CN114818957A

CN114818957A - Application of evidence Wasserstein distance algorithm in component identification

Info

Publication number: CN114818957A
Application number: CN202210503253.5A
Authority: CN
Inventors: 肖富元; 何立蜓; 何华平
Original assignee: Individual
Current assignee: Individual
Priority date: 2022-05-10
Filing date: 2022-05-10
Publication date: 2022-07-29

Abstract

The invention discloses application of an evidence Wasserstein distance algorithm in component identification, wherein the evidence Wasserstein distance is EWD, and provides a new distance measurement algorithm aiming at a distance measurement problem in a D-S evidence theory. Results under extreme conditions. The provided method ensures good characteristics such as symmetry, nonnegativity, non-degeneration and boundary, and the innovation point is that the Wasserstein distance and the Dang entropy are combined for the first time, an evidence theory is introduced, the introduction of the Wasserstein distance and the Deng entropy enables the evidence distance to have the capacity of distributing high conflict factors when measuring conflicts, so that the original attributes of the evidence are well preserved, the possibility of generating confusing results is reduced, and finally, practice and practical application can prove the superiority of the EWD method.

Description

Application of evidence Wasserstein distance algorithm in component identification

Technical Field

The invention belongs to the technical field related to an evidence Wasserstein distance algorithm, and particularly relates to application of the evidence Wasserstein distance algorithm in component identification.

Background

In recent years, uncertainty and incompleteness of related information have attracted increasing attention of scholars. Evidence theory originated from the 1967 published evidence theory based on multi-valued mapping by dengue. Shafer converts the evidence theory from the uncertainty of propositions to the uncertainty relationship between sets, applies to the artificial intelligence category at first, and has the ability to process and express uncertain information. Researchers have proposed various methods for handling information uncertainty, such as D number, Z number, entropy, etc., and related theories have been widely applied to basic theories and practical applications. The theoretical aspects bring about vigorous development, such as fuzzy set theory, measurement, soft likelihood functions and saddle point analysis. Meanwhile, the method is widely applied to practical problems of medicine, engineering systems, network engineering and the like.

Evidence theory has been extended from the real domain to the complex domain. However, in the case of a large and complete conflict between the sources of evidence, the conclusions drawn by Dempster-Shafer (D-S) evidence theory are often contrary to conventional wisdom. Gradually, many methods have been proposed and have been improved effectively. Wherein, three mainstream improvement methods are respectively shown. Firstly, the evidence source is modified, namely, on the premise of keeping the classic D-S evidence theory unchanged, the data set is preprocessed before evidence combination so as to ensure poor collision in subsequent fusion. And secondly, modifying the combination rule, namely directly modifying the classical theory and redistributing the high-conflict evidence after evidence combination. And thirdly, correcting the classical evidence theory and the evidence source to achieve the purpose of reasonably distributing the evidence. The three methods show that the conflict management plays an important role in improving the performance of the fusion system.

The measurement of the degree of conflict between evidence has been an open problem in academia. The evidence distance is one of the criteria for measuring evidence conflict and plays an important role in managing conflict in evidence theory. In this document, we generalize the Wasserstein distance and the belief entropy and propose a new evidence Wasserstein distance, called EWD. The proposed EWD can effectively measure the difference between BBAs and solve the problem of high conflicting factor assignments in a multi-recognition framework. In the aspect of specific application, the algorithm greatly improves the problem of how to effectively identify the source of the component under the condition of detecting high component conflict.

Disclosure of Invention

The invention aims to provide application of an evidence Wasserstein distance algorithm in component identification so as to solve the problems in the background technology.

In order to achieve the purpose, the invention provides the following technical scheme:

the application of an evidence Wasserstein distance algorithm in component identification, wherein the evidence Wasserstein distance is EWD, and the EWD is verified by the following method:

1): let m1 and m2 be the quality function of the multi-intersection element set Θ, where γ i, j is the state transition matrix and Γ n, n is the matrix of all possible probability measures, as follows:

wherein F1 and F2 are subsets of Θ, and

Θ includes multiple elements, so the proposed EWD can consider the case of multiple subsets. Γ n, n is an n × n matrix with rows and columns each n-1. The equation | [ m1(Ai) -m2(Bi) ] - [ m1(Aj) -m2(Bj) ] | can retain the original properties of the data. The thought of the state transformation matrix gamma i, j comes from the Deng entropy, and the problem is intuitively converted into the optimal solution problem. Objectively, since the data dimension of BBA is equal to 1 and p is a norm, the Wasserstein distance becomes the best solution problem that best fits evidence definition when d is 1 and p is 1. Therefore, the EWD method is Wasserstein distance measurement under a one-dimensional, p ═ 1 condition, and is widely applied to measurement of an evidence distance. Furthermore, the Wasserstein distance can only show the calculated dimension d ═ 1 or a gaussian distribution;

2) the proposed EWD represents the distance between two evidentiary bodies. The larger the value obtained, the lower the correlation between the two evidential bodies, and the smaller the value, the higher the correlation between the two evidential bodies. And by correlation it can be concluded that the value of the EWD method is less if the relationship between the two evidences is closer and vice versa. But due to bounded limitations the maximum value cannot exceed 1 and the minimum value cannot be less than 0.

