Attribute reduction method, device and equipment based on neighborhood separability and storage medium

Abstract

The invention discloses an attribute reduction method and device based on neighborhood separability, equipment and a storage medium. The method comprises the following steps: determining dual-neighborhood information grains of each object based on a decision attribute set; based on the dual-neighborhood information particles of each object and the to-be-optimized attribute weight matrix, quantifying the internal aggregation degree and the external dispersion degree of the universe about the condition attribute set; and constructing an objective function based on the internal polymerization degree and the external dispersion degree, and solving the objective function to perform attribute reduction. The local structure information of the object is fully utilized, the internal aggregation degree and the external dispersion degree of the discourse domain about the condition attribute set are quantified, and the target function is established by combining the internal aggregation degree and the external dispersion degree, so that the problem that in the feature selection process, the feature selection efficiency is high is solved. The problem of low algorithm efficiency caused by repeatedly calculating various binary relationships or information particles and selecting attributes one by one is solved, the calculation efficiency of feature selection is improved, and the calculation efficiency of machine learning is further improved.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to an attribute simplification method, device, equipment and storage medium based on neighborhood separability. Background Art

[0002] With the continuous accumulation of high-dimensional data (such as multimedia images and videos, aerospace data, biometrics, financial time series, etc.), feature selection has become an important preprocessing step in machine learning, data mining, and pattern recognition. Among them, attribute reduction, as a method of dealing with data uncertainty, can delete redundant features, thereby reducing computing and storage overhead, while improving machine learning efficiency. It is widely used as a feature selection method in data mining, pattern recognition, machine learning and other fields.

[0003] Attribute reduction is the process of deleting irrelevant or unimportant conditional attributes in the original conditional attribute set while maintaining the classification ability of the knowledge base. The classification ability of a knowledge base is usually based on the basic information granules under the conditional attribute set and the decision class under the decision attribute set, and is quantified by metrics such as the positive domain, dependency, entropy, and identification relationship of the conditional attribute set with respect to the decision attribute set. However, the existing attribute reduction requires repeated calculation of various binary relations or information granules during the search process, and attributes are selected or deleted one by one, making the calculation of attribute reduction very time-consuming. This greatly limits the computational efficiency and application scope of the attribute reduction method, affects the efficiency of feature selection, and further affects the efficiency of machine learning.

[0004] Therefore the prior art still needs to be improved and enhanced. Summary of the invention

[0005] The technical problem to be solved by the present application is to provide an attribute simplification method, device, equipment and storage medium based on neighborhood separability in view of the deficiencies of the prior art.

[0006] In order to solve the above technical problems, the first aspect of the present application provides an attribute reduction method based on neighborhood separability, wherein the attribute reduction method based on neighborhood separability specifically includes:

[0007] Acquire object data, and establish a decision table based on the acquired object data, wherein the decision table includes a domain, a condition attribute set for describing object characteristics, and a decision attribute set for describing category information of the object;

[0008] Determine a dual neighborhood information granule for each object in the decision table based on the decision attribute set, wherein the dual neighborhood information granule includes an internal neighborhood information granule and an external neighborhood information granule;

[0009] Based on the dual-neighborhood information granules and the attribute weight matrix to be optimized, the internal aggregation degree and external dispersion degree of the domain with respect to the conditional attribute set are quantified;

[0010] Constructing an objective function for the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree, and solving the objective function to obtain a target attribute weight matrix;

[0011] The attributes of the decision table are simplified based on the target attribute weight matrix to obtain a simplified decision table.

[0012] The attribute reduction method based on neighborhood separability, wherein the determining of the double neighborhood information granules of each object in the decision table based on the decision attribute set specifically includes:

[0013] Calculate the distance measure between each two objects in the decision table under the condition attribute set to obtain a distance measure set;

[0014] Based on the decision attribute set, determining a first object set and a second object set for each object, wherein the first object set for each object includes all in-class objects of each object, and the second object set for each object includes all inter-class objects of each object;

[0015] Determine the internal neighborhood information granules of each object based on the first object set and the distance measurement set of each object;

[0016] Based on the second object set and the distance metric set of each object, an external neighborhood information granule of each object is determined.

[0017] The attribute reduction method based on neighborhood separability, wherein the internal aggregation and external dispersion of the domain of the conditional attribute set based on the dual neighborhood information granules and the attribute weight matrix to be optimized are specifically comprised of:

[0018] Quantifying the local internal aggregation degree of each object with respect to the conditional attribute set based on the internal neighborhood information granules of each object and the attribute weight matrix to be optimized, and quantifying the internal aggregation degree of the domain with respect to the conditional attribute set based on the local internal aggregation degree of each object and the attribute weight matrix to be optimized;

[0019] The local external dispersion of each object with respect to the conditional attribute set is quantified based on the external neighborhood information granules of each object and the attribute weight matrix to be optimized, and the external dispersion of the domain with respect to the conditional attribute set is quantified based on the local external dispersion of each object and the attribute weight matrix to be optimized.

[0020] The attribute reduction method based on neighborhood separability, wherein constructing an objective function for the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree specifically includes:

[0021] Determining a balance factor based on the internal aggregation degree and the external dispersion degree, wherein the balance factor is used to reflect the importance of the internal aggregation degree and the external dispersion degree under the conditional attribute set;

[0022] Constructing an objective function for a weight matrix of attributes to be optimized based on the balance factor, the internal aggregation degree, and the external dispersion degree;

[0023] Wherein, the objective function is expressed as:

[0024] f(W)=β*IA(U)-(1-β)*ED(U)

[0025] Among them, f(W) represents the objective function, W represents the weight matrix of the attributes to be optimized, IA(U) represents the internal aggregation of the domain with respect to the conditional attribute set, ED(U) represents the external dispersion of the domain with respect to the conditional attribute set, and β represents the balance factor.

