CN114529004A - Quantum clustering method based on nearest neighbor KNN and improved wave function - Google Patents

Abstract

The present invention provides a quantum clustering method based on the nearest neighbor KNN and improved wave function, which includes: acquiring and normalizing the original data of a group of sample points to be classified, and determining the quantum clustering model based on the nearest neighbor KNN. Input parameters, calculate the wave function parameters of all sample points, the wave function parameters include the scale parameters and shape parameters of the distribution that the calculated wave function obeys, calculate the potential energy surface of the quantum clustering, and determine the number of classifications and classifications according to the calculated potential energy surface boundary. The method proposed in the present invention inherits all the advantages of the quantum clustering method, and is more suitable for classifying data subject to Weibull distribution, providing a new choice for data classification, and at the same time, it does not require any artificially given input parameters, The input parameters of the quantum clustering model can be calculated without giving the classification labels of the sample data, which is highly practical and has high accuracy.

Description

Quantum clustering method based on nearest neighbor KNN and improved wave function

technical field

The invention belongs to the technical field of clustering and relates to data classification, in particular to a quantum clustering method based on nearest neighbor KNN and improved wave function.

Background technique

The quantum clustering method is a clustering model based on quantum mechanics. The core idea of this model method is that particles tend to be at the lowest potential energy value, while the same type of particles will gather at the same potential energy minimum value. Therefore, cluster analysis can be performed by calculating the potential energy surface where the particle is located. The minimum value point of each potential energy surface represents the center point of a cluster, and the number of minimum value points of the potential energy value represents the The number of clusters is determined, and finally the center point of the cluster to which the particle belongs is determined by the potential energy value. Compared with other clustering methods, quantum clustering does not need to give the number of clusters in advance, and is more sensitive to changes in data density. Small changes in the parameters input by itself will not affect the classification results. definite classification results. These advantages have given quantum clustering a lot of attention since its invention.

In quantum clustering, it is assumed that the wave function obeys a Gaussian distribution. However, in some cases, the data to be classified may not obey a normal distribution. In addition, although the quantum clustering method is often regarded as a parameter-free clustering method, the quantum clustering method still requires input model parameters. Currently, the KNN method and the "pattern search" method are commonly used to calculate the input model parameters. Among them, the nearest neighbor KNN method can calculate the input parameters without providing sample labels, but its calculation still needs to manually give the parameter of the number of neighbors, which makes it difficult for quantum clustering to become a parameter-free clustering method in the true sense. ; Although the "pattern search" method no longer requires artificially given parameters, this method needs to provide sample classification labels, which is contrary to the core feature of quantum clustering as unsupervised learning. Therefore, in order to be suitable for classifying the data subject to the Weibull distribution common in engineering, and at the same time make the quantum clustering method a parameter-free clustering method in the true sense, a quantum clustering method based on the nearest neighbor KNN and improved wave function is sought. It is very urgent and necessary to use a class method to determine the input parameters of quantum clustering model without artificially given parameters and without providing sample data classification labels, and to provide a new choice for data classification.

SUMMARY OF THE INVENTION

Aiming at the above-mentioned defects in the prior art, the present invention proposes a quantum clustering method based on nearest neighbor KNN and improved wave function. The method includes acquiring and normalizing raw data of a set of sample points to be classified, determining input parameters of a quantum clustering model based on the nearest neighbor KNN, and calculating wave function parameters of all sample points, where the wave function parameters include computational wave The function obeys the scale parameters and shape parameters of the distribution, calculates the potential energy surface of the quantum cluster, and determines the number of classifications and classification boundaries according to the calculated potential energy surface. The method proposed in the present invention inherits all the advantages of the quantum clustering method, and is more suitable for classifying data subject to Weibull distribution, providing a new choice for data classification, and at the same time, it does not require any artificially given input parameters, The input parameters of the quantum clustering model can be calculated without giving the classification labels of the sample data, which is highly practical and has high accuracy.

