Improved D-S evidence theory fusion method and system

Abstract

The invention discloses an improved D-S evidence theory fusion method and system, and relates to the field of data fusion and information processing, and the method comprises the steps: dividing multi-dimensional data into independent information sources according to attributes, and generating basic data for calculating BPA; constructing single and composite assumed BPA by using a fuzzy naive Bayes method and an FCM algorithm; fusing the BPA with different attributes through a synthesis rule to obtain a comprehensive BPA; and converting the comprehensive BPA into Pignistic probability, and determining the prediction category of the test sample according to the maximum value. The method effectively deals with evidence conflicts and improves the reliability of a fusion result by defining an uncertain area and constructing a single and composite hypothesis BPA, generates the BPA by using a fuzzy naive Bayes method and an FCM algorithm, optimizes evidence weight distribution through weight adjustment to reduce complexity, and improves the reliability of the fusion result through probability transformation and a maximum value decision method. And the classification result is more accurate and stable.

Description

Technical Field

[0001] The present invention relates to the field of data fusion and information processing, and in particular to an improved DS evidence theory fusion method and system. Background Art

[0002] Data preprocessing is an essential step in all data fusion, however, in the literature on data fusion, not enough attention is paid to the work of preprocessing. As the data source of data fusion, the quality of data preprocessing results will directly affect the results of data fusion. A good preprocessing result can not only make the fusion result more accurate, but also improve the fusion speed.

[0003] In practical applications, due to the heterogeneity of data from multiple sources, the information collected directly from various data sources will have some problems to varying degrees, such as data integrity, uniqueness, authority, consistency, etc., inconsistent data dimensions, irrelevant information (noise), redundant fields, or multiple indicator values. These problems will lead to high costs for subsequent operations and inaccurate decisions, so data preprocessing is an indispensable part of data fusion. Data preprocessing can be classified into a variety of methods, and can be divided into: data cleaning, data integration and transformation, data reduction, etc. according to the work content. These technologies provide important guarantees for subsequent data fusion operations and will also improve the performance of fusion. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] Therefore, the technical problem solved by the present invention is: how to generate robust basic probability distribution and efficiently handle evidence conflicts in the process of fusing multi-source heterogeneous data to achieve accuracy and reliability of classification decisions.

[0006] To solve the above technical problems, the present invention provides the following technical solutions: an improved DS evidence theory fusion method, which comprises the following steps:

[0007] Divide multidimensional data into independent information sources according to attributes to generate basic data for calculating BPA;

[0008] The fuzzy naive Bayes method and FCM algorithm were used to construct BPA of single and composite hypotheses;

[0009] The BPAs of different attributes are fused through the Dempster synthesis rule to obtain the comprehensive BPA;

[0010] The comprehensive BPA is converted into Pignistic probability, and the predicted category of the test sample is determined according to the maximum value.

[0011] As a preferred solution of the improved DS evidence theory fusion method described in the present invention, wherein: the multidimensional data is divided into independent information sources according to attributes, and the basic data for calculating BPA is generated, including:

[0012] For a given multidimensional data set, each single attribute is an independent source of information. The BPA of each attribute is calculated separately and then synthesized using the DS evidence theory to obtain a reliable comprehensive decision. After the attribute division, the test data set with p attributes is divided and converted into p independent models in this paper.

[0013] As a preferred solution of the improved DS evidence theory fusion method described in the present invention, wherein: the basic data for generating and calculating BPA includes:

[0014] The BPA function is generated by taking set C as the recognition framework, and the expression is:

[0015] Θ=C={C1,C2,…,C n}

[0016] The focal element of the recognition framework power set 2Θ is represented as:

[0017] Ω={{C1},…,{C N}, {C1, C2}, …, {C i , C j}, ..., {C N-1 , C N}}

[0018] Among them, the composite element {C i , C j}(i≠j) is the uncertain assumption in DS evidence theory;

[0019] Using ROU to represent composite hypothesis i , C j}, divide the uncertainty data;

[0020] For each attribute, obtain N Gaussian distributions and C N2 The ROU functions are used as models of single hypothesis and composite hypothesis respectively.