[0026] The attribute reduction method based on neighborhood separability, wherein the expression of the balance factor is:

[0027]

[0028] Among them, β represents the balance factor, IA I (U) represents the internal aggregation degree of the domain with respect to the conditional attribute set when the attribute weight matrix to be optimized takes the identity matrix, ED I (U) represents the external dispersion of the domain with respect to the conditional attribute set when the attribute weight matrix to be optimized takes the identity matrix.

[0029] The attribute simplification method based on neighborhood separability, wherein the attribute simplification of the decision table based on the target attribute weight matrix to obtain the simplified decision table specifically includes:

[0030] Build several classifiers;

[0031] Selecting a number of conditional attributes from the conditional attribute set based on the target attribute weight matrix to obtain a candidate conditional attribute set;

[0032] Perform classification performance testing on several classifiers based on the candidate condition attribute set to obtain a test result;

[0033] The decision table is attribute-reduced based on the detection result to obtain a reduced decision table.

[0034] The classification performance test of several classifiers based on the candidate condition attribute set is performed to obtain the test results, which specifically include:

[0035] Divide the data set corresponding to the domain into a training data set and a validation data set;

[0036] Several classifiers are trained based on the candidate condition attribute set on the training data set, and the classification accuracy of several classifiers trained with the training data set is verified through the verification data set to obtain the detection results.

[0037] The second aspect of the present application provides an attribute simplification device based on neighborhood separability, wherein the attribute simplification device based on neighborhood separability specifically includes:

[0038] An acquisition module, used for acquiring object data, and establishing a decision table based on the acquired object data, wherein the decision table includes a domain, a conditional attribute set for describing object characteristics, and a decision attribute set for describing category information of the object;

[0039] A determination module, configured to determine a dual-neighborhood information granule of each object in the decision table based on the decision attribute set, wherein the dual-neighborhood information granule comprises an internal neighborhood information granule and an external neighborhood information granule;

[0040] A quantification module, used for quantifying the internal aggregation and external dispersion of the domain with respect to the conditional attribute set based on the dual-neighborhood information granules and the attribute weight matrix to be optimized;

[0041] A construction module, used to construct an objective function about the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree, and solve the objective function to obtain a target attribute weight matrix;

[0042] The simplification module is used to simplify the attributes of the decision table based on the target attribute weight matrix to obtain a simplified decision table.

[0043] A third aspect of the present application provides a computer-readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the steps in any of the attribute reduction methods based on neighborhood separability as described above.

[0044] A fourth aspect of the present application provides a terminal device, comprising: a processor and a memory;

[0045] The memory stores a computer-readable program executable by the processor;

[0046] When the processor executes the computer-readable program, the processor implements the steps in any of the above-mentioned attribute reduction methods based on neighborhood separability.

[0047] Beneficial effects:

[0048] 1. The internal aggregation and external dispersion of all objects with respect to the conditional attribute set are quantified by the local aggregation of objects within a class and the local dispersion of objects between classes, which makes full use of the local structural information of the objects, thus better describing the spatial structural relationship between objects.

[0049] 2. Combine the internal aggregation and external dispersion to establish the objective function of attribute importance. By solving the objective function, the target attribute weight matrix that can well reflect the importance of each conditional attribute is determined. Then, the attribute weight matrix is ​​used to simplify the attributes, avoiding the problem of low calculation rate caused by selecting attributes one by one, and improving the computational efficiency of machine learning. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0051] Figure 1 A flowchart of an attribute reduction method based on neighborhood separability provided in an embodiment of the present application.

[0052] Figure 2 FIG. 4 is a flowchart of an example of step S20 .

[0053] Figure 3 A flowchart of an attribute simplification device based on neighborhood separability provided in an embodiment of the present application.

[0054] Figure 4 A functional block diagram of a terminal device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0055] The embodiments of the present application provide an attribute simplification method, device, equipment and storage medium based on neighborhood separability. In order to make the purpose, technical solution and effect of the present application clearer and more specific, the present application is further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0056] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present application refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be an intermediate element. In addition, the "connection" or "coupling" used herein may include wireless connection or wireless coupling. The term "and / or" used herein includes all or any unit and all combinations of one or more associated listed items.

[0057] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with those in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless specifically defined as here.

[0058] It should be understood that the sequence numbers and sizes of the steps in this embodiment do not mean the order of execution. The execution order of each process is determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present application.

[0059] After research, it was found that with the continuous accumulation of high-dimensional data (such as multimedia images and videos, aerospace data, biometrics, financial time series, etc.), feature selection has become an important preprocessing step in machine learning, data mining, and pattern recognition. Among them, attribute reduction, as a method of dealing with data uncertainty, can delete redundant features, thereby reducing computing and storage overhead, while improving machine learning efficiency. It is widely used as a feature selection method in data mining, pattern recognition, machine learning and other fields.