The present invention provides a quantum clustering method based on nearest neighbor KNN and improved wave function, which comprises the following steps:

S1. Obtain the raw data of a set of sample points to be classified and normalize them;

S2, determine the input parameter of the quantum clustering model based on the nearest neighbor KNN, and the input parameter is the variance s _weibull of the distribution that the wave function obeys;

S21. Calculate the nearest neighbor KNN results of all possible neighbors K in turn

S22. Calculate the increment of the nearest neighbor KNN result

的最大值

并找到所对应的近邻个数K_max；S23. Find the number of neighbors corresponding to the incremental maximum value of the nearest neighbor KNN result: find the nearest neighbor KNN result increment

the maximum value of

and find the corresponding number of neighbors K _max ;

根据步骤S23获得的K_max获取相应的最近邻KNN结果

并以此作为量子聚类模型的输入参数

S24. Obtain the nearest neighbor KNN results corresponding to the number of neighbors sought as the input parameters of the quantum clustering model: based on all the nearest neighbor KNN results obtained in step S21

Obtain the corresponding nearest neighbor KNN result according to the K _max obtained in step S23

and use it as the input parameter of the quantum clustering model

S3, according to the input parameter s _weibull provided in step S2, calculate the wave function parameters of all sample points, and the wave function parameters include the scale parameters and shape parameters of the distribution obeyed by the calculated wave function;

和步骤S2中所提供的输入参数s_weibull；S31. Obtain the i-th sample point normalized in step S1

and the input parameter _sweibull provided in step S2;

和输入参数s_weibull的商，利用两者的商和形状参数的关系公式获得第i个样本点

所对应的形状参数β_i：S32. Calculate the ith sample point

and the quotient of the input parameter s _weibull , use the relational formula between the quotient of the two and the shape parameter to obtain the i-th sample point

The corresponding shape parameter β _i :

Among them, Γ( ) represents the gamma function;

所对应的尺度参数η_i：S33. Calculate the ith sample point

The corresponding scale parameter η _i :

S34, repeat steps S31 to S33, calculate the shape parameter β _i and scale parameter η _i corresponding to all sample points;

S4. Calculate the potential energy surface of quantum clustering;

S41. Calculate the wave function ψ _wei (x):

S42. Calculate the potential energy surface function V _wei (x):

Among them, E represents the energy constant set by the quantum clustering model;

S5, determine the number of classifications and the classification boundary according to the potential energy surface calculated in step S4, the determined number of classifications is equal to the number of minimum value points of the potential energy surface function V _wei (x), and the determined classification boundary is determined by the extreme The potential energy saddle point and the potential energy maximum value point between the small value points are jointly determined.

Further, the step S21 specifically includes the following steps:

寻找距离该样本点最近的K个数据点

S211, normalized data for the i-th sample point to be classified

Find the K data points closest to the sample point

计算第i个待分类样本点和距离其最近的K个样本点的距离平均值y_i ^K，即S212, normalized data based on sample points to be classified

Calculate the average distance y _i ^K between the i-th sample point to be classified and the K nearest sample points, namely

其中N表示待分类样本点的个数；S213. Repeat steps S211 to S212 to calculate the average distances corresponding to all sample points to be classified from i=1 to i=N

where N represents the number of sample points to be classified;

的平均值，作为K个近邻个数下的最近邻KNN结果

即：S214. Calculate the average distance of all sample points to be classified

The average value of , as the nearest neighbor KNN result under the number of K nearest neighbors

which is:

S215. Repeat steps S211 to S214 to calculate all the nearest neighbor KNN results with the number of neighbors from K=1 to K=N-1

The step S22 specifically includes the following steps:

计算近邻个数为K下的最近邻KNN结果增量

即：S221. According to all the calculated nearest neighbor KNN results

Calculate the nearest neighbor KNN result increment when the number of neighbors is K

which is:

S222. Repeat step S221 to calculate the result increment of all nearest neighbors KNN whose number of neighbors is K=1 to K=N-2

Further, the step S1 specifically includes the following steps:

S11. Obtain a set of raw data X=[x ₁ , x ₂ , x ₃ ,...,x _N ] of the sample points to be classified;

S12, find the maximum value x _max and the minimum value x _min in the original data X of the sample points to be classified;

和最小值

S13. Set the maximum value of the normalized data

and minimum

其中

为：S14. Calculate the normalized data of the sample points to be classified based on the normalization method based on the normalization of the maximum and minimum values.

in

for:

Preferably, the calculated shape parameter β _i >2 is required in the step S32 .

Preferably, the wave function in the quantum clustering model in the step S2 obeys a Weibull distribution.

