Classification method based on interval particle neighborhood rough set three-way decision

Abstract

The invention discloses an interval particle neighborhood rough set three-way decision-making-based classification method, which comprises the following steps of 1, acquiring a data set, and converting the data set into a tetrad decision-making information system; 2, obtaining an interval particle set of the decision information system; 3, obtaining a threshold pair through a three-branch approximation method of the shadow set, and obtaining the average ambiguity of the interval grain shadow set according to the threshold pair; 4, obtaining a threshold pair corresponding to the minimum fuzzy loss between the average ambiguity of the interval grain set and the average ambiguity of the interval grain shadow set, and taking the threshold pair as an optimal threshold pair; and 5, according to the optimal threshold pair, identifying an interval particle neighborhood of the prediction object, and classifying the prediction object. According to the method, higher-quality decision information system processing and expression are achieved, and the accuracy and robustness of the model are further enhanced.

Description

Technical Field

[0001] The invention relates to a classification method, in particular to a classification method based on interval granular neighborhood rough set three-branch decision. Background Art

[0002] Three-way decision making (3WD) is an effective method to solve complex uncertainty problems. 3WD uses the threshold (β * ,a * ) divides the domain into different and mutually exclusive areas and adopts corresponding strategies for different areas. This "divide and conquer" approach can handle uncertainty more accurately and comprehensively. Compared with the two-way decision model, the non-commitment boundary decision of 3WD can provide more opportunities to reduce decision risks when considering the cost and uncertainty of problem solving.

[0003] The idea of ​​3WD is combined with the neighborhood rough set (NRS) model to construct a three-branch decision framework based on neighborhood rough sets (3WDNRS). 3WDNRS reduces the decision risk of uncertain concept approximation by establishing a three-branch neighborhood space. However, the above 3WDNRS works all use a single neighborhood particle as input, which reduces the decision efficiency and versatility. In addition, the determination of the threshold is often subjective and heavily depends on the judgment of experts.

[0004] Granular computing (GrC) simulates the cognitive mechanism of multiple granularities and provides a new paradigm for dealing with large-scale complex problems and managing uncertain information. Granular computing can simplify massive data into meaningful granularities, help extract core information, reduce the impact of useless or redundant information, effectively simplify complex problems, and reduce the scale of problems and computational difficulty.

[0005] In order to solve the problem that 3WDNRS works with a single neighborhood granule as input, the information granules generated by granule computing are used as the input of 3WDNRS to improve decision efficiency. However, there are still some problems with the existing information granules, such as the loss of boundary information; the size of the information granule is easily affected by data distribution and boundary samples; the method of randomly or by classifying the center to generate information granules will bring uncertainty and reduce robustness. Summary of the invention

[0006] In view of the deficiencies in the prior art, the present invention provides a classification method based on interval granular neighborhood rough set three-branch decision to solve the technical problems of low accuracy, low stability and poor robustness in classification in the prior art.

[0007] The present invention provides a classification method based on interval granular neighborhood rough set three-branch decision, comprising the following steps:

[0008] Step 1: Obtain the data set and convert it into a four-tuple decision information system;

[0009] Step 2: Obtain the interval granular set of the decision information system;

[0010] Step 3: Obtain the threshold pair through the three-branch approximation method of the shadow set, and obtain the average blur of the interval particle shadow set according to the threshold pair;

[0011] Step 4: Obtain the threshold pair corresponding to the minimum blur loss between the average blur of the interval particle set and the average blur of the interval particle shadow set as the optimal threshold pair;

[0012] Step 5: Based on the optimal threshold pair, identify the interval particle neighborhood of the predicted object and classify the predicted object.

[0013] Furthermore, the specific process of step 2 is as follows:

[0014] Step 21: Obtain the granulation center of the decision information system through the DBSCAN clustering method;

[0015] Step 22: Taking the granulation center as the center, perform interval granulation on the decision information system to generate interval granulation sets.

[0016] Furthermore, the specific method of step 21 is: firstly calculate the local density of each sample in the decision information system, and then select the sample with the largest local density as the granulation center.

[0017] Furthermore, the calculation formula of the local density of each sample is:

[0018]

[0019] Where U is a finite sample set; L(x) represents the label of x after being processed by the DBSCAN clustering method; Represents x i The Gaussian kernel density of Among them, d ij Represents x i With Ux j The distance between c Is a constant value.

[0020] Furthermore, the calculation formula for the average blur of the interval particle shadow set in step 3 is:

[0021]

[0022] In the formula, Among them, U is a finite sample set, is the membership of sample x in IG, x is a sample in IG, Equal to m(IG); β* ,α * is the threshold pair (β * ,α * ); m(IG) is the membership degree of each interval particle.

