Approximate rough set discernibility classification decision algorithm

Abstract

The application provides a rough set approximation resolution classification decision algorithm. The method comprises the following steps: judging the sample data attribute division capability by using rough set approximation, taking the proportion of samples with attribute membership function value greater than the set approximation as the attribute probability, and substituting the attribute probability into the decision resolution algorithm, taking the attribute with the maximum decision resolution as the split feature to establish a classification decision tree, and obtaining the leaf node of the test sample in the classification decision tree as the classification decision result. The method can improve the classification decision time efficiency and tree complexity on the basis of improving the sample classification decision accuracy.

Description

(I) Technical Field

[0001] This invention relates to the field of classification decision-making for uncertain sample data, and more particularly to a method for classifying sample data using approximate rough sets and decision discrimination. (II) Background Technology

[0002] In recent years, the rapid development of modern information technology has driven social progress. The social informatization brought about by information technology is profoundly changing the social structure, bringing great convenience and significant impact to people's lifestyles, work methods, and learning methods. More and more data is being collected, acquired, and processed. Data collection is not a short-term endeavor; the long-term collection of data leads to massive data storage. We must recognize the positive changes that information technology brings to our lives, but we must also remain vigilant and guard against the negative impacts that accompany massive amounts of data.

[0003] It is estimated that the total amount of global data is expanding rapidly at a rate of approximately 40% per year, reaching a new peak by 2025. In data processing and application, higher demands are placed on how to extract implicit correlations from large amounts of irregular and unrelated data and effectively utilize it. Due to insufficient precision of machinery and equipment, and omissions in data processing by personnel, data information is often chaotic and contains errors, omissions, redundancy, or inconsistencies. If we directly confront this situation, decision-making systems may be unable to arrive at accurate results, easily leading to misjudgments and potentially putting themselves in a dangerous situation. Therefore, data classification decision-making algorithms are crucial for obtaining complete and reliable classification decision results and improving decision accuracy.

[0004] Data classification and decision-making are highly complex tasks, involving information stored in various formats. The rapid development of equipment and classification algorithms has not only greatly enriched the forms and quantities of data but also significantly expanded the scope and domain of classification and decision-making techniques. Classical statistical pattern recognition and structural pattern recognition have led to different identification and decision-making methods and techniques for specific tasks, such as neural network methods, association rule models, decision tree algorithms, and regression analysis models. Training sets of varying quality pose a severe test to the effectiveness and accuracy of classification decisions. Therefore, using different methods to classify sample data and identifying the algorithm with the highest fitness has significant applied research value in classification decision-making across various fields. (III) Summary of the Invention

[0005] This invention addresses the problems of existing classification decision algorithms requiring multiple scans and calculations of continuous attribute values ​​in sample data, and low classification time efficiency when the proportion of continuous attributes is too high. It proposes a classification decision algorithm based on approximate rough set and decision discrimination.

[0006] A classification decision algorithm based on approximate rough set resolution.

[0007] (1.1) Use rough set approximation to judge the ability of attributes to divide sample data, and take the proportion of samples whose membership function value of sample attributes is greater than the set approximation as the probability of that attribute;

[0008] (1.2) Substitute the obtained attribute probabilities into the decision discrimination algorithm, and use the attribute with the highest decision discrimination as the splitting feature to build a classification decision tree. The leaf node obtained by the test sample in the classification decision tree is the classification decision result.

[0009] The method features (1.1) include:

[0010] (2.1) A training information system S can be represented as S=(U,A,V,f), where the non-empty sample set U is called the universe of discourse and contains L samples, where U={x1,x2,…,x L Let A = C ∪ D represent the set of attributes, and C be the set of conditional attributes C = {a1, a2, ..., a...}. v Let D be the set of decision attributes D = {d1, d2, ..., d} m Let V represent the range of attributes, and let f be the set of relations between U and A. Any set of attributes R is an equivalence relation on A, and an indistinguishable relation on the universe of discourse U is defined as:

[0011]

[0012] The indistinguishable relation IND(R) is an equivalence relation, denoted as [x]. IND(R) Let {y∈U|y∈IND(R)} be the equivalence class of the indiscernible relation IND(R) containing the object x. All equivalence classes in U constitute a partition of U, denoted as U|IND(R)={[x]}. IND(R) The indistinguishable relation IND(R) on a subset of attributes R is simplified to R, where [x] ∈ U. IND(R) Simplified to [x] R express;

[0013] (2.2) To construct the optimal approximate rough set of the target set X, we first need to obtain the membership function of x belonging to the target set:

[0014]

[0015] Membership degree Belonging to [0,1], it represents the probability that any element x belongs to set X. When the membership degree is equal to 1, it represents the lower approximation set of the rough set. When the membership degree is between 0 and 1, it represents an element between the upper approximation set and the lower approximation set.