[0060] Attribute reduction is the process of deleting irrelevant or unimportant conditional attributes in the original conditional attribute set while maintaining the classification ability of the knowledge base. The classification ability of a knowledge base is usually based on the basic information granules under the conditional attribute set and the decision class under the decision attribute set, and is quantified by metrics such as the positive domain, dependency, entropy, and identification relationship of the conditional attribute set with respect to the decision attribute set. However, the existing attribute reduction requires repeated calculation of various binary relations or information granules during the search process, and attributes are selected or deleted one by one, making the calculation of attribute reduction very time-consuming. This greatly limits the computational efficiency and application scope of the attribute reduction method, affects the efficiency of feature selection, and further affects the efficiency of machine learning.

[0061] In order to solve the above problems, in an embodiment of the present application, object data is obtained, and a decision table is established based on the obtained object data; dual-neighborhood information granules of each object in the decision table are determined based on the decision attribute set; the internal aggregation and external dispersion of the domain with respect to the conditional attribute set are quantified based on the dual-neighborhood information granules and the attribute weight matrix to be optimized; an objective function with respect to the attribute weight matrix to be optimized is constructed based on the internal aggregation and external dispersion, and the objective function is solved to obtain the target attribute weight matrix; and the decision table is attribute simplified based on the target attribute weight matrix to obtain a simplified decision table. The embodiment of the present application first makes full use of the local structural information of the object, quantifies the internal aggregation and external dispersion of all objects with respect to the conditional attribute set, and then combines the internal aggregation and external dispersion to establish an objective function with respect to the attribute matrix for attribute importance, and finally performs attribute simplification according to the target attribute matrix determined by solving the objective function, thereby solving the problem of low algorithm efficiency caused by repeated calculation of each binary relationship or information granule and selecting attributes one by one in the feature selection process, improving the computational efficiency of feature selection, and further improving the computational efficiency of machine learning.

[0062] The application content is further explained below through the description of embodiments in conjunction with the accompanying drawings.

[0063] This embodiment provides an attribute reduction method based on neighborhood separability, such as Figure 1 As shown, the method includes:

[0064] S10: Obtain object data, and establish a decision table based on the obtained object data.

[0065] Specifically, the object data may be data used for data mining, pattern recognition, and machine learning. For example, the object data may be power data, identity object data of credit card applicants, etc. The decision table is established based on the acquired object data, wherein the decision table is the object data stored in the form of an information table, each row in the decision table represents the value of an object in the object data under the feature of interest, and each column represents the value of all objects under a certain feature. For example, the object data is the identity object data of the credit card applicant required for the evaluation problem of the credit card applicant. Each row in the decision table represents the credit card applicant, and each column represents the value of all applicants under the feature of interest (such as the applicant's age, education level, income status, debt status, credit status, etc.).

[0066] The decision table includes an object set (denoted as a domain), a conditional attribute set for describing the characteristics of the object, and a decision attribute set for describing the category information of the object. Accordingly, the decision table can be expressed as DS = (U, C, D), where DS represents the decision table, U = {x 1 ,x 2 ,Λ,x i ,Λ,x m} represents the domain (i.e., the object set), m represents the number of objects, C = {a 1 ,a 2 ,Λ,a j ,Λ,a n} represents the conditional attribute set, n represents the number of conditional attributes, D={d 1 ,d 2 ,Λ,d l ,Λ,d r} represents the decision attribute set, and r represents the number of categories.

[0067] S20. Determine the dual-neighborhood information granules of each object in the decision table based on the decision attribute set.

[0068] Specifically, the dual-neighborhood information granules include internal neighborhood information granules and external neighborhood information granules, the internal neighborhood information granules are used to reflect the similarity between objects within a class, and the external neighborhood information granules are used to reflect the similarity between objects between classes, wherein the similarity can be determined based on the distance information between objects, or based on the cosine similarity between objects, etc.

[0069] For example, Figure 2 As shown, the determining of the dual-neighborhood information granules of each object in the decision table based on the decision attribute set specifically includes:

[0070] S21, respectively calculating the distance measure between each two objects in the decision table under the condition attribute set to obtain a distance measure set;

[0071] S22, determining a first object set and a second object set for each object based on the decision attribute set;

[0072] S23, determining the internal neighborhood information granules of each object based on the first object set and the distance measurement set of each object;

[0073] S24. Based on the second object set and the distance measurement set of each object, determine the external neighborhood information granules of each object.

[0074] Specifically, in step S21, the distance metric set includes the distance metric between any two objects in the decision table. That is, when determining the distance metric set, the distance metric between any two objects in the decision table under the conditional attribute set is calculated respectively. The calculation formula for the distance metric between any two objects under the conditional attribute set can be:

[0075]

[0076] Among them, d W (x, y) represents the distance measure between object x and object y under the conditional attribute set. Represent the feature vectors of objects x and y respectively, which are n-dimensional row vectors; W represents the attribute weight matrix to be optimized, which is an n-order real diagonal matrix. The i-th element w on the main diagonal of W is ii Indicates conditional attribute a i Regarding the importance of decision attributes; T represents the transpose of the matrix; n represents the number of conditional attributes in the conditional attribute set.

[0077] It should be noted that in practical applications, the distance measurement between two objects can also be calculated using other methods. For example, The Euclidean distance of is used as the distance metric of objects x and y, or The cosine similarity is used as the distance metric of x, y, etc.

[0078] Further, in step S22, the first object set and the second object set are both included in the decision table, and the first object set of each object includes all the intra-class objects of each object, and the second object set of each object includes all the inter-class objects of each object. That is, the objects in the first object set of each object have the same category information as the object, and the objects in the second object set corresponding to each object have different category information from the object. Specifically, when determining the first object set and the second object set of each object, the category information of each object can be obtained first, and then other objects with the same category information can be selected in the domain according to the category information to form a first object set, and then the set consisting of all the unselected objects can be used as the second object set of the object. Of course, all the objects in the decision table can also be divided according to the category information to obtain a number of object groups, each object group corresponds to a category information, and then for each object, the object group corresponding to its category information is used as its corresponding first object set, and the set consisting of the object groups corresponding to other category information is used as its corresponding second object set.