[0021] As a preferred solution of the improved DS evidence theory fusion method described in the present invention, the BPA of single and composite hypotheses constructed by using the fuzzy naive Bayes method and the FCM algorithm includes:

[0022] When using the fuzzy naive Bayes method and the FCM algorithm to calculate the basic probability assigned to each focal element, the fuzzy membership value Indicates the degree to which each attribute belongs to different categories. Given an input sample, for attribute x, the calculated membership value is:

[0023]

[0024] For the composite hypothesis {C i , C j}, after classification, calculate the variance of the membership degree under each fuzzy partition. The expression is:

[0025]

[0026] where M is the expectation;

[0027] The membership matrix is:

[0028]

[0029] Set a variance value D(u) as the threshold. When dividing, the average value of the variance of the membership degrees of each row of the membership matrix U is used as the value of D(u);

[0030] When D(u i ) < D(u), then the current sample has the properties of both category labels.

[0031] As a preferred solution of an improved D-S evidence theory fusion method described in the present invention, wherein: the construction of the BPA of single and composite hypotheses using the fuzzy Naive Bayes method and the FCM algorithm further includes,

[0032] For an object in the uncertain region that belongs to both class C i and class C j , use the fuzzy AND operator to assign the mass function related to the composite hypothesis. The basic probability assignment function of each hypothesis calculated by the fuzzy Naive Bayes method is:

[0033]

[0034] where μ{Ci} represents the membership value belonging to class Ci;

[0035] According to the FCM algorithm, use the Euclidean distance between the input sample and the class centroid vector to determine the discriminant class basic probability. Take ROU as the intersection point V{C i , C j} of the composite hypothesis as the class centroid of the composite hypothesis, which is the point with the minimum AND value calculated from the distributions of two different classes C i , C j . The expression is:

[0036]

[0037] The method of defining the discriminative BPA function is to use the exponential function of the distance between the sample and the category centroid, expressed as:

[0038]

[0039] Use a weighted mediation framework to collect and integrate different evidence;

[0040] Generative class BPA produced by the fuzzy naive Bayes method: And the distance-based discriminant class BPA: The integration expression is:

[0041]

[0042] Among them, 0≤α, β≥1 are adjustment parameters for adaptively determining the importance of two types of evidence;

[0043] Grid search is used to minimize the training error and find the optimal adjustment parameters.

[0044] As a preferred solution of the improved DS evidence theory fusion method described in the present invention, wherein: the fusion of BPAs of different attributes by Dempster synthesis rule to obtain a comprehensive BPA includes:

[0045] The BPAs generated by different attributes were combined using Dempster’s composition rule to obtain the comprehensive BPA;

[0046] The Dempster synthesis rule single category synthesis and multi-category synthesis;

[0047] Single category synthesis involves setting a proposition A, Proposition A For two mass functions m1, m2 on Θ in the same recognition frame, the synthesis rule expression is:

[0048]

[0049] Among them, represents orthogonal sum;

[0050] If K = 1, the two pieces of evidence conflict, so there is no orthogonal sum; if K ≠ 1, the orthogonal sum of the BPA of the two pieces of evidence forms a new distribution function; if K-1 = 0, m1 and m2 are contradictory, and there is no joint basic probability distribution function;

[0051] Diverse category synthesis includes, when it is necessary to process a finite number of mass functions m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m22, m12, m13, m23, m14, m25, m15, m26, m16, m27, m17, m28, m29, m30, m31, m32, m13, m29, m33, m14, m29, m15 ...16, m29, m17, m29, m17, m29, m17, m29, m17, m29, m29, m33, m29, m17, m29, m17, m29, m17, m29, m17, m29, m17, When mn, the orthogonal sum of multiple basic probability distribution functions is used to form a basic trust function. The synthesis rule expression is:

[0052]

[0053] If the two synthesis objects are not completely conflicting, the orthogonal sum of any two functions is valid. Regardless of the synthesis order, the synthesis result of multiple evidences is certain. The synthesis method of multiple evidences is derived from the synthesis formula of two evidences.

[0054] As a preferred solution of the improved DS evidence theory fusion method described in the present invention, wherein: the conversion of the comprehensive BPA into Pignistic probability and the determination of the prediction category of the test sample according to the maximum value include:

[0055] Use Pignistic transformation to make a decision, and select the predicted category of the sample in the pseudo test data from the hypothesis category with the maximum Pignistic probability;

[0056] The Pignistic transformation is to transform the mass function into a Pignistic probability function. m(A) is a basic probability distribution function defined on the recognition framework Θ. The Pignistic probability function on the recognition framework Θ is Bet P m : Θ→[0, 1], the expression is:

[0057]

[0058] Where B is time B.