[0016] (2.3) Construct an approximate rough set R between the upper and lower approximate sets. λ (X), which is defined as:

[0017]

[0018] λ is the range of membership degree values. When the approximation degree is in the interval [0.5, 1], R λ The approximation of (X) is greater than R (X) is closer to the target set, and R 0.5 (X) is the optimal approximation set of the target set. It is not necessarily optimal on the interval [0, 0.5], but it can be used as the optimal approximation set of X when certain conditions are met.

[0019] The method feature (1.2) includes:

[0020] (3.1)p j Indicates condition a j In this case, it belongs to the decision value d i And it satisfies the conditional probability of rough set approximation;

[0021] (3.2)q j Indicates the decision value d i The proportion of all possible values ​​for a given conditional attribute in the sample set is also known as uncertainty. The sample set has a sample size of L.

[0022] q j =|d i | / L

[0023] (3.3) The decision discrimination power is:

[0024]

[0025] Where, p j Indicates condition a j In this case, it belongs to the decision value d i And it satisfies the conditional probability of rough set approximation, q j Indicates the decision value d i The proportion of all possible values ​​for a given conditional attribute in the sample set is also called the uncertainty, i.e., q. j =|d i | / L.

[0026] The core technical content of this invention lies in:

[0027] Based on the predictive performance of traditional classification decision algorithms on sample data, a classification decision algorithm based on approximate rough sets and decision discrimination is invented. The rough set approximation is used to judge the ability of attributes to divide sample data. The proportion of samples whose membership function value of an attribute is greater than a set approximation value is taken as the probability of that attribute, and it is substituted into the decision discrimination algorithm. The attribute with the highest decision discrimination is used as the splitting feature to build a classification decision tree. The leaf node obtained by the test sample in the classification decision tree is the classification decision result.

[0028] The beneficial effects of this invention are as follows:

[0029] This invention discloses a classification decision algorithm based on approximate rough set and decision discrimination, which can achieve good processing results even when the data has a certain amount of noise. Furthermore, when there is a large amount of continuous data, this invention can reduce computational complexity, improve computational efficiency, and increase classification decision accuracy by relying on rough set partitioning. (iv) Description of the attached drawings

[0030] Figure 1 This is a flowchart of a classification decision algorithm based on approximate rough set resolution. (V) Detailed Implementation

[0031] The method of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The following embodiments are used to illustrate this application, but are not intended to limit the scope of this application.

[0032] This application proposes a classification decision algorithm based on rough set theory and maximum decision resolution, taking into account the uncertainty of sample data. The proposed method uses rough set approximation to describe the attributes of the sample data and utilizes the maximum decision resolution method to generate a classification decision tree. This improves classification accuracy and reduces overfitting.

[0033] To more clearly illustrate the proposed method, this application embodiment uses simulation experiments to explain the process and demonstrate the effects, but does not limit the scope of this application embodiment. The experimental conditions are as follows: From a dataset containing 19,799 aircraft samples, the flight parameters of 500 ordinary aircraft and 97 spy aircraft were extracted to form the spy plane finder dataset. The parameters are: duration (flight time for each flight segment), box (area of ​​the rectangular bounding box drawn around each flight segment), speed (flight speed), altitude (flight vertical altitude), steer (compass orientation change), squawk (transponder transmission code), flight (total number of flight segments), and observation (total number of transponder detections). In the actual training set, the parameters duration, box, speed, and altitude are calculated according to the proportions of five flight segments, and the parameter steer is calculated according to the proportions of eight divided angle intervals, forming a set of 31 conditional attributes.