所对应的形状参数β_i。Preferably, in the step S32, a numerical solution is used to obtain the ith sample point

The corresponding shape parameter β _i .

Preferably, the normalization method in step S14 includes maximum and minimum normalization or zero-mean z-score normalization.

Compared with the prior art, the technical effect of the present invention is:

1. A quantum clustering method based on the nearest neighbor KNN and improved wave function designed by the present invention, compared with other existing clustering methods, the proposed method inherits all the advantages of the quantum clustering method, that is, it does not require advance The classification can be achieved by giving the number of clusters. Compared with other clustering methods, it is more sensitive to changes in data density. Small changes in the parameters input by itself will not affect the classification results, and it has a completely definite classification under the given parameters. Results; Compared with the existing quantum clustering methods, the proposed method, as a supplement to the quantum clustering method, is more suitable for classifying the data obeying Weibull distribution, and provides a new option for data classification.

2. A quantum clustering method based on the nearest neighbor KNN and the improved wave function designed by the present invention traverses the nearest neighbor KNN results of the possible number of neighbors, and determines the number of neighbors by calculating the maximum value of the increment of the nearest neighbor KNN results, And the corresponding nearest neighbor KNN result is used as the input parameter of the quantum clustering model, which is simple and practical and has high accuracy; the input parameters of the quantum clustering model can be calculated without any artificially given input parameters, and do not need to be given. The classification labels of sample data are greatly improved compared to the existing methods of parameter setting for quantum clustering.

Description of drawings

Other features, objects and advantages of the present application will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings.

Fig. 1 is the quantum clustering method flow chart of the present invention based on nearest neighbor KNN and improved wave function;

Fig. 2 is the input parameter flow chart of determining quantum clustering model of the present invention;

Fig. 3 is an example diagram of three types of one-dimensional sample data randomly generated according to the present invention;

4 is an example diagram of three types of one-dimensional sample data randomly generated after normalization of the present invention;

Fig. 5 is the graph of the corresponding sample data divided by the input parameter under different Weibull shape parameters of the present invention;

Fig. 6 is the quantum clustering potential energy curve example diagram that the present invention calculates;

7 is an example diagram of two types of one-dimensional sample data randomly generated according to the present invention;

8 is an example diagram of two types of one-dimensional sample data randomly generated after normalization of the present invention;

9 is an example diagram of the nearest neighbor KNN result under different numbers of neighbors of the present invention;

10 is an example diagram of the nearest neighbor KNN increment under different neighbor numbers of the present invention;

FIG. 11 is an example diagram of a quantum clustering potential energy curve calculated by the input parameters provided by the present invention.

Detailed ways

The present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the related invention, but not to limit the invention. In addition, it should be noted that, for the convenience of description, only the parts related to the related invention are shown in the drawings.

It should be noted that the embodiments in the present application and the features of the embodiments may be combined with each other in the case of no conflict. The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

Fig. 1 shows the quantum clustering method based on the nearest neighbor KNN and improved wave function of the present invention, and the method comprises the following steps:

S1. Obtain the raw data of a set of sample points to be classified and normalize them.

S11. Obtain a set of raw data X=[x ₁ , x ₂ , x ₃ , . . . , x _N ] of the sample points to be classified.

S12. Find the maximum value x _max and the minimum value x _min in the original data X of the sample points to be classified.

和最小值

步骤S212中要求计算得到的形状参数β_i＞2。S13. Set the maximum value of the normalized data

and minimum

In step S212, the calculated shape parameter β _i >2 is required.

其中

为：S14. Calculate the normalized data of the sample points to be classified based on the normalization method based on the normalization of the maximum and minimum values.

in

for:

Normalization methods include, but are not limited to, max-min normalization or zero-mean z-score normalization.

S2. Determine the input parameters of the quantum clustering model based on the nearest neighbor KNN. In the quantum clustering model, the wave function obeys the _Weibull distribution, and the input parameter is the variance s weibull of the distribution obeyed by the wave function. as shown in picture 2.