[0059] Another object of the present invention is to provide an improved DS evidence theory fusion system, which can solve the problems of insufficient evidence conflict handling ability, high computational complexity and low classification accuracy of the existing DS evidence theory through attribute division of multidimensional data, BPA generation of single and composite hypotheses, and evidence fusion and Pignistic probability decision based on Dempster rules.

[0060] In order to solve the above technical problems, the present invention provides the following technical solutions: an improved DS evidence theory fusion system, comprising: a data preprocessing module, a BPA generation module, an evidence fusion module, and a decision module;

[0061] The data preprocessing module is to complete the division of multi-dimensional data, regard each attribute as an independent information source, and generate BPA to provide basic data;

[0062] The BPA generation module generates BPAs of single and composite hypotheses using the fuzzy naive Bayes method and the FCM algorithm, defines the probability of allocating composite hypotheses to the uncertain region, constructs a Gaussian distribution model by calculating the membership and variance, and determines the quality function of each category and composite category;

[0063] The evidence fusion module integrates BPAs of different attributes using Dempster synthesis rules to generate comprehensive BPAs, handle orthogonal sum calculations of single and multiple categories, and resolve evidence conflicts.

[0064] The decision module converts the comprehensive BPA through Pignistic transformation, calculates the Pignistic probability distribution of each hypothesis, selects the prediction category of the test sample according to the maximum Pignistic probability value, converts the mass function into the Pignistic probability function, and outputs the decision result intuitively.

[0065] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the improved DS evidence theory fusion method as described above when executing the computer program.

[0066] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the improved DS evidence theory fusion method as described above.

[0067] Beneficial effects of the present invention: The present invention effectively copes with evidence conflicts and improves the reliability of fusion results by defining uncertainty regions (ROUs) and constructing BPAs of single and composite hypotheses. The present invention generates BPAs using the fuzzy naive Bayes method and the FCM algorithm, and optimizes the distribution of evidence weights through weight adjustment, which greatly reduces the complexity. The classification results are made more accurate and stable through Pignistic probability conversion and maximum decision methods. Through multi-dimensional attribute division and independent construction of models, the present invention is suitable for complex data scenarios and realizes efficient integration and processing of multi-source data. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. 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 creative work. Among them:

[0069] Figure 1 An overall flow chart of an improved DS evidence theory fusion method provided for the first embodiment of the present invention;

[0070] Figure 2 A schematic diagram of an uncertain region in an improved DS evidence theory fusion method provided in the second embodiment of the present invention. DETAILED DESCRIPTION

[0071] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described in detail below in conjunction with the drawings of the specification. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative work should fall within the scope of protection of the present invention.

[0072] Example 1, reference Figure 1 As an embodiment of the present invention, an improved DS evidence theory fusion method is provided, comprising:

[0073] Divide multidimensional data into independent information sources according to attributes to generate basic data for calculating BPA;

[0074] The fuzzy naive Bayes method and FCM algorithm were used to construct BPA of single and composite hypotheses;

[0075] The BPAs of different attributes are fused through the Dempster synthesis rule to obtain the comprehensive BPA;

[0076] The comprehensive BPA is converted into Pignistic probability, and the predicted category of the test sample is determined according to the maximum value.

[0077] For a given multidimensional data set, each single attribute is an independent source of information. The BPA of each attribute is calculated separately and then synthesized using the DS evidence theory to obtain a reliable comprehensive decision. After the attribute division, the test data set with p attributes is divided and converted into p independent models in this paper.

[0078] The BPA function is generated by taking set C as the recognition framework, and the expression is:

[0079] Θ=C={C1,C2,…,C n}

[0080] The focal element of the recognition framework power set 2Θ is represented as:

[0081] Ω={{C1},…,{C N}, {C1, C2}, …, {C i , C j}, ..., {C N-1 , C N}}

[0082] Among them, the composite element {Ci , C j}(i≠j) is the uncertain assumption in DS evidence theory;

[0083] Using ROU to represent composite hypothesis i , C j}, divide the uncertainty data;

[0084] In order to more intuitively understand the composite elements in the recognition framework, we use intuitive confidence allocation to model the uncertainty of the hypothesis. For each category, we use Gaussian distribution to model, such as Figure 2 As shown, it means that the kth attribute belongs to category C i or C j The dark green area on the left and the blue area on the right represent the degree of membership of C i and C j The Gaussian distribution of the sample is the region of uncertainty (ROU), so the samples falling in the ROU are difficult to identify because they have the properties of two different categories at the same time. Therefore, the recognition task of this part of the samples may produce classification errors. Therefore, it is obvious that we need to use ROU to represent the composite hypothesis {C i , C j}, in order to divide the uncertainty data. In this way, for each attribute, N Gaussian distributions and C N2 ROU functions are used as models for single hypothesis and composite hypothesis respectively.