[0034] Figure 1 This is a flowchart of the method described in this invention, which includes:

[0035] S110. Introduce a training information system S, which can be represented as S=(U,A,V,f). The non-empty sample set U is called the universe of discourse, and it contains L samples, where U={x1,x2,…,x…} L Let A = C ∪ D represent the set of attributes, and C be the set of conditional attributes C = {a1, a2, ..., a...}. v Let D be the set of decision attributes D = {d1, d2, ..., d} m Let V represent the range of attributes, and let f be the set of relations between U and A. Any set of attributes R is an equivalence relation on A, and an indistinguishable relation on the universe of discourse U is defined as:

[0036]

[0037] The indistinguishable relation IND(R) is an equivalence relation, denoted as [x]. IND(R) Let {y∈U|y∈IND(R)} be the equivalence class of the indiscernible relation IND(R) containing the object x. All equivalence classes in U constitute a partition of U, denoted as U|IND(R)={[x]}. IND(R) The indistinguishable relation IND(R) on a subset of attributes R is simplified to R, where [x] ∈ U. IND(R) Simplified to [x] R express.

[0038] S120.U is a non-empty sample set, the universe of discourse U has an equivalence relation U / IND(R) on any attribute set R, the target subset X belongs to U, and for any x belonging to U, the membership function of x belonging to the target set X is defined as:

[0039]

[0040] The value range is [0,1]. It represents the probability that any element x belongs to set X. When the membership degree is equal to 1, it means that the rough set is a lower approximate set. When the membership degree is between 0 and 1, it means that the element is between the upper approximate set and the lower approximate set.

[0041] S130. By describing the membership degree, the upper and lower bounds of the rough set can be fuzzy, thereby constructing an approximate rough set R that lies between the upper and lower approximate sets. λ (X), which is defined as:

[0042]

[0043] λ is the range of membership degree values. When the approximation degree is in the interval [0.5, 1], R λ The approximation of (X) is greater than R (X) is closer to the target set, and R 0.5 (X) is the optimal approximation set of the target set. It is not necessarily optimal on the interval [0, 0.5], but it can be used as the optimal approximation set of X when certain conditions are met.

[0044] S140. A non-empty sample set U contains L samples, C is an attribute set containing v conditions, and the decision attribute set D has m values. The decision discrimination power is defined as:

[0045]

[0046] Where, p j Indicates condition a j In this case, it belongs to the decision value d i And it satisfies the conditional probability of rough set approximation, q j Indicates the decision value d i The proportion of all possible values ​​for a given conditional attribute in the sample set is also called the uncertainty, i.e., q. j =|d i | / L;

[0047] When the uncertainty q of the conditional attribute in the sample set j The larger the value, the higher the conditional probability p. jThe larger the value, the greater the decision-discriminating power of the conditional attribute, indicating a stronger ability to classify samples in a balanced manner. Therefore, using it as a classification attribute yields better results. Decision-discriminating power can be used as an extension of the information entropy algorithm. When there are only two decision attribute values, the decision-discriminating power is equivalent to the traditional information entropy algorithm. When there are more than two decision attribute values, its time efficiency in decision tree classification algorithms is relatively improved, and the complexity of the decision tree structure is reduced, making the algorithm simple and efficient.

[0048] In summary, the method in this embodiment improves the accuracy of classification decisions by mining information from sample data. Traditional rough set theory can only handle discrete data and is not flexible enough in practical applications. Traditional classification decision tree algorithms involve multiple sorting and sequential scanning of continuous data, resulting in low computational efficiency. The method in this application improves the time efficiency of the algorithm and reduces the tree complexity, avoiding the overfitting problem caused by excessive tree complexity in classification decision trees.

[0049] This invention utilizes the rough set approximation to determine the ability of attributes to partition sample data and incorporates this into a decision-making algorithm. The attribute with the highest decision-making power is used as the splitting feature to build a classification decision tree. The algorithm improves computational efficiency and reduces overfitting while maintaining classification accuracy. The specific implementation steps are as follows:

[0050] Input: The training information system S can be represented as S = (U, A, V, f), the non-empty training set U contains L samples, A = C ∪ D represents the attribute set, and C is the conditional attribute set C = {a1, a2, ..., a...} v Let D be the set of decision attributes D = {d1, d2, ..., d} m The rough set approximation degree is λ.

[0051] Output: A classification decision tree, where each node contains four elements: tree.feature is the node splitting feature; tree.location is the splitting interval when the splitting feature is a continuous attribute, and the discrete value of the attribute when the splitting feature is a discrete attribute; tree.child is the structure that stores the child nodes; and tree.value is the attribute sample value.