[0023] Furthermore, the formula for obtaining the threshold pair is:

[0024]

[0025] In the formula, m1 and m2 satisfy: 0 <m1≤0.5、0.5≤m2<1、m1+m2=1。

[0026] Furthermore, the calculation formula of the membership degree of the interval particle is:

[0027]

[0028] In the formula, μ l (IG i ) means IG i Purity, Where f(x,d) is a mapping function, f:U×(A∪{d})→V, V=V a ∪V d , V a is the set of values ​​of conditional attribute a, V d ={l1,l2,…,l z} is the set of values ​​or labels of d, l(IG) is the label of IG; ρ(IG i ) is IG i The local density of Among them, d c is a constant, d ij Indicates IG i Center and IG i Inner sample x j The distance between.

[0029] Furthermore, the specific process of step 5 is as follows:

[0030] Step 51: Obtain the distance between the predicted object and the center of the interval particle, and sort the distances from near to far to obtain a distance set;

[0031] Step 52: Select several interval grains with the closest distance as the interval grain neighborhood of the prediction object, and calculate the membership degree of the prediction object according to the label of each interval grain in the interval grain neighborhood;

[0032] Step 53: According to the membership of the predicted object, the predicted object is classified into three categories through the optimal threshold pair.

[0033] Furthermore, the calculation formula for obtaining the distance between the predicted object and the center of the interval particle in step 51 is:

[0034]

[0035] Where Δ(·) represents the Euclidean distance function; c i Show IG i The center point of Indicates IG i The proportion of samples included in IGs to the samples included in all IGs.

[0036] Furthermore, in step 52, the membership degree calculation formula is:

[0037]

[0038] Where l(IG) is the label of IG, is the interval particle neighborhood of x relative to R, is the number of interval particles in the neighborhood of the interval particle; is the sum of the particle labels in each interval.

[0039] Beneficial effects of the present invention:

[0040] The present invention can reduce the loss of boundary information and achieve better domain coverage; the size of the interval granules can be adaptively adjusted according to the data of each dimension. The present invention has higher quality decision information system processing and expression, and further enhances the accuracy and robustness of the model. The present invention is based on minimizing fuzzy loss and avoids the need to subjectively define certain risk parameters when calculating thresholds. The parameter-free characteristics of the present invention enable it to have better generalization performance.

[0041] The present invention can reduce the loss of boundary information and achieve better domain coverage by acquiring interval granules of the decision system, and can adaptively adjust the size of the interval granules according to the data of each dimension.

[0042] The present invention takes the distribution of samples in the entire sample into account according to the local density, so that the selection of granulation center is more reasonable, and a more reasonable initial granulation center is obtained. It can generate higher quality and more reasonable interval granules, and has higher quality decision information system processing and expression, which further enhances the accuracy and robustness of the model.

[0043] The method for obtaining threshold pairs of the present invention makes the selection of threshold pairs objective and has stronger generalization. The method for obtaining the membership of interval particles of the present invention takes into account the traditional purity and the local density of samples in the interval particles, which can better measure the generation quality of interval particles. The present invention determines the optimal threshold pair based on minimizing the fuzzy loss, avoiding the need to subjectively define certain risk parameters when calculating the threshold. The parameter-free characteristic of the present invention enables it to have better generalization performance. The distance formula of the present invention takes into account the distribution of samples in the interval particles, selects the interval particles containing more samples as the neighborhood of the prediction object, and the calculated distance is more reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The features and advantages of the present invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the present invention in any way. In the accompanying drawings:

[0045] Figure 1 is a flow chart of a specific embodiment of the present invention;

[0046] Figure 2 This is a comparison chart of algorithm effects;

[0047] Figure 3 is a flow chart for obtaining an optimal threshold pair in a specific embodiment of the present invention;

[0048] Figure 4 is a flow chart of prediction sample classification in a specific embodiment of the present invention;

[0049] Figure 5 This is a ranking diagram of the accuracy of the method of the present invention and the existing algorithm method under 10% noise rate on 12 decision information systems;

[0050] Figure 6 This is a ranking diagram of the accuracy of the method of the present invention and the existing algorithm method under 20% noise rate on 12 decision information systems;

[0051] Figure 7 This is a ranking diagram of the accuracy of the method of the present invention and the existing algorithm method under 30% noise rate on 12 decision information systems;

[0052] Figure 8 This is a ranking diagram of the accuracy of the method of the present invention and the existing algorithm method under a noise rate of 40% on 12 decision information systems. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0054] The present invention is further illustrated below in conjunction with specific embodiments. Those skilled in the art should understand that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention, and modifications to various equivalent forms of the present invention fall within the scope defined by the appended claims of this application.