[0085] When using the fuzzy naive Bayes method and the FCM algorithm to calculate the basic probability assigned to each focal element, the fuzzy membership value Indicates the degree to which each attribute belongs to different categories. Given an input sample, for attribute x, the calculated membership value is:

[0086]

[0087] For the composite hypothesis {C i , C j}, after classification, the variance of the membership degree under each fuzzy partition is calculated, and the expression is:

[0088]

[0089] Where M is the expectation;

[0090] The membership matrix is:

[0091]

[0092] Set a variance value D(u) as the threshold, and take the average of the variances of the membership degrees of each row of the membership matrix U during partitioning as the value of D(u).

[0093] When D(u i ) < D(u), then the current sample has the properties of two class labels simultaneously.

[0094] Since the objects in the uncertain region can belong to both C i class and C j class, a fuzzy AND operator is used to assign the mass function related to the composite hypothesis. The basic probability assignment function of each hypothesis calculated by the fuzzy Naive Bayes method is as follows:

[0095]

[0096] where μ{Ci} represents the membership degree value belonging to the Ci class.

[0097] Similarly, without proper normalization, Formulas 5 and 6 may not produce valid BPA. For the ∧ operation, any triangular norm (T-Norm) can be used, and the minimum value is selected as the triangular norm in the present invention.

[0098] Next, according to the FCM algorithm, the Euclidean distance between the input sample and the class centroid vector is used to determine the discriminant class basic probability. Taking ROU as the intersection point V{C i , C j} of the composite hypothesis as the class centroid of the composite hypothesis, which is the point with the minimum AND value calculated from the distributions of two different classes C i , C j . The expression is as follows:

[0099]

[0100] The method of defining the discriminant BPA function is to use the exponential function of the distance between the sample and the class centroid. The expression is as follows:

[0101]

[0102] To make this framework more flexible and better play in practical applications, a weighted adjustment framework is proposed to collect and integrate different evidences. The generative class BPA generated by the fuzzy Naive Bayes method: and the distance-based discriminant class BPA: are integrated. The expression is as follows:

[0103]

[0104] Among them, 0≤α, β≥1 are adjustment parameters for adaptively determining the importance of the two types of evidence; this weighted adjustment mechanism enables us to find appropriate weights for different sources of evidence from the training data, use grid search to minimize the training error, and find the optimal adjustment parameters. The training process is not described here. In addition, it is still necessary to emphasize that m in formulas 5, 6, 8, and 9 xg and m xd Not the final BPA itself.

[0105] Overall BPA of feature x: m x The definition of ({·}) is:

[0106]

[0107] Among them, K is the normalization factor, and there is an optimal set (α, β) corresponding to each attribute:

[0108]

[0109] The BPAs generated by different attributes were combined using Dempster’s composition rule to obtain the comprehensive BPA;

[0110] It is further explained that:

[0111] Obtaining a comprehensive decision requires a method to calculate the combined impact of multiple pieces of evidence on each hypothesis in the identification framework, and to derive the comprehensive degree of confidence that the hypothesis is valid under the influence of multiple pieces of evidence. BPA is the basis of trust function and likelihood function. In practical applications, it often happens that for the same hypothesis or problem, evidence comes from different data sources, which will result in two or even more different BPAs. Therefore, in order to better use likelihood function and trust function to measure the credibility of propositions in the future, we need a synthesis rule that synthesizes BPAs from different data sources.

[0112] Dempster's evidence synthesis rule is also called the evidence synthesis formula. Sharer made further research based on Dempster, generalized the synthesis rule of evidence theory to more general application scenarios, and proposed

[0113] Dempster's Combinational Rule. In evidence theory, when several pieces of evidence are not completely conflicting, if we can obtain a trust function or BPA on the same identification framework Θ, we can use Dempster's Combinational Rule to calculate a new trust function, which is generated by the above evidence.

