CN-121980454-A - Entropy based on fuzzy beta-coverage relation and anomaly detection method thereof

CN121980454ACN 121980454 ACN121980454 ACN 121980454ACN-121980454-A

Abstract

The invention belongs to the technical field of data anomaly detection, and particularly relates to entropy based on a fuzzy beta-coverage relation and an anomaly detection method thereof, comprising the following steps that step 1, a method for migrating a traditional fuzzy beta-neighborhood operator into a variable-scale fuzzy beta-coverage approximate space is provided; step 2, two parameterization fuzzy beta-co-neighborhoods are proposed, step 3, a fuzzy beta-coverage relation and fuzzy beta-coverage information granule based on the fuzzy beta-co-neighborhoods are proposed, step 4, a fuzzy beta-coverage entropy and a fuzzy beta-coverage relative entropy are proposed, step 5, a fuzzy beta-coverage relative entropy and a weight function based on a sequence are proposed, step 6, an anomaly score is constructed based on the contents of steps 1 to 5, an anomaly detection method based on the fuzzy beta-coverage entropy is proposed, and an anomaly sample obtained through detection is output according to an input information table. The invention not only expands the application of the fuzzy beta-coverage rough set theory in the field of anomaly detection, but also makes up the defect of the traditional method when processing the data existing in the coverage form.

Inventors

ZHANG XIAOHONG
FAN YAOYAO
WANG JINGQIAN

Assignees

陕西科技大学

Dates

Publication Date: 20260505
Application Date: 20260119

Claims (8)