[0055] The present invention provides a classification method based on interval granular neighborhood rough set three-branch decision, comprising the following steps:

[0056] Step S1: Obtain a data set and convert it into a four-tuple decision information system:

[0057] NS=(U,A∪d,V,f)

[0058] Where U is a finite sample set; x is a sample in U; ​​A represents a non-empty finite set of conditional attributes; d is a decision attribute; V = V A ∪V d , V a is the set of values ​​of conditional attribute a, V d ={l1,l2,…,l z} is the set of values ​​or labels of d; f:U×(A∪{d})→V is a mapping function, such as f(x,a)∈V a ,f(x,d)∈V d .

[0059] Step S2: Process the decision information system through the density-based interval granulation method to generate interval granule sets. The specific steps are as follows:

[0060] Step S21: Obtaining the granulation center by using the DBSCAN clustering method, wherein the specific process of determining the granulation center is as follows:

[0061] First calculate the local density of each sample, and then select the sample with the largest local density as the granulation center, where sample x i ∈U local density D(x i ) is calculated as:

[0062]

[0063] In the formula, L(x) represents the label of x after being processed by the DBSCAN algorithm; Represents x i Gaussian kernel density, where d ij Represents x i With U in x j The distance between c Is a constant value.

[0064] Step S22: Then, starting from the granulation center, the decision information system is interval granulated to generate an interval granulation set;

[0065] The interval granulation set of the decision information system includes equivalence relations, specifically:

[0066] As step S1 gives an information decision system a∈A is a quantitative attribute, V a is the value range of a.

[0067] Induce a partition of U, expressed as: Abbreviated as: IGs, where IG j represents the jth interval particle in IGs, IG j (j=1,2,…,n)), and The definition is as follows:

[0068]

[0069] The inducing factors is an interval equivalence relation:

[0070]

[0071] in, is the i-th granulation interval of attribute value a; and They are The left and right ends of a is the number of intervals of a, n a ≤|V a |, when the value of a is continuous, n a The value of is less than or equal to |U|.

[0072] V a The interval granulation satisfies the following three conditions: in, V a The minimum and maximum values ​​in ; 3) For every x∈U and a∈A, there is a make

[0073] The interval-granular decision information system also includes lower approximation and upper approximation, specifically:

[0074] IGs={IG1,IG2,…,IG n} is the interval granular space generated on the decision information system. and For a given threshold pair (β, α) ((0≤β<α≤1), the lower approximation and upper approximation of X to R are defined as follows:

[0075]

[0076] Step S3: obtaining a threshold pair by a three-branch approximation method of the shadow set, and obtaining the average blur of the interval particle shadow set according to the threshold pair;

[0077] Average blurriness of interval-granular shadow set The calculation formula is:

[0078]

[0079] In the formula, That is, the ratio of the total number of samples with 4 times the membership between the threshold pairs to the total number of samples in U, where U is a finite sample set. is the membership of sample x in IG, x is a sample in IG, Equal to m(IG); β * ,α * is the threshold pair (β * ,α * ); m(IG) is the membership degree of each interval particle.

[0080] In the three-branch approximation method of the shadow set, constants m1 and m2 are used to control the threshold pair (β * ,α * ), the formula for obtaining the threshold pair is:

[0081]

[0082] In the formula, m1 and m2 satisfy: 0 <m1≤0.5、0.5≤m2<1、m1+m2=1。

[0083] Step S4: obtaining a threshold pair corresponding to the minimum blur loss between the average blur of the interval particle set and the average blur of the interval particle shadow set as the optimal threshold pair;

[0084] Average fuzziness of interval granular set The calculation formula is:

[0085]

[0086] In the formula, ξ(IG)=4m(IG)(1-m(IG)).

[0087] The calculation formula of the membership degree m(IG) of each interval particle in the average fuzziness of the interval particle set and the average fuzziness of the interval particle shadow set is:

[0088]

[0089] In the formula, μ l (IG i ) means IG i Purity, Among them, f(x,d) is a mapping function; k(IG) is the label of IG; ρ(IG i ) is IG i The local density of Among them, d c is a constant, d ij Indicates IG i Center and IG i Inner sample x j The distance between.

[0090] The objective function of minimizing the fuzzy loss is specifically:

[0091]

[0092] In the formula, for:

[0093]

[0094] The threshold pair (β * ,α * ) is traversed and calculated, and the threshold pair (β * ,α * ) as the optimal threshold pair.