[0079] For example: Assuming that the values ​​of the decision attributes in the decision table include cats, dogs, and rabbits, then when the category information of the object is cat, the set consisting of all objects with the category information of cat is taken as the first object set corresponding to cat, and then the set consisting of all objects with the category information of dog and rabbit is taken as the second object set corresponding to cat. In other words, when an object is a cat, the first object set of the object includes all cats in the domain, and the second object set of the object includes all dogs and all rabbits in the domain.

[0080] Further, in step S23, after obtaining the first object set of the object, some neighboring objects of the object are selected from the first object set according to the distance metric set to obtain the internal neighborhood information granules of the object, that is, the internal neighborhood information granules include several neighboring objects of the same category as the object. Accordingly, the internal neighborhood information granules can be expressed as:

[0081] IG(x)={y|y∈K(x,[x] D )}

[0082] Among them, IG(x) represents the internal neighborhood information granule of object x about the conditional attribute set C, [x] D ={y|D(x)=D(y), y∈U} represents the first object set, K(x, ) represents the set of k neighboring objects in the set · (such as the first object set) and the object x under the distance metric, D(x) represents the category information of the object x, and D(y) represents the category information of the object y.

[0083] Further, in step S24, after obtaining the second object set of the object, some objects are selected from the second object set according to the distance metric set to obtain the external neighborhood information granules of the object, that is, the external neighborhood information granules include several neighboring objects of different categories from the object. Accordingly, the external neighborhood information granules can be expressed as:

[0084]

[0085] Among them, EG(x) represents the external neighborhood information granule of object x about the conditional attribute set C, Represents the second object set, which is [x] D Regarding the complement of the domain U, K(x,·) represents the set consisting of k neighboring objects in the set · (such as the second object set) and the object x under the distance metric, and z represents the object.

[0086] It should be noted that when determining the internal neighborhood information granules and the external neighborhood information granules of each object, the attribute weight matrix to be optimized when calculating the distance metric set can use the unit matrix, or, use other preset default weight matrices. In an embodiment of the present application, the attribute weight matrix to be optimized when calculating the distance metric set uses the unit matrix.

[0087] S30, quantifying the internal aggregation degree and external dispersion degree of the domain with respect to the conditional attribute set based on the dual-neighborhood information granules and the attribute weight matrix to be optimized.

[0088] Specifically, the internal aggregation degree is used to reflect the distribution concentration of objects within a class, and the external dispersion degree is used to reflect the distribution dispersion of objects between classes. The smaller the internal aggregation degree of the domain with respect to the conditional attribute set, the greater the distribution concentration of objects within the class, that is, the more concentrated the distribution of objects within the class is; the greater the external dispersion degree of the domain with respect to the conditional attribute set, the greater the distribution dispersion of objects between classes, that is, the more dispersed the distribution of objects between classes is. At the same time, the neighborhood separability of the domain with respect to the conditional attribute set can also be reflected through the internal aggregation degree and the external dispersion degree. The smaller the internal aggregation degree and the greater the external dispersion degree, the greater the neighborhood separability of the domain with respect to the conditional attribute set is.

[0089] Furthermore, the internal aggregation is the global internal aggregation of the domain, which includes the local internal aggregation of each object with respect to the conditional attribute set, and the external dispersion is the global external dispersion of the domain, which includes the local external dispersion of each object with respect to the conditional attribute set. In other words, the internal aggregation and external dispersion are characterized from the local and global levels, respectively. From the local level, the local internal aggregation of a single object with respect to the conditional attribute set is characterized by the distance measurement between the object and all objects in its internal neighborhood information granules; the local external dispersion of a single object with respect to the conditional attribute set is characterized by the distance measurement between the object and all objects in its external neighborhood information granules. From the global level, the internal aggregation of the domain with respect to the conditional attribute set is characterized by the internal aggregation of all objects with respect to the conditional attribute set; the external dispersion of the domain with respect to the conditional attribute set is characterized by the external dispersion of all objects with respect to the conditional attribute set.

[0090] Exemplarily, the internal aggregation degree and external dispersion degree of the domain of quantification about the conditional attribute set based on the dual-neighborhood information granules and the attribute weight matrix to be optimized specifically include:

[0091] Quantifying the local internal aggregation degree of each object with respect to the conditional attribute set based on the internal neighborhood information granules of each object and the attribute weight matrix to be optimized, and quantifying the internal aggregation degree of the domain with respect to the conditional attribute set based on the local internal aggregation degree of each object and the attribute weight matrix to be optimized;

[0092] The local external dispersion of each object with respect to the conditional attribute set is quantified based on the external neighborhood information granules of each object and the attribute weight matrix to be optimized, and the external dispersion of the domain with respect to the conditional attribute set is quantified based on the local external dispersion of each object and the attribute weight matrix to be optimized.