S21. Calculate the nearest neighbor KNN results of all possible neighbors K in turn

寻找距离该样本点最近的K个数据点

S211, normalized data for the i-th sample point to be classified

Find the K data points closest to the sample point

计算第i个待分类样本点和距离其最近的K个样本点的距离平均值y_i ^K，即S212, normalized data based on sample points to be classified

Calculate the average distance y _i ^K between the i-th sample point to be classified and the K nearest sample points, namely

其中N表示待分类样本点的个数。S213. Repeat steps S211 to S212 to calculate the average distances corresponding to all sample points to be classified from i=1 to i=N

where N represents the number of sample points to be classified.

的平均值，作为K个近邻个数下的最近邻KNN结果

即：S214. Calculate the average distance of all sample points to be classified

The average value of , as the nearest neighbor KNN result under the number of K nearest neighbors

which is:

S215. Repeat steps S211 to S214 to calculate all the nearest neighbor KNN results with the number of neighbors from K=1 to K=N-1

S22. Calculate the increment of the nearest neighbor KNN result

计算近邻个数为K下的最近邻KNN结果增量

即：S221. According to all the calculated nearest neighbor KNN results

Calculate the nearest neighbor KNN result increment when the number of neighbors is K

which is:

S222. Repeat step S221 to calculate the result increment of all nearest neighbors KNN whose number of neighbors is K=1 to K=N-2

的最大值

并找到所对应的近邻个数K_max。S23. Find the number of neighbors corresponding to the incremental maximum value of the nearest neighbor KNN result: find the nearest neighbor KNN result increment

the maximum value of

And find the corresponding number of neighbors K _max .

根据步骤S23获得的K_max获取相应的最近邻KNN结果

并以此作为量子聚类模型的输入参数

S24. Obtain the nearest neighbor KNN results corresponding to the number of neighbors sought as the input parameters of the quantum clustering model: based on all the nearest neighbor KNN results obtained in step S21

Obtain the corresponding nearest neighbor KNN result according to the K _max obtained in step S23

and use it as the input parameter of the quantum clustering model

S3. Calculate the wave function parameters of all sample points according to the input parameter s _weibull provided in step S2, where the wave function parameters include scale parameters and shape parameters of the distribution obeyed by the calculated wave function.

和步骤S2中所提供的输入参数s_weibull。S31. Obtain the i-th sample point normalized in step S1

and the input parameter _sweibull provided in step S2.

和输入参数s_weibull的商，利用两者的商和形状参数的关系公式采用数值解获得第i个样本点

所对应的形状参数β_i：S32. Calculate the ith sample point

and the quotient of the input parameter s _weibull , use the relationship between the quotient of the two and the shape parameter to use the numerical solution to obtain the i-th sample point

The corresponding shape parameter β _i :

where Γ(·) represents the gamma function.

The calculated shape parameter β _i >2 is required.

所对应的尺度参数η_i：S33. Calculate the ith sample point

The corresponding scale parameter η _i :

S34. Repeat steps S31 to S33 to calculate the shape parameter β _i and scale parameter η _i corresponding to all the sample points.

S4. Calculate the potential energy surface of the quantum clustering.

S41. Calculate the wave function ψ _wei (x):

S42. Calculate the potential energy surface function V _wei (x):

Among them, E represents the energy constant set by the quantum clustering model.

S5, determine the number of classifications and the classification boundary according to the potential energy surface calculated in step S4, the determined number of classifications is equal to the number of minimum value points of the potential energy surface function V _wei (x), and the determined classification boundary is determined by the extreme The potential energy saddle point and the potential energy maximum value point between the small value points are jointly determined.

The present invention will be further described in detail below in conjunction with specific cases.

In a specific embodiment, FIG. 3 is three types of one-dimensional data samples randomly generated according to three sets of different Weibull distribution parameters, which are used to illustrate the calculation process of the present method. In Figure 3, the first type of samples contains 50 data points, the second type of samples contains 30 data points, and the third type of samples contains 20 data points.

S1. Acquire 100 pieces of data to be classified in FIG. 3 and normalize the data.

和最小值

Set the maximum value of the normalized data

and minimum

The normalized data is calculated according to formula (1), and the normalized data is shown in FIG. 4 .

S2. Provide the input parameter s of the quantum clustering model, and the provided input parameter s is the variance s weibull of the _Weibull distribution obeyed by the wave function.

The K value of the nearest neighbor KNN method is set to 25, and this determines the provided input parameters.

S3. Calculate the wave function parameters of all sample points according to the input parameter s _weibull provided in step S2.