[0095] Step S5: According to the optimal threshold pair, the interval particle neighborhood of the prediction object is identified, and the prediction object is classified. The specific process is as follows:

[0096] Step S51: Obtain the distance between the predicted object and the center of the interval particle, and sort them from near to far according to the distance, and obtain the distance set DIS = {d1, d2, d3, ..., d n};

[0097] The calculation formula for obtaining the distance between the predicted object and the center of the interval particle is:

[0098]

[0099] Where Δ(·) represents the Euclidean distance function; c i Show IG i The center point of Indicates IG i The proportion of samples included in IGs to the samples included in all IGs.

[0100] Step S52: Select K nearest interval particles as the interval particle neighborhood of the prediction object x relative to R And the labels of each interval grain in the neighborhood of the interval grain are used as the membership of the prediction object;

[0101] The membership calculation formula is:

[0102]

[0103] Where l(IG) is the label of IG, is the interval particle neighborhood of x relative to R, is the number of interval particles in the neighborhood of the interval particle; is the sum of the particle labels in each interval.

[0104] Step S53: According to the membership of the predicted object, the predicted object is classified into three categories by using the optimal threshold pair. Specifically, according to the threshold pair (β * ,α * ) The three classification rules obtained can be expressed as:

[0105] When v(x test )≥α * When v(x test )≤β * When β * ≤v(x test )≤α * When , the prediction object is delayed in decision making.

[0106] The following is an experimental simulation of the method of the present invention compared with the existing method.

[0107] In the simulation process of this experiment, 12 decision information system information as shown in Table 1 are selected.

[0108]

[0109] Table 1

[0110] Four widely used machine learning metrics were calculated in the experimental simulation: Accuracy, Precision, Recall and F1 score. The larger the value of the metric, the better the classification performance. The Wilcoxon rank-sum test was used to determine whether there were significant differences between classifiers. The performance of the proposed method was verified in terms of noise resistance and stability. A 10-fold cross-validation method was used in each experiment to reduce the risk of inflated performance metrics due to overfitting and ensure an accurate assessment of the true generalization ability of the proposed method.

[0111]

[0112]

[0113] Table 2

[0114] As shown in Table 2 above, the Win / Loss indicator represents the win / loss ratio of the present invention when compared pairwise with existing algorithms. The p-value quantifies the difference between the present invention and the comparison method; p-value < 0.05 indicates that the difference is statistically significant, otherwise there is no statistical difference. Finally, the Rank indicator reflects the average ranking, where a higher value indicates a more effective algorithm. As shown in Table 3, the present invention won 318 out of 336 comparisons with existing algorithms. In addition, based on p-value, the present invention showed statistically significant differences from all compared algorithms. Regarding the overall ranking, the present invention (3WD-IGNRS) won the first place, followed by KNN and traditional SVM.

[0115] For the evaluation of noise resistance, the present invention is compared with three state-of-the-art classifiers: GBKNN (granular ball KNN classifier), ACC-GBKNN (accelerated granular ball KNN classifier) ​​and GBKNN++ (a fast and stable granular ball KNN classifier). The evaluation process includes the following steps: (1) randomly selecting samples from each dataset and changing their labels to introduce noise; (2) performing 10-fold cross validation on datasets with different noise ratios to measure the robustness of these classifiers based on test accuracy. The results are shown in the heat map. Figures 5 to 8 As shown in , the test accuracy ranking of each classifier under different data sets and label noise ratios is intuitively shown. For example, on the "breast cancer" data set with a label noise ratio of 10%, the present invention obtains the highest test accuracy, as shown in Figure 5 Ranked 1 in the chart. Figures 5 to 8 It can be seen that the present invention performs best on most data sets. No matter under various noise ratios such as 10%, 20%, 30% or 40%, the present invention outperforms GBKNN, ACC-GBKNN and GBKNN++ in terms of test accuracy.

[0116] For the evaluation of stability, the present invention is compared with three state-of-the-art classifiers: GBKNN, ACC-GBKNN and GBKNN++. All classifiers are cross-validated with 10 folds. The average, minimum and maximum test accuracy are considered to comprehensively evaluate their performance. Error bars are used to intuitively represent the experimental results, where the center line represents the average test accuracy, and the top and bottom lines correspond to the maximum and minimum test accuracy obtained by 10 times of 10-fold cross validation. The data partitioning remains consistent throughout the evaluation process. When the test is repeated on the same data set, the present invention has the highest classification stability on most data sets, outperforming the other three classifiers.