[0114] The Dempster synthesis rule single category synthesis and multi-category synthesis;

[0115] Single category synthesis involves setting a proposition A, Proposition A For two mass functions m1, m2 on Θ in the same recognition frame, the synthesis rule expression is:

[0116]

[0117] Among them, represents orthogonal sum;

[0118] If K = 1, the two pieces of evidence conflict, so there is no orthogonal sum; if K ≠ 1, the orthogonal sum of the BPA of the two pieces of evidence forms a new distribution function; if K-1 = 0, m1 and m2 are contradictory, and there is no joint basic probability distribution function;

[0119] Diverse category synthesis includes, when it is necessary to process a finite number of mass functions m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m22, m12, m13, m23, m14, m25, m15, m26, m16, m27, m17, m28, m29, m30, m31, m32, m13, m29, m33, m14, m29, m15 ...16, m29, m17, m29, m17, m29, m17, m29, m17, m29, m29, m33, m29, m17, m29, m17, m29, m17, m29, m17, m29, m17, When mn, the orthogonal sum of multiple basic probability distribution functions is used to form a basic trust function. The synthesis rule expression is:

[0120]

[0121] From the above formula, we can see that if the two synthesis objects are not completely conflicting, the orthogonal sum of any two functions is calculable and valid, and the mathematical properties of the synthesis rule satisfy the associative law and commutative rate. Therefore, regardless of the synthesis order, the synthesis result of multiple evidences is certain. The synthesis method of multiple evidences can be derived from the synthesis formula of two evidences. Figure 2 .

[0122] It is further explained that:

[0123] According to the working process of DS evidence theory introduced above, how to make a decision after completing the combination of evidence requires specific analysis in practical applications, depending on its application field. In theory, there are generally the following categories:

[0124] (A) Decision-making based on trust function.

[0125] Based on the quality function obtained by evidence synthesis, the trust function Bel is calculated. Generally, the judgment result is obtained based on the value of this function, and the decision with the highest trust is taken.

[0126] If you want to further narrow the scope of the decision set, you can use the "minimum point" principle: the confidence function of set A is Bel(A), if the set after removing an element bi from A is B, and |Bel(B)-Bel(A)|<ε, then it is considered that the element bi can be removed, where ε is a sufficiently small constant. Repeat this operation until no element can be removed.

[0127] (II) Decision-making based on basic confidence. satisfy:

[0128]

[0129]

[0130] If yes: Then A1 is the fused decision result, where ε1 and ε2 are pre-set thresholds.

[0131] 3. Decision-making based on minimal risk

[0132] Recognition framework Θ={θ1, θ2,…,θ n}, decision set A = {a1, a2, ..., a p}In state θ l If the decision is a i , the risk function is r(a i , x l ), i = 1, 2, ..., p, 1 = 1, 2, ..., q, if the evidence E produces a corresponding quality function m(A1, ...A n ),make:

[0133]

[0134] If there is a k ∈A such that a k =arg min{R(a1),…,R(a p )}, then a k This is the optimal decision we seek.

[0135] (IV) Methods of probability functions

[0136] The class probability function method is a quantitative discrimination method. First, the definition of the class probability function is:

[0137]

[0138] After DS evidence fusion, the class probability function is used as a point estimate of the probability P(A), and then the decision is made using discriminant criteria such as maximum a posteriori probability or minimum Bayesian cost.

[0139] It is further explained that:

[0140] DS evidence theory has a strong theoretical foundation and has efficient processing capabilities when faced with uncertain, ambiguous and incomplete information. It can continuously narrow the scope of hypotheses by accumulating evidence; it does not require the density of conditional probability and prior probability when fusing evidence data; it can describe the support of evidence through evidence intervals and has better processing capabilities for uncertainties caused by randomness and ambiguity.

[0141] In DS evidence theory, the number of focal elements in the recognition framework Θ will affect the computational complexity of the fusion calculation, because the number of focal elements is related to the number of operations in evidence synthesis, which will cause an exponential growth trend in the computational complexity. This has a great limitation in applications with large-scale data. There are usually two solutions to this problem: use experience or known information to reduce the number of focal elements before evidence synthesis, or merge the simpler assumptions in the recognition framework before performing the next operation; construct algorithms that can be processed quickly for certain specific data structures, such as tree structures, or use approximate calculations, or modify the DS synthesis rules.