1. The entropy and the abnormality detection method based on the fuzzy beta-coverage relation are characterized by comprising the following steps: Step 1, a method for migrating a traditional fuzzy beta-neighborhood operator into a variable-scale fuzzy beta-coverage approximate space is proposed; step 2, two parameterized fuzzy beta-co-neighborhood are proposed; step 3, providing a fuzzy beta-coverage relation and fuzzy beta-coverage information particles based on a fuzzy beta-co-neighborhood; step 4, providing fuzzy beta-coverage entropy and fuzzy beta-coverage relative entropy; Step 5, providing a fuzzy beta-coverage relative entropy and a weight function based on the sequence; And 6, constructing an anomaly score based on the contents of the steps 1 to 5, providing an anomaly detection method based on fuzzy beta-coverage entropy, obtaining output according to an input information table, and outputting a detected anomaly sample.
2. The entropy and anomaly detection method based on fuzzy beta-coverage relation of claim 1, wherein in step 1: The design definition is a design Is a non-empty talk domain which is not a empty talk domain, Representing the domain of discussion The set of the whole fuzzy sets, if the fuzzy set families ( , ) Satisfy that for arbitrary And All have Then call it For the domain of discussion The blurred beta-coverage of the upper part, Approximating space for ambiguous β -coverage; In addition, set up Representing non-empty index sets, if Is a blurred beta-coverage of the object, Wherein the method comprises the steps of Is a blur -Cover ) Then call it Covering an approximate space for the variable-scale blur beta-coverage; the upscaled blurred β -coverage approximation space is a reasonable generalization of the blurred β -coverage approximation space, in particular for any given upscaled blurred β -coverage approximation space If for all All satisfy Then the variable-scale blurred beta-coverage approximation space Approximation of space with a blurred beta-coverage Equivalently, at this point, In (3) blur Covering of Satisfy the following requirements The fuzzy beta-neighborhood operator defined in the variable-scale fuzzy beta-coverage approximation space is directly applied to the fuzzy beta-coverage approximation space, otherwise, if the fuzzy beta-neighborhood operator defined in the fuzzy beta-coverage approximation space is applied to the variable-scale fuzzy beta-coverage approximation space, the fuzzy is applied to the variable-scale fuzzy beta-coverage approximation space Covering of Seen as a blur Covering of Based on the method, the mutual conversion is realized between a fuzzy beta-neighborhood operator defined on a fuzzy beta-coverage approximate space and a fuzzy beta-neighborhood operator defined on a variable-scale fuzzy beta-coverage approximate space.
3. The entropy and anomaly detection method based on fuzzy beta-coverage relation of claim 2, wherein in step 2: Set definition two, set Is a variable-scale blurred beta-coverage approximation space, Is a function of the overlap of the two, Is a grouping function, for any Definition of Is a parameterized fuzzy beta-co-neighborhood And The method comprises the following steps: ; ; Wherein the method comprises the steps of And (3) ; 。
4. The entropy and anomaly detection method thereof based on fuzzy beta-coverage relation of claim 3, wherein in step 3: design definition III Is a variable-scale blurred beta-coverage approximation space, To any one Definition of class I fuzzy beta-coverage relation The method comprises the following steps: ; Set definition four Is a variable-scale blurred beta-coverage approximation space, and To any one of Definition of the relation covered by ambiguous beta Domain of theory of induction generation The structure of the fuzzy beta-coverage particle is as follows: , Wherein the method comprises the steps of Is based on fuzzy beta-coverage relation Generating fuzzy beta-coverage information grain, deriving a grain structure by a fuzzy beta-coverage relation, and Is defined as the domain of theory Fuzzy set of the upper part meets the following conditions The calculation formula of the fuzzy information grain base is Obviously have 。
5. The entropy and anomaly detection method based on fuzzy beta-coverage relation of claim 4, wherein in step 4: five-definition of setting Is a variable-scale blurred beta-coverage approximation space, and Definition of the definition The fuzzy beta-coverage entropy of (2) is: ; For any one Definition of The fuzzy β -coverage relative entropy of (2) is: ; Wherein the method comprises the steps of Representing the slave Remove samples from Rear part (S) Is used to determine the fuzzy beta-coverage entropy.
6. The entropy and anomaly detection method based on fuzzy beta-coverage relation of claim 5, wherein in step 5: Definition of the design six An approximation space is covered for a variable-scale blur beta-cover, defining attribute sequences as Wherein , Defining the attribute subset sequence as Wherein , , And (2) and , ; Definition of the device Is a variable-scale blurred beta-coverage approximation space, and For any one , And Definition of The fuzzy beta-coverage relative entropy and the weight function based on the sequence are respectively as follows: ; Wherein the method comprises the steps of Representation adopts the first Fuzzy-like beta-coverage relation Is used for the fuzzy beta-coverage entropy of (c), Is a sample With respect to attributes Is a fuzzy beta-coverage relative entropy of (c), Is a sample With respect to attribute subsets Is of (2) ambiguous beta-coverage cover relative entropy.
7. The entropy and anomaly detection method thereof based on fuzzy beta-coverage relation of claim 6, wherein in step 6: Definition of the device For a variable-scale blurred beta-coverage approximation space, define The anomaly score of (2) is: ; input of input information sheet Outputting the detected abnormal sample.
8. The method for detecting entropy and abnormality thereof based on fuzzy beta-coverage relation of claim 7, wherein the implementation of step 6 comprises: Step 61, inducing variable-scale fuzzy beta-coverage approximate space, in the pretreatment stage, all data are represented as different integers, and all attribute values are normalized to [0,1] interval by means of minimum-maximum normalization method, and at this time the obtained information table Approximation space for a variable-scale blurred beta-coverage Wherein ; Step 62, calculate all In a single attribute Is a fuzzy beta-coverage relative entropy of (c), Step 63, calculating an attribute sequence AS and an attribute subset sequence ASS; step 64, calculate all In attribute subset Is a fuzzy beta-coverage relative entropy of (c), Step 65, calculating the anomaly score to obtain an anomaly sample set Wherein An abnormal sample threshold set for an expert.