所对应的形状参数β_i，其中要求计算得到的形状参数β_i＞2；若令

则f_i随x_i的变化曲线如图5所示。The step S32 in the step S3 needs to use a numerical solution to obtain the sample points

The corresponding shape parameter β _i , which requires the calculated shape parameter β _i >2; if let

Then the change curve of f _i with _xi is shown in Figure 5.

S4. Calculate the potential energy surface of the quantum clustering, and the variation curve of the obtained potential energy surface function with x is shown in FIG. 6 .

S5. Determine the number of classifications and classification boundaries according to the potential energy surface calculated in step S4. As shown in Figure 6, it can be seen that the potential energy curve contains three minima, so this set of data is divided into three categories. The classification boundary is determined by the maximum points between the minimum values. In Figure 6, it can be seen that there are three sample data in the second type of sample data that are misclassified, while the other data are classified accurately. It can be seen that this method has a high classification accuracy.

In another specific embodiment, FIG. 7 shows two types of one-dimensional data samples randomly generated, which is used to illustrate the calculation process of determining the input parameters of the quantum clustering model based on the nearest neighbor KNN in step S2 of the method. In Figure 7, the first type of samples contains 50 data points, and the second type of samples contains 30 data points.

S1. Obtain the values of all data samples in Figure 7 and normalize them.

The maximum value in the data sample is 5.7283, and the minimum value is 0.6202;

The normalized data is calculated according to formula (1), and the normalized data is shown in FIG. 8 .

S21. Calculate the KNN result when the number of neighbors K ranges from 1 to 79 in sequence. Figure 9 shows the results of the nearest neighbor KNN under different numbers of neighbors K obtained by calculation.

S22. Calculate the increment of the nearest neighbor KNN result. Figure 10 shows the change curve of the calculated nearest neighbor KNN increment with different number of neighbors K.

是所有不同近邻个数K下的最近邻KNN结果增量的最大值。S23. Find the maximum value of the nearest neighbor KNN increment, and find the corresponding nearest neighbor number K _max . According to Figure 10, it can be seen that the increment of the nearest neighbor KNN result reaches the maximum value when K=29, that is,

is the maximum value of the nearest-neighbor KNN result increment for all different number of neighbors K.

以此作为量子聚类模型的输入参数s_weibull＝0.1108。S24. According to K _max =29 obtained in step S23, obtain the corresponding nearest neighbor KNN result calculated in step S21:

Take this as the input parameter of the quantum clustering model s weibull = _0.1108 .

Figure 11 shows the quantum clustering potential energy curve calculated according to the input parameters. The number of minimum points of the potential energy curve represents the number of classifications. The sample data belonging to the same minimum point is classified by quantum clustering. obtained samples of the same type.

Compared with other existing clustering methods, the proposed method inherits all the advantages of the quantum clustering method, that is, it does not need to be given in advance. The number of clusters can achieve classification, and it is more sensitive to changes in data density than other clustering methods. Small changes in the parameters input by itself will not affect the classification results, and the classification results can be completely determined under the given parameters; Compared with the existing quantum clustering methods, the proposed method, as a supplement to the quantum clustering method, is more suitable for classifying data subject to Weibull distribution, and provides a new choice for data classification; traversing the possible neighbors The number of nearest neighbor KNN results, the number of nearest neighbors is determined by calculating the maximum value of the increment of the nearest neighbor KNN result, and the corresponding nearest neighbor KNN result is used as the input parameter of the quantum clustering model, which is simple and practical and has high accuracy; The input parameters of the quantum clustering model can be calculated without artificially specifying any input parameters, and the classification labels of the sample data do not need to be given, which is a great improvement compared with the existing methods of specifying parameters for quantum clustering.

Finally, it should be noted that the above embodiments are only to illustrate rather than limit the technical solutions of the present invention, although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the present invention can still be modified or Equivalent replacements, and any modifications or partial replacements that do not depart from the spirit and scope of the present invention, shall all be included in the scope of the claims of the present invention.