[0142] Due to the definition of evidence theory, the rules of evidence synthesis cannot be used when there is a large conflict between the evidence involved in the synthesis, otherwise unreliable conclusions will be drawn. This limitation has largely restricted the further widespread use of evidence theory. In order to solve this problem, many scholars have conducted research and proposed some solutions. The main idea is to analyze the causes of the conflict and modify them in combination with the application background. Among them, the causes of evidence conflict are as follows:

[0143] (1) The target recognition framework is incomplete. Since the generation of target recognition depends on people’s understanding of the overall hypothesis, but people’s cognitive scope is limited, there may be situations such as ignoring a certain hypothesis or not knowing the emergence of a new thing, which will lead to the lack of certain hypotheses in the target recognition framework. As a result, the description of the target by multi-source data will deviate from the actual situation, resulting in conflicts and making it impossible to make accurate decisions.

[0144] (2) Sensor data is unreliable. Sensors are not immune to the environment, and when faced with some human or other interference, erroneous information is inevitable, which will lead to conflicts between evidence. In addition to the external environment, internal factors of the sensor, such as its own accuracy and performance, may also result in inaccurate evidence information, leading to conflicts in evidence.

[0145] (3) Unreasonable construction of the basic probability distribution function. Since the fusion results of evidence theory are all constructed based on BPA, and the establishment of BPA is very complicated, if the construction method of BPA is inappropriate, the obtained quality function cannot truly reflect the trust of the evidence in the hypothesis, and it may also cause conflicts and affect the fusion results.

[0146] The probability assignment problem in DS evidence theory refers to the establishment of BPA, which is a very important process in the theory. Although the establishment methods of BPA are different in different application scenarios, they must all complete the multi-source data through this function. Θ →[0, 1]. The construction of basic probability distribution function can be roughly divided into the following two types:

[0147] (1) Neural network. Neural networks have high computing speed, strong associative ability, adaptability, fault tolerance and self-organization ability, and can make good use of prior knowledge through training and learning. When processing data after training, the data range can be controlled to [0, 1], which is in good accordance with the function of the basic probability distribution function. However, the use of neural networks requires certain prior knowledge and a certain amount of training time.

[0148] (2) Mathematical calculation. The probability distribution function can also be constructed by converting data between [0, 1] through linear and nonlinear functions in mathematics. The choice of mathematical function depends on the specific application. For example, in the image data processing scenario, a linear method can be used to correlate image features with the image database to be analyzed, and the BPA can be constructed through the correlation coefficient between them. This method is simple and easy to operate with fast calculation speed. Nonlinear functions may lose source data information in the process of processing data, and the obtained data information must also be normalized.

[0149] Use Pignistic transformation to make a decision, and select the predicted category of the sample in the pseudo test data from the hypothesis category with the maximum Pignistic probability;

[0150] It is further explained that:

[0151] Pignistic transformation converts the mass function into a Pignistic probability function. m(A) is a basic probability distribution function defined on the recognition framework Θ. The Pignistic probability function on the recognition framework Θ is BetP m : Θ→[0, 1], the expression is:

[0152]

[0153] Where B is time B.

[0154] The above methods quantify the evidence from each information source and construct the basic probability distribution function for single hypothesis and composite hypothesis respectively. In our method, ROU is used to define composite hypothesis. In order to take into account the characteristics of different sources, a weighted adjustment framework is used to assign probabilities to single and composite hypotheses. In practical applications, a training mechanism can be used to find appropriate weighting coefficients (α, β) and apply them to different evidence categories.

[0155] Embodiment 2 is an embodiment of the present invention, which provides a system for an improved DS evidence theory fusion method, including: a data preprocessing module, a BPA generation module, an evidence fusion module, and a decision module;

[0156] The data preprocessing module is to complete the division of multi-dimensional data, regard each attribute as an independent information source, and generate BPA to provide basic data;

[0157] The BPA generation module generates BPAs of single and composite hypotheses using the fuzzy naive Bayes method and the FCM algorithm, defines the probability of allocating composite hypotheses to the uncertain region, constructs a Gaussian distribution model by calculating the membership and variance, and determines the quality function of each category and composite category;

[0158] The evidence fusion module integrates BPAs of different attributes using Dempster synthesis rules to generate comprehensive BPAs, handle orthogonal sum calculations of single and multiple categories, and resolve evidence conflicts.

[0159] The decision module converts the comprehensive BPA through Pignistic transformation, calculates the Pignistic probability distribution of each hypothesis, selects the prediction category of the test sample according to the maximum Pignistic probability value, converts the mass function into the Pignistic probability function, and outputs the decision result intuitively.

[0160] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc., which can store program code.

[0161] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute instructions), or in conjunction with such instruction execution systems, devices or apparatuses. For the purposes of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in conjunction with such instruction execution systems, devices or apparatuses.