[0093] Specifically, the local internal aggregation degree IA(x) and local external dispersion degree ED(x) of any object x in the domain U under the conditional attribute set C can be expressed as:

[0094]

[0095] Among them, IG(x) represents the internal neighborhood information granule of object x with respect to conditional attribute set C, and EG(x) represents the external neighborhood information granule of object x with respect to conditional attribute set C. Represents the square of the distance between objects x and y under the conditional attribute set C. represents the self matrix, which is composed of the eigenvectors of k objects x A real matrix of order k×n concatenated by rows; represents the aggregation matrix, which is a real matrix of order k×n formed by concatenating the feature vectors of k objects in the internal neighborhood information granules of object x in rows; represents the divergence matrix, which is a real matrix of order k×n formed by concatenating the feature vectors of k objects in the external neighborhood information granules of object x in rows. W represents the attribute weight matrix to be optimized, which is a real diagonal matrix of order n. It represents the square of the Frobenius norm of the matrix, that is, the sum of the squares of all elements in the matrix.

[0096] By converting the calculation formulas of local internal aggregation degree IA(x) and local external dispersion degree ED(x) into matrix calculation expressions, the present application can further improve the calculation efficiency of internal aggregation degree and external dispersion degree, thereby improving the efficiency of attribute simplification, thereby improving the processing efficiency of the problem to be processed.

[0097] Furthermore, after obtaining the local internal aggregation and local external dispersion of each object, the internal aggregation and external dispersion of the domain with respect to the conditional attribute set are quantified based on the local internal aggregation and local external dispersion of all objects. Among them, the internal aggregation IA(U) and external dispersion ED(U) of the domain U under the conditional attribute set C can be expressed as:

[0098]

[0099] Among them, IA(U) represents the internal aggregation degree of the domain U under the conditional attribute set C, and ED(U) represents the external dispersion degree of the domain U under the conditional attribute set C. represents the self-matrix of the domain, which is a real matrix of order mk×n formed by concatenating the self-matrices of m objects in the object set row by row; represents the domain aggregation matrix, which is a real matrix of order mk×n formed by concatenating the aggregation matrices of m objects row by row; represents the domain divergence matrix, which is a real matrix of order mk×n formed by concatenating the divergence matrices of m objects row by row; Represents the square of the Frobenius norm of the matrix, that is, the sum of the squares of all elements in the matrix.

[0100] S40: constructing an objective function for the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree, and solving the objective function to obtain a target attribute weight matrix.

[0101] Specifically, the weight matrix of the attribute to be optimized includes the quantification of the importance of each conditional attribute, where importance refers to the role played by the conditional attribute in decision making. Internal aggregation and external dispersion are the internal aggregation and external dispersion of the domain with respect to the conditional attribute set, both of which are functions of the weight matrix of the attribute to be optimized. Therefore, the objective function of the weight matrix of the attribute to be optimized can be constructed based on the internal aggregation and external dispersion, and then the target attribute weight matrix can be obtained by solving the objective function. In other words, the difference between the internal aggregation and the external dispersion can be directly used as the objective function, etc.

[0102] Furthermore, since the internal aggregation degree of the domain in actual use is generally smaller than the external dispersion, when constructing the objective function, the internal aggregation degree and the external dispersion can be balanced first, and then the objective function can be constructed so that based on the objective function, the parameters that maximize the neighborhood separability of the domain with respect to the conditional attribute set can be found. In this way, the internal aggregation degree and the external dispersion can be optimized simultaneously, rather than the external dispersion dominating.

[0103] Based on this, the objective function of constructing the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree specifically includes:

[0104] determining a balance factor based on the internal degree of polymerization and the external degree of dispersion;

[0105] An objective function for a weight matrix of attributes to be optimized is constructed based on the balance factor, the internal aggregation degree, and the external dispersion degree.

[0106] Specifically, the balance factor is used to reflect the importance of the internal aggregation and external dispersion under the conditional attribute set, and the internal aggregation and external dispersion in the objective function are balanced by the balance factor. In other words, the balance factor is a parameter for balancing the internal aggregation and external dispersion. The balance factor can be pre-set or determined according to the internal aggregation and external dispersion of the domain.

[0107] In the embodiment of the present application, the balance factor is determined according to the internal aggregation degree and the external dispersion degree of the domain, and the balance factor satisfies the balance relationship, wherein the balance relationship is:

[0108]

[0109] Among them, β represents the balance factor, IA I (U) represents the internal aggregation degree of the domain with respect to the conditional attribute set when the attribute weight matrix to be optimized takes the identity matrix, ED I (U) represents the external dispersion of the domain with respect to the conditional attribute set when the attribute weight matrix to be optimized takes the identity matrix.

[0110] From the equilibrium relationship satisfied by the balance factor, it can be seen that the expression of the balance factor is:

[0111]

[0112] Among them, β represents the balance factor, IA I (U) represents the internal aggregation degree of the domain with respect to the conditional attribute set when the attribute weight matrix to be optimized takes the identity matrix, ED I (U) represents the external dispersion of the domain with respect to the conditional attribute set when the attribute weight matrix to be optimized takes the identity matrix.

[0113] Furthermore, after obtaining the balance factor, an objective function can be constructed based on the balance factor, internal aggregation and external dispersion, where the objective function is expressed as:

[0114] f(W)=β*IA(U)-(1-β)*ED(U)

[0115] Among them, f(W) represents the objective function, W represents the weight matrix of the attributes to be optimized, IA(U) represents the internal aggregation of the domain with respect to the conditional attribute set, ED(U) represents the external dispersion of the domain with respect to the conditional attribute set, and β represents the balance factor.

[0116] Of course, in practical applications, other methods can also be used to construct the objective function, for example, the objective function can be twice f(W), etc. The objective function given in the embodiment of the present application is only a typical implementation method, and other methods that can construct the objective function based on the balance factor, internal aggregation degree and external dispersion degree are also possible.