Description

Entropy based on fuzzy beta-coverage relation and anomaly detection method thereof Technical Field The invention belongs to the technical field of data anomaly detection, and particularly relates to entropy based on a fuzzy beta-coverage relation and an anomaly detection method thereof. Background The core goal of anomaly detection is to identify anomaly data in a dataset that differs significantly from most samples, so how to measure the degree of anomalies in the samples in the data is very important. Coarse entropy is an uncertainty measure based on coarse set theory, and is used to characterize the ability of a subset of attributes to distinguish samples, and is therefore often used in anomaly detection tasks. However, the classical rough set relies on binary equivalence relations to divide the sample set, which makes it difficult to effectively characterize large amounts of data in real world in overlay form. For this reason, coverage asperities were proposed by Zakowski in the 80 s of the 20 th century, which is an important extension of the Pawlak asperity theory. Unlike Pawlak asperities which rely strictly on equivalence relations, overlay asperities relax equivalence relations to a common overlay structure, allowing overlap between sets without ensuring that each element belongs to only a single set. This structural design significantly enhances the classification flexibility of the model, and is particularly applicable to incomplete data in which one or more attribute values of a sample are lost. However, both models can only process nominal data, i.e. discrete data, resulting in a discretization process that must be performed when processing continuous data, resulting in significant information loss. To overcome this limitation, dubois et al and Deng et al extended Pawlak and overlay asperities to fuzzy asperities and fuzzy overlay asperities, respectively, based on the fuzzy set theory of Zadeh. Because the advantages of the rough set theory and the fuzzy set theory are combined, the models can reduce information loss in data processing to the greatest extent, become important mathematical tools for processing uncertainty and incomplete information, and are widely applied to practical application scenes such as feature selection, language knowledge acquisition, decision making and the like. In view of the definition of the ambiguous coverage being too strict, ma creatively replaces "1" in the definition of the ambiguous coverage with a parameter β (0 < β < 1), generalizes the ambiguous coverage, and obtains the definition of the ambiguous β -coverage. In fact, when β=1, the blurred β -coverage is a blurred coverage. Therefore, not only is the fuzzy coverage extended from one of the theoretical aspects, but the capability of solving the actual problem of the fuzzy coverage rough set is improved. In general, the fuzzy coverage coarse set is the fuzzification of the coverage coarse set and the popularization of the fuzzy coarse set in theory, the fuzzy coverage is a family of fuzzy subsets meeting specific conditions obtained by replacing the classical set with the fuzzy set, and the limitation of the coarse set theory in theory and application is skillfully overcome. Therefore, on the basis of the fuzzy beta-coverage rough set theory, a novel rough entropy construction method based on the fuzzy beta-coverage relation is provided and is applied to abnormal sample detection tasks. Disclosure of Invention The invention aims at dividing a sample set according to the prior rough entropy dependency binary equivalence relation, is only suitable for nominal data, is difficult to effectively describe a large amount of data existing in a coverage form, and provides a new solution idea. Firstly, a traditional method for spreading a fuzzy beta-neighborhood operator to a variable-scale fuzzy beta-coverage approximate space is provided, and on the basis, a fuzzy beta-coverage relation based on a fuzzy beta-co-neighborhood is constructed, so that the differential characteristics among samples can be depicted from a reverse view angle, and the requirements of an abnormality detection task are met. Further, a fuzzy beta-coverage entropy and a fuzzy beta-coverage relative entropy are provided, and an anomaly detection method is designed according to the fuzzy beta-coverage entropy and the fuzzy beta-coverage relative entropy. Experiments carried out on 10 data sets from different fields show that compared with the existing 7 anomaly detection methods, the method has obvious advantages, and can effectively detect the anomaly samples in the data. The invention not only expands the application of the fuzzy beta-coverage rough set theory in the field of anomaly detection, but also effectively makes up the defect of the traditional method in processing the data existing in the coverage form, and provides reliable technical support for the actual application scene. The technical scheme adopted by the invention is as fol