[0117] The present invention can be used in various real-time applications. In the selected UCI dataset, the breast cancer dataset contains 9 attributes extracted from images to identify different breast cancer types. These attributes come from breast cancer images, each of which is labeled with the breast cancer type. As shown in Table 3 below, A_1 to A_9 represent continuous attributes, and D is a label column, where 0 and 1 represent benign or malignant breast cancer.

[0118] A_1 A_2 A_3 … A_9 D X_1 5 1 1 … 1 1 X_2 5 4 4 … 1 1 … … … … … … … X_699 4 8 8 … 1 0

[0119] Table 3

[0120] Experiments show that the present invention is superior to other classifiers. Several existing algorithms with good performance and representativeness are selected for comparison. The comparison results are as follows: Figure 2 As shown. Analysis shows that the combination with interval particles gives the present invention an advantage that cannot be matched by the existing three classifiers. The classification process combines the shadow set and the proposed classification rules, which provides further advantages over the existing particle-sphere classifier. In addition, the present invention is compared with the SVM algorithm, which has the best effect among the existing algorithms, to more comprehensively illustrate the advantages of the present invention.

[0121] Although the embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art may make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations are all within the scope defined by the appended claims.

Claims

1. A classification method based on interval granular neighborhood rough set three-branch decision, characterized in that: The steps include: Step 1: Obtain the data set and convert it into a four-tuple decision information system; Step 2: Obtain the interval granular set of the decision information system; Step 3: Obtain the threshold pair through the three-branch approximation method of the shadow set, and obtain the average blur of the interval particle shadow set according to the threshold pair; Step 4: Obtain the threshold pair corresponding to the minimum blur loss between the average blur of the interval particle set and the average blur of the interval particle shadow set as the optimal threshold pair; Step 5: Based on the optimal threshold pair, identify the interval particle neighborhood of the predicted object and classify the predicted object.

2. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 1, characterized in that: The specific process of step 2 is: Step 21: Obtain the granulation center of the decision information system through the DBSCAN clustering method; Step 22: Taking the granulation center as the center, perform interval granulation on the decision information system to generate interval granulation sets.

3. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 2, characterized in that: The specific method of step 21 is: first calculate the local density of each sample in the decision information system, and then select the sample with the largest local density as the granulation center.

4. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 3, characterized in that: The calculation formula of the local density of each sample is: Where U is a finite sample set; L(x) represents the label of x after being processed by the DBSCAN clustering method; Represents x i The Gaussian kernel density of Among them, d ij Represents x i With Ux j The distance between c Is a constant value.

5. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 1, characterized in that: The calculation formula of the average blur of the interval particle shadow set in step 3 is: In the formula, Among them, U is a finite sample set, is the membership of sample x in IG, x is a sample in IG, Equal to m(IG); β * ,α * is the threshold pair (β * ,α * ); m(IG) is the membership degree of each interval particle.

6. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 5, characterized in that: The formula for obtaining the threshold pair is: In the formula, m1 and m2 satisfy: 0 <m1≤0.5、0.5≤m2<1、m1+m2=1。 7. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 5 or 6, characterized in that: The calculation formula of the membership degree of the interval particle is: In the formula, μ l (IG i ) means IG i Purity, Where f(x,d) is a mapping function, f:U×(A∪{d})→V, V=V a ∪V d , V a is the set of values ​​of conditional attribute a, V d ={l1,l2,…,l z } is the set of values ​​or labels of d, l(IG) is the label of IG; ρ(IG i ) is IG i The local density of Among them, d c is a constant, d ij Indicates IG i Center and IG i Inner sample x j The distance between.

8. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 1, characterized in that: The specific process of step 5 is as follows: Step 51: Obtain the distance between the predicted object and the center of the interval particle, and sort the distances from near to far to obtain a distance set; Step 52: Select several interval grains with the closest distance as the interval grain neighborhood of the prediction object, and calculate the membership degree of the prediction object according to the label of each interval grain in the interval grain neighborhood; Step 53: According to the membership of the predicted object, the predicted object is classified into three categories through the optimal threshold pair.

9. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 8, characterized in that: The calculation formula for obtaining the distance between the predicted object and the center of the interval particle in step 51 is: Where Δ(·) represents the Euclidean distance function; c i Show IG i The center point of Indicates IG i The proportion of samples included in IGs to the samples included in all IGs.

10. The classification method based on interval granular neighborhood rough set three-branch decision as claimed in claim 8 or 9, characterized in that: In step 52, the membership degree calculation formula is: Where l(IG) is the label of IG, is the interval particle neighborhood of x relative to R, is the number of interval particles in the neighborhood of the interval particle; is the sum of the particle labels in each interval.

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