[0117] Furthermore, after the objective function is constructed, the objective function is solved to obtain the optimal solution of the objective function, and the optimal solution is used as the objective attribute weight matrix. The optimal solution is the weight matrix that makes the objective function obtain the minimum value when the termination condition is met. The termination condition is pre-set, for example, the increase of the objective function value under the maximum number of iterations or the number of consecutive iterations is less than a certain threshold.

[0118] When solving the objective function, the gradient descent method can be used. When solving the minimum value of the objective function in an unconstrained optimization problem, the gradient descent method continuously updates the parameters in the direction of their negative gradient. To this end, the specific process of solving the objective function by the gradient descent method can be:

[0119] Step 1: Determine the optimization problem regarding attribute importance based on the objective function

[0120] First, a constrained optimization problem is constructed based on the objective function. The specific form of the constrained optimization problem can be:

[0121]

[0122] st0≤w ii ≤1,0<∑w ii ≤n

[0123] Secondly, let is a real number, 0 <w ii <1, express function, accordingly, the constrained optimization problem can be transformed into an unconstrained optimization problem, which can be expressed as:

[0124]

[0125] in,

[0126] Step 2: Solve the unconstrained optimization problem by gradient descent to obtain the target attribute weight matrix

[0127] First, given the maximum number of iterations Γ, the learning rate α, and the random initialization According to the internal and external neighborhood information particles of each object, the self-matrix E of the universe is determined. U , the domain aggregation matrix A U , the universe divergence matrix D U .

[0128] Next, let t = 1:Γ and calculate the IA of the tth iteration t (U) and ED t (U), I.A. t (U) represents the internal aggregation degree at the tth iteration, ED t (U) represents the external dispersion at the tth iteration, and then the objective function of the tth iteration can be obtained in,

[0129] Again, if Terminate the loop; otherwise, for all parameters To update, About parameters The first-order partial derivative of is:

[0130]

[0131] Where M = E U -A U ,N=E U -D U , M i ,N iis the i-th column vector of matrix M, N. When the termination condition is met, the optimal parameters are output

[0132] Finally, according to the optimal parameters nGet the optimal weight for each attribute To obtain the target attribute weight matrix.

[0133] It should be noted that in practical applications, other methods may also be used to solve the objective function, for example, using an ant colony algorithm.

[0134] S50: Simplify the attributes of the decision table based on the target attribute weight matrix to obtain a simplified decision table.

[0135] Specifically, after obtaining the target attribute weight matrix, the attributes of the decision table are simplified according to the target attribute weight matrix. When the attributes of the decision table are simplified according to the target attribute weight matrix, the classification performance of the classifier on the simplified condition attribute set after the attribute simplification can be used to determine the final simplified condition attribute set, and then obtain the simplified decision table.

[0136] Exemplarily, the performing attribute simplification on the decision table based on the target attribute weight matrix to obtain a simplified decision table specifically includes:

[0137] Build several classifiers;

[0138] Selecting a number of conditional attributes from the conditional attribute set based on the target attribute weight matrix to obtain a candidate conditional attribute set;

[0139] Perform classification performance testing on several classifiers based on the candidate condition attribute set to obtain a test result;

[0140] The decision table is attribute-reduced based on the detection result to obtain a reduced decision table.

[0141] Specifically, the several classifiers may be one or more, and the classifiers may be the classic K nearest neighbor KNN, radial basis support vector machine SVM, classification regression tree CART, etc. The candidate condition attribute set includes some condition attributes in the condition attribute set, and the attribute weight of each condition attribute in the candidate condition attribute set is higher than the condition attribute that is not selected in the condition attribute set. Among them, the selection process of the candidate condition attribute set may be: firstly, the condition attribute set is arranged in order from high to low according to the attribute weight matrix of the target attribute to obtain a descending condition attribute set, and then a preset number of candidate attributes are selected from the descending condition attribute set in order from front to back to obtain the candidate condition attribute set, wherein the preset number is less than the preset maximum number of candidate attributes, and the preset maximum number of candidate attributes can be determined according to the number of condition attributes of the object, for example, when the number of condition attributes n is greater than 100, the preset maximum number of candidate attributes L=50 can be set; otherwise, the preset maximum number of candidate attributes L=n can be set, that is, the preset maximum number of candidate attributes is adaptive to the condition attribute set. Of course, in practical applications, the preset maximum number of candidate attributes can also be directly set.

[0142] Further, the test result is obtained by verifying the classification accuracy of several classifiers, which can be the classification accuracy of one classifier among several classifiers or the average classification accuracy of several classifiers. Exemplarily, the classification performance test of several classifiers based on the candidate condition attribute set is performed to obtain the test result specifically including:

[0143] Divide the data set corresponding to the domain into a training data set and a validation data set;

[0144] Several classifiers are trained based on the candidate condition attribute set on the training data set, and the classification accuracy of several classifiers trained with the training data set is verified through the verification data set to obtain the detection results.

[0145] Specifically, the data set corresponding to the domain is randomly divided into two equal parts, one as the training data set and the other as the verification data set. The training data corresponding to the candidate condition attribute set is selected from the training data set, and several classifiers are trained by the selected training data to obtain trained classifiers. Then, the classification accuracy of several classifiers trained by the training data set is verified in the verification data set to obtain the detection results.

