen that the first hit rates of Markov method 1 and Markov method 2 are 94.76% and 94.37% respectively, and the first hit rates of the three individual biometric recognition algorithms are 81.55%, 74.76% and 85.05% respectively. This proves that the recognition performance of the ranking-level fusion method based on Markov chain is better than that of the three individual algorithms.

[0093] Figure 3 This is a CMC curve comparison diagram of the method of the present invention and other sorting level fusion algorithms. Figure 3 As shown, the first hit rates of the highest sequence number method, the Borda counting method, and the logistic regression method are 91.07%, 92.04%, and 93.40%, respectively, which are slightly lower than the first hit rates of Markov method 1 and Markov method 2, which are 94.76% and 94.37%. By comparing the CMC curve trends of different ranking-level fusion algorithms, the recognition performance of the ranking-level fusion algorithms in this experiment is ranked from high to low as follows: the Markov chain-based method, the logistic regression method, the Borda counting method, and the highest sequence number method. Here, there is a slight difference in the recognition results of individual test samples between the two forms of the Markov chain-based method, so the two CMC curves of Markov method 1 and Markov method 2 are almost the same but do not completely overlap. The method of the present invention starts from the definition of the Markov chain, constructs a state transition rule that meets the Condorcet criterion, and verifies the performance advantages of the Markov chain-based method over the other three ranking-level fusion methods and three separate biometric recognition algorithms through specific experiments.

[0094] The Markov chain-based multi-biometric feature sorting-level fusion method of the present invention can well handle the situation where the initial sorting list is a small number of registered users in the registration template library, provide a more comprehensive comparison between candidate users, and can also process and compare when the results of each initial sorting list are very different, with high accuracy. Therefore, it has a wider range of application scenarios in the sorting-level fusion of multi-biometric recognition systems.

[0095] Those skilled in the art will appreciate that the accompanying drawings are merely schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0096] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A Markov chain-based multi-biometric ranking fusion method, applied to a multi-biometric recognition system, characterized in that: include: Step S1: Input the corresponding biometric information of the user to be tested into different single biometric recognition algorithms to obtain the initial ranking list of each algorithm for the user; Step S2: The set of user identities obtained from the initial sorting list of all algorithms is used as the state space S. According to the state transition rule agreement that meets the Condorcet standard, a Markov chain {X n |n=0,1,2,…}, where the corresponding state transition rules are specifically agreed upon as follows: Step S21: Assume that the current state is i, i∈S, and randomly select state j with equal probability, where j∈S, S is the state space; Step S22: If more than half of the initial sorted lists output by each algorithm have j ranked higher than i, that is, j is ranked higher than i, then the next state jumps to j; otherwise, the next state remains at i; At the same time, suppose the user identity is randomly selected in the state space S, and the identity state changes only at time n, and the user identity is selected according to the above state transition rule. If X n represents the user identity selection at time n, then {X n |n=0,1,2,…} is a Markov chain; Step S3: Check the number of user identities in the initial sorting list of each algorithm. If there are any unlisted user identities, fill in the unlisted user identities in the corresponding list; Step S4: All the completed initial sorted lists are fused at the sorting level to calculate the state transition matrix P; Step S5: Obtain a consensus ranking list according to the state transition matrix P.

2. The Markov chain-based multi-biometric feature ranking fusion method according to claim 1, characterized in that: The specific process of obtaining the initial sorted list of single biometric features by each single biometric feature recognition algorithm in step S1 is as follows: Step S11: extracting the biometric information of the user to be tested by using a corresponding algorithm; Step S12: Match the extracted features with the template library and output the matching results; Step S13: Obtain an initial sorted list of corresponding biometric features according to the output matching results.

3. The Markov chain-based multi-biometric feature ranking fusion method according to claim 1, characterized in that: In step S3, the method for completing the unlisted user identities in the corresponding list is any of the following: Use random insertion to randomly insert unlisted user identities at the end of the corresponding initial sorted list; or The position insertion method is used to insert the corresponding user identity at the relative position of the unlisted user identity to form a complete sorted list.

4. The Markov chain-based multi-biometric ranking fusion method according to claim 1, characterized in that: The specific process of step S4 is: Step S41: For any state i in the state space S, i∈S, obtain the set J(i) of all states that meet the state transition rule except state i itself according to the state transition rule; Step S42: Solve p using the following formula based on equal probability randomness: ij : ∑ j∈S p ij ＝1 Among them, p ij is the probability that the next state is j when the current state is i, p ii is the probability that the next state will still be i when the current state is i; Further Step S43: Repeat steps S41 to S42 for all states in the state space S to obtain the entire state transfer matrix P.

5. The Markov chain-based multi-biometric feature ranking fusion method according to claim 1, characterized in that: The first method of calculating the consensus ranking list in step S5 is specifically as follows: Step S511: For any state j, j∈S, the consensus ranking list score s is obtained by the difference between the sum of the j-th column elements and the sum of the j-th row elements of the state transition matrix P. j , or the consensus ranking list score s is obtained by calculating the difference between the in-degree and out-degree of the j-th node in the transition graph corresponding to the state transition matrix P j , the specific calculation formula is: s j =∑ i∈S p ij -∑ i∈S p ji =∑ i∈S p ij -1; Step S512: Calculate all states j and score all the consensus ranking lists obtained s j Arrange them in descending order to get a consensus sorted list.

6. The Markov chain-based multi-biometric feature ranking fusion method according to claim 1, characterized in that: The second method of calculating the consensus ranking list in step S5 is specifically as follows: Step S521: For any state j, j∈S, the consensus ranking list score s is obtained by calculating the difference between the sum of the elements in the jth column and the sum of the elements in the jth row of the matrix W, that is, the difference between the number of edges with the jth node as the end point and the number of edges with the jth node as the starting point in the transition graph corresponding to the state transition matrix P. j , the specific calculation formula is: s j =∑ i∈S oh ij -∑ i∈S oh ji , Among them, any element Denoted as a matrix Step S522: Calculate all states j and score all the consensus ranking lists obtained s j Arrange in descending order to obtain a consensus sorted list.

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