[0162] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0163] It should be understood that the various parts of the present invention can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, a plurality of steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0164] Embodiment 3: In this embodiment, in order to verify the beneficial effects of the present invention, scientific demonstration is carried out through economic benefit calculation and simulation experiments. This embodiment experiments the existing traditional method and the method of this embodiment respectively.

[0165] The performance of the proposed weighted fuzzy DS evidence theory is compared with that of four fusion algorithms, namely: two data fusion methods based on DS evidence theory: k-nearest neighbor DS theory (KNN-DST, K-Nearest Neighbor Classification Rule Based on Dempster-Shafer Theory) and normal distribution-based classifier (NDBC, Normal Distribution-Based Classifier), and two common fusion methods: Naive Bayes (NBC, Bayes Classifier), Nearest Mean Classifier (NMC).

[0166] The datasets used are still the datasets generated by three real data in the UCI machine learning library: Iris plant dataset, wine quality dataset and forest type mapping dataset. The basic information of these UCI datasets is shown in Table 1. For each comparison model, five-fold cross validation is applied in the experiment, that is, 80% (four-fold) of the dataset is randomly selected to establish the training dataset, and the remaining 20% ​​of the data (one-fold) is used as the test data. This process is repeated 5 times, and the average of the 5 runs is used for comparison.

[0167] Table 1 Basic information of experimental dataset

[0168] Dataset Number of samples Number of categories Number of attributes Iris plant 150 3 4 Red sprinkle quality 178 3 13 Forest Type 326 4 27

[0169] The algorithm proposed in this paper was tested on several data sets, and the average classification accuracy was 94.46%±3.94%, which is higher than other schemes and has a lower standard deviation than other schemes. The specific data are shown in Table 2.

[0170] Table 2 Comparison of classification accuracy

[0171]

[0172] 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 preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. An improved DS evidence theory fusion method, characterized in that: include: Divide multidimensional data into independent information sources according to attributes to generate basic data for calculating BPA; The fuzzy naive Bayes method and FCM algorithm were used to construct BPA of single and composite hypotheses; The BPAs of different attributes are fused through the Dempster synthesis rule to obtain the comprehensive BPA; The comprehensive BPA is converted into Pignistic probability, and the predicted category of the test sample is determined according to the maximum value.

2. The improved DS evidence theory fusion method as claimed in claim 1, characterized in that: The method of dividing the multidimensional data into independent information sources according to attributes and generating basic data for calculating BPA includes: For a given multidimensional data set, each single attribute is an independent source of information. The BPA of each attribute is calculated separately and then synthesized using the DS evidence theory to obtain a reliable comprehensive decision. After the attribute division, the test data set with p attributes is divided and converted into p independent models in this paper.

3. The improved DS evidence theory fusion method as claimed in claim 2, characterized in that: The basic data for generating and calculating BPA includes: The BPA function is generated by taking set C as the recognition framework, and the expression is: Θ=C={C1,C2,…,C n } The focal element of the recognition framework power set 2Θ is represented as: Ω={{C1},…,{C N },{C1,C2},…,{C i ,C j },…,{C N-1 ,C N }} Among them, the composite element {C i ,C j }(i≠j) is the uncertain assumption in DS evidence theory; Using ROU to represent composite hypothesis i ,C j }, divide the uncertainty data; For each attribute, obtain N Gaussian distributions and C N2 The ROU functions are used as models of single hypothesis and composite hypothesis respectively.

4. The improved DS evidence theory fusion method as claimed in claim 3, characterized in that: The BPA using the fuzzy naive Bayes method and the FCM algorithm to construct single and composite hypotheses includes: When the fuzzy naive Bayes method and FCM algorithm are used to calculate the basic probability assigned to each focal element, the fuzzy membership values ​​{μ{C1},μ{C2},…,μ{C N }} represents the degree to which each attribute belongs to different categories, giving Given an input sample, for attribute x, the calculated membership value is: For the composite hypothesis {C i ,C j }, after classification, the variance of the membership degree under each fuzzy partition is calculated, and the expression is: Where M is the expectation; The membership matrix is: Set a variance value D(u) as the threshold, and take the average value of the variance of the membership degree of each row of the membership matrix U as the value of D(u) during the partitioning; When D(u i ) < D(u), the current sample has the property of having two class labels simultaneously.