[0146] In addition, it is worth noting that when the classification performance of several classifiers is tested based on the candidate condition attribute set, the test will be repeated multiple times, and the candidate condition attribute set used in each test is different. For example, the candidate condition attribute set corresponding to each preset number from 1 to the preset maximum number of candidate attributes can be selected respectively, and the test result corresponding to each candidate condition attribute set can be determined, and then the candidate condition attribute set corresponding to the optimal test result can be selected from all the test results as the simplified condition attribute set; or, the preset number can be determined according to the preset value (for example, 2, 3, etc.) at each interval from 1 to the preset maximum number of candidate attributes.

[0147] The time complexity of the attribute reduction method in the embodiment of the present application is O(mn*max{logm,kΓ}), where m is the number of samples in the data, n is the number of features, k is the number of neighbors, Γ is the maximum number of iterations, and r is the number of categories. The proposed attribute reduction method greatly improves the computational efficiency.

[0148] Furthermore, after obtaining the simplified decision table, the simplified data set corresponding to the simplified decision table can be determined, and then data mining can be performed based on the simplified data set, or it can be used as a training sample for machine learning, or it can be used as sample data for model recognition, etc. For example, the data set corresponding to the decision table is a training sample set for a classification model. When the classification model is trained using the training sample set, the training sample set can be simplified by the method provided in the embodiment of the present application, and then the simplified training sample set can be used to train the classification model to improve the training efficiency of the classification model.

[0149] In summary, the present embodiment provides an attribute simplification method based on neighborhood separability, the method comprising acquiring object data, and establishing a decision table based on the acquired object data; determining the double neighborhood information granules of each object in the decision table based on the decision attribute set; quantifying the internal aggregation and external dispersion of the domain with respect to the conditional attribute set based on the double neighborhood information granules and the attribute weight matrix to be optimized; constructing an objective function with respect to the attribute weight matrix to be optimized based on the internal aggregation and external dispersion, and solving the objective function to obtain the target attribute weight matrix; and performing attribute simplification on the decision table based on the target attribute weight matrix to obtain a simplified decision table. The present application embodiment first makes full use of the local structural information of the object, quantifies the internal aggregation and external dispersion of all objects with respect to the conditional attribute set, and then combines the internal aggregation and external dispersion to establish an objective function with respect to the attribute matrix for attribute importance, and finally performs attribute simplification according to the target attribute matrix determined by solving the objective function, which solves the problem of low algorithm efficiency caused by repeated calculation of various binary relations or information granules and selection of attributes one by one in the feature selection process, thereby improving the computational efficiency of feature selection, and further improving the computational efficiency of machine learning.

[0150] Based on the above attribute reduction method based on neighborhood separability, this embodiment provides an attribute reduction device based on neighborhood separability, such as Figure 3 As shown, the attribute simplification device based on neighborhood separability specifically includes:

[0151] An acquisition module 100 is used to acquire object data and establish a decision table based on the acquired object data, wherein the decision table includes a domain, a condition attribute set for describing object characteristics, and a decision attribute set for describing category information of the object;

[0152] A determination module 200, configured to determine a dual-neighborhood information granule of each object in the decision table based on the decision attribute set, wherein the dual-neighborhood information granule includes an internal neighborhood information granule and an external neighborhood information granule;

[0153] A quantization module 300, for quantifying the internal aggregation and external dispersion of the domain with respect to the conditional attribute set based on the dual-neighborhood information granules and the attribute weight matrix to be optimized;

[0154] A construction module 400 is used to construct an objective function about the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree, and solve the objective function to obtain a target attribute weight matrix;

[0155] The reduction module 500 is used to reduce the attributes of the decision table based on the target attribute weight matrix to obtain a reduced decision table.

[0156] Based on the above-mentioned attribute reduction method based on neighborhood separability, this embodiment provides a computer-readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the steps in the attribute reduction method based on neighborhood separability as described in the above-mentioned embodiment.

[0157] Based on the above attribute reduction method based on neighborhood separability, the present application also provides a terminal device, such as Figure 4 As shown, it includes at least one processor 20, a display screen 21, and a memory 22, and may also include a communication interface 23 and a bus 24. The processor 20, the display screen 21, the memory 22, and the communication interface 23 may communicate with each other through the bus 24. The display screen 21 is configured to display a preset user guide interface in the initial setting mode. The communication interface 23 may transmit information. The processor 20 may call the logic instructions in the memory 22 to execute the method in the above embodiment.

[0158] In addition, the logic instructions in the memory 22 can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product.

[0159] The memory 22 is a computer-readable storage medium that can be configured to store software programs, computer executable programs, such as program instructions or modules corresponding to the methods in the embodiments of the present disclosure. The processor 20 executes functional applications and data processing by running the software programs, instructions or modules stored in the memory 22, that is, implementing the methods in the above embodiments.

[0160] The memory 22 may include a program storage area and a data storage area, wherein the program storage area may store an operating system and at least one application required for a function; the data storage area may store data created according to the use of the terminal device, etc. In addition, the memory 22 may include a high-speed random access memory and may also include a non-volatile memory. For example, a variety of media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a disk or an optical disk, may also be a transient storage medium.

[0161] In addition, the specific process of loading and executing the multiple instruction processors in the above storage medium and the terminal device has been described in detail in the above method and will not be described here one by one.

[0162] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit it. Although the present application 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 application.