Claims (7)

1. A quantum clustering method based on nearest neighbor KNN and improved wave function is characterized by comprising the following steps:

s1, acquiring and normalizing the original data of a group of sample points to be classified;

s2, determining input parameters of the quantum clustering model based on the nearest neighbor KNN, wherein the input parameters are the variance S of the distribution obeyed by the wave function_weibull；

S21, calculating the nearest neighbor KNN result of all possible neighbor numbers K in sequence

S22, calculating the increment of the nearest neighbor KNN result

S23, searching the neighbor number corresponding to the increment maximum value of the nearest neighbor KNN result: finding nearest neighbor KNN result increment

Maximum value of

And find the corresponding neighbor number K_max；

S24, acquiring a nearest neighbor KNN result corresponding to the number of the obtained neighbors as an input parameter of the quantum clustering model: based on all nearest neighbor KNN results obtained in step S21

K obtained according to step S23_maxObtaining corresponding nearest neighbor KNN result

And the parameters are used as input parameters of a quantum clustering model

S3, providing the input parameter S according to the step S2_weibullCalculating wave function parameters of all sample points, wherein the wave function parameters comprise scale parameters and shape parameters of distribution obeyed by the calculated wave function;

s31, obtaining the ith sample point normalized in the step S1

And the input parameter S provided in step S2_weibull；

S32, calculating the ith sample point

And an input parameter s_weibullThe ith sample point is obtained by using the quotient of the two and the relation formula of the shape parameters

Corresponding shape parameter beta_i：

Wherein Γ (·) represents a gamma function;

s33, calculating the ith sample point

Corresponding scale parameter eta_i：

S34, repeating the steps S31 to S33, and calculating the shape parameters beta corresponding to all the sample points_iAnd a scale parameter η_i；

S4, calculating the potential energy surface of the quantum cluster;

s41, calculating wave function psi_wei(x)：

S42, calculating a potential energy surface function V_wei(x)：

Wherein E represents an energy constant set by the quantum clustering model;

s5, determining the classification number and the classification boundary according to the potential energy surface calculated in the step S4, wherein the determined classification number is equal to the potential energy surface function V_wei(x) The determined classification boundary is determined by potential energy saddle points and potential energy maximum points between the minimum value points.

2. The quantum clustering method based on nearest neighbor KNN and improved wave function as claimed in claim 1, wherein the step S21 specifically comprises the following steps:

s211, normalizing data aiming at ith sample point to be classified

Searching K data points nearest to the sample point

S212, normalizing data based on sample points to be classified

Calculating the distance average value y of the ith sample point to be classified and K sample points nearest to the ith sample point to be classified_i ^KI.e. by

S213, repeating steps S211 to S212, and calculating the distance average corresponding to all sample points to be classified, where i is 1 to i is N

Wherein N represents the number of sample points to be classified;

s214, calculating the distance average value of all sample points to be classified

As the nearest neighbor KNN result for the number of K neighbors

Namely:

s215, repeating steps S211 to S214, and calculating all nearest neighbor KNN results with the number of neighbors K-1 to K-N-1

The step S22 specifically includes the following steps:

s221, all nearest neighbor KNN results obtained by calculation

Calculating nearest neighbor KNN result increment under K nearest neighbor number

Namely:

s222, repeatedly executing step S221, and calculating all nearest neighbor KNN result increments with the number of neighbors K-1 to K-N-2

3. The quantum clustering method based on nearest neighbor KNN and improved wave function as claimed in claim 1, wherein the step S1 specifically comprises the following steps:

s11, acquiring a group of classes to be classifiedRaw data X ═ X for sample points₁,x₂,x₃,...,x_N]；

S12, finding the maximum value X in the original data X of the sample points to be classified_maxAnd the minimum value x_min；

S13, setting the maximum value of the normalized data

And minimum value

S14, calculating the normalized data of the sample points to be classified based on the normalization method of the maximum and minimum value normalization

Wherein

Comprises the following steps:

4. the quantum clustering model of improved wave function as claimed in claim 1, wherein the step S32 requires the calculated shape parameter β_i＞2。

5. The quantum clustering model for improving the wave function as claimed in claim 1, wherein the wave function in the quantum clustering model in the step S2 follows a weibull distribution.

6. The quantum clustering model of improved wave function as claimed in claim 1, wherein the step S32 adopts numerical solution to obtain the i-th sample point

Corresponding shape parameter beta_i。

7. The method for determining the input parameter of the quantum clustering model of claim 1, wherein the normalization method in the step S14 comprises maximum-minimum normalization or zero-mean z-score normalization.

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