5. The improved DS evidence theory fusion method as claimed in claim 4, characterized in that: The BPA using the fuzzy naive Bayes method and the FCM algorithm to construct single and composite hypotheses also includes: Objects in the uncertainty region belong to C i Class, also belongs to C j Class, the fuzzy AND operator is used to assign the quality function associated with the composite hypothesis. The basic probability assignment function of each hypothesis calculated by the fuzzy naive Bayes method is: Among them, μ{C i } means belonging to C i The membership value of the class; According to the FCM algorithm, using the input samples and the category centroid vectors {v{C1},v{C2},…,v{C N The Euclidean distance between them is used to determine the basic probability of the discriminant class, and the intersection point V{C is defined using ROU as the composite hypothesis i ,C j } is the centroid of the composite hypothesis, which is obtained by combining two different categories C i ,C j The distribution of is calculated to find the point with the minimum AND value, expressed as: The method of defining the discriminative BPA function is to use the exponential function of the distance between the sample and the class centroid, expressed as: Use a weighted mediation framework to collect and integrate different evidence; Generative class BPA produced by the fuzzy naive Bayes method: And the distance-based discriminant class BPA: The integration expression is: Among them, 0≤α,β≥1 are adjustment parameters for adaptively determining the importance of two types of evidence; Grid search is used to minimize the training error and find the optimal adjustment parameters.

6. The improved DS evidence theory fusion method as claimed in claim 5, characterized in that: The Dempster synthesis rule is used to fuse BPAs of different attributes to obtain a comprehensive BPA including: The BPAs generated by different attributes were combined using Dempster’s composition rule to obtain the comprehensive BPA; The Dempster synthesis rule single category synthesis and multi-category synthesis; Single category synthesis involves setting a proposition A, Proposition A For two mass functions m1, m2 on Θ in the same recognition frame, the synthesis rule expression is: Among them, represents orthogonal sum; If K = 1, the two pieces of evidence conflict, so there is no orthogonal sum; if K ≠ 1, the orthogonal sum of the BPA of the two pieces of evidence forms a new distribution function; if K-1 = 0, m1 and m2 are contradictory, and there is no joint basic probability distribution function; Diverse category synthesis includes, when it is necessary to process a finite number of mass functions m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m22, m12, m13, m23, m14, m15, m26, m16, m27, m17, m28, m29, m30, m31, m32, m13, m29, m33, When mn, the orthogonal sum of multiple basic probability distribution functions is used to form a basic trust function. The synthesis rule expression is: If the two synthesis objects are not completely conflicting, the orthogonal sum of any two functions is valid. Regardless of the synthesis order, the synthesis result of multiple evidences is certain. The synthesis method of multiple evidences is derived from the synthesis formula of two evidences.

7. The improved DS evidence theory fusion method as claimed in claim 6, characterized in that: The step of converting the comprehensive BPA into Pignistic probability and determining the predicted category of the test sample according to the maximum value includes: Use Pignistic transformation to make a decision, and select the predicted category of the sample in the pseudo test data from the hypothesis category with the maximum Pignistic probability; The Pignistic transformation is to transform the mass function into a Pignistic probability function. m(A) is a basic probability distribution function defined on the recognition framework Θ. The Pignistic probability function on the recognition framework Θ is BetP m : Θ→[0,1], the expression is: Where B is time B.

8. A system using an improved DS evidence theory fusion method as claimed in any one of claims 1 to 7, characterized in that: It includes data preprocessing module, BPA generation module, evidence fusion module and decision-making module; The data preprocessing module is to complete the division of multi-dimensional data, regard each attribute as an independent information source, and generate BPA to provide basic data; The BPA generation module generates BPAs of single and composite hypotheses using the fuzzy naive Bayes method and the FCM algorithm, defines the probability of allocating composite hypotheses to the uncertain region, constructs a Gaussian distribution model by calculating the membership and variance, and determines the quality function of each category and composite category; The evidence fusion module integrates BPAs of different attributes using Dempster synthesis rules to generate comprehensive BPAs, handle orthogonal sum calculations of single and multiple categories, and resolve evidence conflicts. The decision module converts the comprehensive BPA through Pignistic transformation, calculates the Pignistic probability distribution of each hypothesis, selects the prediction category of the test sample according to the maximum Pignistic probability value, converts the mass function into the Pignistic probability function, and outputs the decision result intuitively.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of an improved DS evidence theory fusion method described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of an improved DS evidence theory fusion method described in any one of claims 1 to 7 are implemented.

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