Claims

1. A neighborhood separability-based attribute reduction method, characterized in that: The attribute reduction method based on neighborhood separability specifically includes: Acquire object data, and establish a decision table based on the acquired object data, wherein the decision table includes a domain, a condition attribute set for describing object characteristics, and a decision attribute set for describing category information of the object; Determine a dual neighborhood information granule for each object in the decision table based on the decision attribute set, wherein the dual neighborhood information granule includes an internal neighborhood information granule and an external neighborhood information granule; Based on the dual-neighborhood information granules and the attribute weight matrix to be optimized, the internal aggregation degree and external dispersion degree of the domain with respect to the conditional attribute set are quantified; Constructing an objective function for the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree, and solving the objective function to obtain a target attribute weight matrix; The attributes of the decision table are simplified based on the target attribute weight matrix to obtain a simplified decision table.

2. The attribute reduction method based on neighborhood separability according to claim 1, characterized in that: Determining the dual-neighborhood information granules of each object in the decision table based on the decision attribute set specifically includes: Calculate the distance measure between each two objects in the decision table under the condition attribute set to obtain a distance measure set; Based on the decision attribute set, determining a first object set and a second object set for each object, wherein the first object set for each object includes all in-class objects of each object, and the second object set for each object includes all inter-class objects of each object; Determine the internal neighborhood information granules of each object based on the first object set and the distance measurement set of each object; Based on the second object set and the distance metric set of each object, an external neighborhood information granule of each object is determined.

3. The attribute reduction method based on neighborhood separability according to claim 1, characterized in that: The internal aggregation degree and external dispersion degree of the domain of quantization about the conditional attribute set based on the dual-neighborhood information granules and the attribute weight matrix to be optimized specifically include: Quantifying the local internal aggregation degree of each object with respect to the conditional attribute set based on the internal neighborhood information granules of each object and the attribute weight matrix to be optimized, and quantifying the internal aggregation degree of the domain with respect to the conditional attribute set based on the local internal aggregation degree of each object and the attribute weight matrix to be optimized; The local external dispersion of each object with respect to the conditional attribute set is quantified based on the external neighborhood information granules of each object and the attribute weight matrix to be optimized, and the external dispersion of the domain with respect to the conditional attribute set is quantified based on the local external dispersion of each object and the attribute weight matrix to be optimized.

4. The attribute reduction method based on neighborhood separability according to claim 1, characterized in that: The objective function of constructing the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree specifically includes: Determining a balance factor based on the internal aggregation degree and the external dispersion degree, wherein the balance factor is used to reflect the importance of the internal aggregation degree and the external dispersion degree under the conditional attribute set; Constructing an objective function for a weight matrix of attributes to be optimized based on the balance factor, the internal aggregation degree, and the external dispersion degree; Wherein, the objective function is expressed as: f(W)=β*IA(U)-(1-β)*ED(U) Among them, f(W) represents the objective function, W represents the weight matrix of the attributes to be optimized, IA(U) represents the internal aggregation of the domain with respect to the conditional attribute set, ED(U) represents the external dispersion of the domain with respect to the conditional attribute set, and β represents the balance factor.

5. The attribute reduction method based on neighborhood separability according to claim 4, characterized in that: The expression of the balance factor is: Among them, β represents the balance factor, IA I (U) represents the internal aggregation degree of the domain with respect to the conditional attribute set when the attribute weight matrix to be optimized takes the identity matrix, ED I (U) represents the external dispersion of the domain with respect to the conditional attribute set when the attribute weight matrix to be optimized takes the identity matrix.

6. The attribute reduction method based on neighborhood separability according to claim 1, characterized in that: The step of performing attribute simplification on the decision table based on the target attribute weight matrix to obtain a simplified decision table specifically includes: Build several classifiers; Selecting a number of conditional attributes from the conditional attribute set based on the target attribute weight matrix to obtain a candidate conditional attribute set; Perform classification performance testing on several classifiers based on the candidate condition attribute set to obtain a test result; The decision table is attribute-reduced based on the detection result to obtain a reduced decision table.

7. The attribute reduction method based on neighborhood separability according to claim 6, characterized in that: The classification performance test of several classifiers based on the candidate condition attribute set is performed to obtain the test results, which specifically include: Divide the data set corresponding to the domain into a training data set and a validation data set; Several classifiers are trained based on the candidate condition attribute set on the training data set, and the classification accuracy of several classifiers trained with the training data set is verified through the verification data set to obtain the detection results.

8. An attribute simplification device based on neighborhood separability, characterized in that: The attribute simplification device based on neighborhood separability specifically includes: An acquisition module, used for acquiring object data, and establishing a decision table based on the acquired object data, wherein the decision table includes a domain, a conditional attribute set for describing object characteristics, and a decision attribute set for describing category information of the object; A determination module, configured to determine a dual-neighborhood information granule of each object in the decision table based on the decision attribute set, wherein the dual-neighborhood information granule comprises an internal neighborhood information granule and an external neighborhood information granule; A quantification module, used for quantifying the internal aggregation and external dispersion of the domain with respect to the conditional attribute set based on the dual-neighborhood information granules and the attribute weight matrix to be optimized; A construction module, used to construct an objective function about the attribute weight matrix to be optimized based on the internal aggregation degree and the external dispersion degree, and solve the objective function to obtain a target attribute weight matrix; The simplification module is used to simplify the attributes of the decision table based on the target attribute weight matrix to obtain a simplified decision table.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the steps in the attribute reduction method based on neighborhood separability as described in any one of claims 1-7.

10. A terminal device, characterized in that: include: Processor and memory; The memory stores a computer-readable program executable by the processor; When the processor executes the computer-readable program, the processor implements the steps in the attribute reduction method based on neighborhood separability as described in any one of claims 1 to 7.

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