The application is as follows: the proposed evidence Wasserstein distance algorithm is a core algorithm for component identification in the component identification industry. The composition of each element can be identified by the online composition detection device built by the composition detection system.

Compared with the prior art, the invention provides the application of the evidence Wasserstein distance algorithm in component identification, and has the following beneficial effects:

the invention firstly proposes Evidence Wasserstein Distance (EWD) to measure the distance between BBAs;

the proposed EWD strictly meets the boundedness requirement of a conflict coefficient, and has the ideal characteristics of nonnegativity, nondegeneration, symmetry, boundedness and the like, so that the EWD can produce more specific and intuitive results when solving the situation of high conflict;

aiming at the distance measurement problem in the D-S evidence theory, a new distance measurement algorithm is provided, and the fact that a more reasonable conclusion can be obtained under the condition of high conflict is proved, so that the defect that the D-S evidence theory cannot obtain persuasion is overcome. Results under extreme conditions. The provided method ensures good characteristics such as symmetry, nonnegativity, non-degeneration and boundary, and the innovation point is that the Wasserstein distance and the Dang entropy are combined for the first time, an evidence theory is introduced, the introduction of the Wasserstein distance and the Deng entropy enables the evidence distance to have the capacity of distributing high conflict factors when measuring conflicts, so that the original attributes of the evidence are well preserved, the possibility of generating confusing results is reduced, and finally, practice and practical application can prove the superiority of the EWD method.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention without limiting the invention in which:

FIG. 1 is a flowchart of an evidence Wasserstein distance algorithm proposed by the present invention;

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1, the present invention provides a technical solution:

wherein F1 and F2 are subsets of Θ, and

2) the proposed EWD represents the distance between two evidentiary bodies. The larger the value obtained, the lower the correlation between the two evidential bodies, and the smaller the value, the higher the correlation between the two evidential bodies. And by correlation it can be concluded that the value of the EWD method is less if the relationship between the two evidences is closer and vice versa. But due to bounded limitations the maximum cannot exceed 1 and the minimum cannot be less than 0, which has the following properties in general:

(1) non-negative number: EWD (m) ₁ ,m ₂ )≥0。

(2) Non-degeneration:

(3) symmetry: EWD (m) ₂ ,m ₁ )＝EWD(m ₁ ,m ₂ )

(4) The characteristics of the bounding: 0. ltoreq. EWD (m) ₁ ,m ₂ )≤1。

The following applies: the proposed evidence Wasserstein distance algorithm is a core algorithm for component identification in the component identification industry. The composition of each element can be identified by the online composition detection device built by the composition detection system.

Examples

Taking the wine dataset as an example, there are 3 wine varieties, 13 different attributes, and the resulting 45 BBAs are shown in table 6. We need to determine the origin of the sample from the sample provided and compare it with other methods to draw conclusions.

Table 1 BBA generated from wine sample dataset

Table 2 shows the results of our determination of the origin of the sample using four methods. As can be seen from Table 2, the confusion of results caused by the classical D-S evidence theory rules directly determines that the experimental results are completely b-type. The simple judgment is too absolute, and the influence of high conflict factors on the experimental result is not considered. The Yagers method is also unsatisfactory. First, it is clear that it is too much concerned about the mixing result (i.e. m (a, b, c)), and it is not possible to accurately determine the exact source of the sample. Secondly, the support degree of the method to the variety b type is not more than half of 0.4371, and the conclusion that the support degree to the variety b type is extremely weak is obtained. Specifically, the support degree of m (a, b, c) is 0.337, and the support degree of m (a, b, c) is 0.1001 more than that of m (b). The results are not convincing. The EWD method supports type b more than the rules of dune et al, not only to draw an accurate conclusion, but also not to deny the contribution of type a and type c. The test sample belongs to the type b species. The method provided by the invention also considers the influence of high conflict factors on the experiment under the condition of accurate conclusion, so that the result analysis is more comprehensive and reliable. In conclusion, the new process EWD has clear advantages.

Table 2 comparison of several methods

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims

1. The application of the evidence Wasserstein distance algorithm in component identification is characterized in that: the Wasserstein distance is EWD, and the EWD is verified by the following method:

wherein F1 and F2 are subsets of Θ, and

2. Use of the evidence Wasserstein distance algorithm according to claim 1 for component discrimination, characterized in that: the application is as follows: the proposed evidence Wasserstein distance algorithm is a core algorithm for component identification in the component identification industry. The composition of each element can be identified by the online composition detection device built by the composition detection system.