[0052] Step 1: Determine the discreteness of the values ​​of v attributes in the conditional attribute set C of the training samples. Let attributes with more than 10 possible values ​​be continuous attributes; loop through conditional attribute a. j If attribute a j If it is discrete, then proceed to Step 2; if attribute a j It's continuous, proceed to Step 3;

[0053] Step 2: Calculate the sample in aj The membership degree μ of each value under the given conditions to the decision value j ;

[0054] Step 3: Place a j The condition values ​​are sorted and unique, and each value is iterated sequentially to calculate the sample in a. j The membership degree μ of the decision attribute value when the condition is greater than or less than or equal to the condition value. j ;

[0055] Step 4: Calculate μ j The proportion of samples in the conditional attribute set > λ to the total number of samples is p. j ;

[0056] Step 5: Calculate a j The proportion of samples included in the conditional attribute set to the total number of samples is q. j ;

[0057] Step 6: Obtain H(p,q) for each conditional attribute based on the decision discrimination algorithm, and use the attribute with the highest decision discrimination as the tree.feature splitting feature of the node, and continue classification according to the value of this attribute.

[0058] Step 7: Recursively call the internal nodes of the classification decision tree built in Step 1 until all sample decision values ​​in the set are exactly the same or contain only a single conditional attribute, then stop the recursion.

[0059] After constructing the decision tree, the newly collected test sample set is substituted into the classification decision tree, and the leaf nodes are the classification decision results.

[0060] This invention provides a classification decision algorithm based on approximate rough set resolution. The method includes: utilizing the approximation of rough sets to determine the ability of attributes to partition sample data; taking the proportion of samples whose membership function value is greater than a set approximation as the probability of that attribute; substituting this probability into the decision resolution algorithm; using the attribute with the highest decision resolution as the splitting feature to build a classification decision tree; and the leaf node obtained by the test sample in the classification decision tree is the classification decision result. This method can improve the accuracy of sample classification decisions while also improving the time efficiency and tree complexity of classification decisions.

[0061] Those skilled in the art will understand that in the above methods of the specific embodiments of this application, the number of each step does not imply the order of execution. The execution order of each step should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the specific embodiments of this application.

[0062] Finally, it should be noted that the above embodiments are only used to describe the technical solutions of the present invention and not to limit the technical methods. The present invention can be extended to other modifications, variations, applications and embodiments, and therefore all such modifications, variations, applications and embodiments are considered to be within the spirit and teachings of the present invention.

Claims

1. A classification decision method based on the discriminative power of approximate rough sets, characterized in that: Includes the following steps: (1) The flight parameters constitute the Spy Plane Finder dataset, which includes the following parameters: duration (flight time for each flight segment), box (area of ​​the rectangular bounding box drawn around each flight segment), speed (flight speed), altitude (flight vertical altitude), steer (compass orientation change), squawk (transponder transmission code), flight (total number of flight segments), and observation (total number of transponder detections). The parameters duration, box, speed, and altitude are calculated according to their respective proportions for each flight segment, and the parameter steer is calculated according to its proportion across 8 angular intervals, forming a set of 31 conditional attributes. The training information system is then constructed. ,in, For a non-empty sample set, , Represents a collection of attributes. For conditional attribute set , For decision attribute set , Represents the value range of an attribute, information function set yes and Relation sets; rough set approximation is ; (2) For each set of conditional attributes middle The discreteness of attribute values ​​is considered; attributes with more than 10 possible values ​​are considered continuous. Conditional attributes are called iteratively. If attribute If it is discrete, continue to step (3); if it is continuous, proceed to step (4). (3) Calculate the sample in The membership degree of each value under the given conditions to the decision value ; (4) The condition values ​​are sorted and unique, and each value is iterated sequentially to calculate the sample value. Membership degree of the decision attribute value under the condition that the value is greater than or less than or equal to the condition value. ; (5) Calculation The proportion of samples included in the conditional attribute set to the total number of samples is ; (6) Calculation The proportion of samples included in the conditional attribute set to the total number of samples is: ; (7) Obtain each conditional attribute based on the decision discrimination algorithm. The attribute with the highest decision-making power is used as the tree.feature splitting feature of the node, and the classification continues according to the value of this attribute; (8) Recursively call the internal nodes of the classification decision tree constructed in Step 1 until all sample decision values ​​in the set are exactly the same or contain only a single condition attribute, then stop the recursion. (9) After constructing the decision tree, substitute the newly collected test sample set into the classification decision tree, and the leaf nodes are the classification decision results.

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