A data classification method based on discrete Gaussian distribution probability limitation

Abstract

The present invention relates to a data classification method based on discrete Gaussian distribution probability limitation, which belongs to the field of simulation service platform data processing technology, and solves the problem that the efficiency and accuracy of the existing industrial design and virtual simulation service fields cannot meet the requirements for high-dimensional and large-scale data classification. The method includes: obtaining simulation data output by the simulation service platform to form a first data set to be classified; constructing a nested lattice system matching the first data set to be classified; the nested lattice system is obtained by combining a coarse lattice and a fine lattice; mapping each simulation data in the first data set to be classified to the fine lattice of the nested lattice system, and summarizing the obtained second simulation data to form a second data set to be classified; clustering the second data set to be classified, and dynamically adjusting the clustering of each cluster according to the probability distribution range of the discrete Gaussian distribution of each second simulation data under each cluster in each round of iterative optimization process; and realizing data classification.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation service platform data processing, and in particular to a data classification method based on discrete Gaussian distribution probability limitation. Background Art

[0002] In industrial design and virtual simulation services, it is often necessary to process high-dimensional, large-scale data sets. These data sets often contain complex structural information and a large number of details, making it difficult for traditional data processing and classification methods to meet actual needs in terms of computational efficiency and accuracy. At the same time, high computing costs and long processing cycles not only increase the operating costs of enterprises, but also extend the product development and listing cycles, limiting the market competitiveness of enterprises.

[0003] Although nested lattice theory has been widely used in fields such as data compression, signal processing and cryptography, its application in industrial design and virtual simulation services is still insufficient. In particular, when dealing with the relationship between fine lattices and coarse lattices, there is a lack of effective probability-limited calculation methods, which limits the further application of nested lattice theory in this field.

[0004] Therefore, the present application provides a data classification method based on discrete Gaussian distribution probability limitation to solve the problem that the efficiency and accuracy of high-dimensional and large-scale data classification in the prior art cannot meet the requirements. Summary of the invention

[0005] In view of the above analysis, an embodiment of the present invention aims to provide a data classification method based on discrete Gaussian distribution probability limitation, so as to solve the problem that the efficiency and accuracy of high-dimensional and large-scale data classification in the existing industrial design and virtual simulation service fields cannot meet the requirements.

[0006] The present invention discloses a data classification method based on discrete Gaussian distribution probability limitation, the method comprising:

[0007] Acquire simulation data output by the simulation service platform to form a first data set to be classified; construct a nested lattice system matching the first data set to be classified; the nested lattice system is obtained by combining a coarse lattice and a fine lattice;

[0008] Mapping each simulation data in the first data set to be classified to the fine lattice of the nested lattice system, respectively, and summarizing the obtained second simulation data to form a second data set to be classified;

[0009] Data clustering is performed on the second data set to be classified, and in each round of iterative optimization, the clustering of each cluster is dynamically adjusted according to the probability distribution range of the discrete Gaussian distribution of each second simulation data under each cluster, so as to achieve data classification.

[0010] On the basis of the above scheme, the present invention also makes the following improvements:

[0011] Furthermore, the probability distribution range of the discrete Gaussian distribution of each cluster is calculated as follows:

[0012] (1)

[0013] in, For fine lattice, is a coarse lattice, and ; Represents fine lattice Above As the cluster center, is a discrete Gaussian distribution with standard deviation; Representation lattice Data points on Represents a coarse lattice ; represents the quotient set between the fine lattice and the coarse lattice; Represents the planar factor of the coarse lattice.

[0014] Furthermore, the planar factor of the coarse lattice It is expressed as:

[0015] (2)

[0016] Where VNR represents the coarse lattice The volume noise ratio is coarse lattice The volume V is a function of The ratio of The data dimension representing the coarse lattice; represents the Theta series, ; By traversing the coarse lattice All lattice points in ,calculate Theta series is obtained by adding up the values ​​of .

[0017] Furthermore, the planar factor of the coarse lattice It can be expressed approximately as:

[0018] (3)

[0019] in, ; VNR represents coarse lattice The volume noise ratio is coarse lattice The volume V is a function of The ratio of The data dimension representing the coarse lattice.

[0020] Further, the second data set to be classified is clustered by executing:

[0021] Initialize the number of clusters to be classified, the cluster center and standard deviation of each cluster;

[0022] For each cluster, according to the standard deviation of the current cluster, the probability distribution range of the discrete Gaussian distribution of each second simulation data under the current cluster is calculated respectively; each second simulation data is respectively assigned to the cluster corresponding to the maximum value of the upper limit of the corresponding probability distribution range, so as to realize the cluster update, and update the cluster center and standard deviation of each cluster;

[0023] Jump to the step of respectively calculating the probability distribution range of the discrete Gaussian distribution of each second simulation data under the current cluster until the clustering termination condition is reached to obtain the data classification result.

[0024] Furthermore, the clustering termination condition is that the intra-cluster variance reaches a minimum, or the number of iterations reaches a preset upper limit.

[0025] Further, each simulation data in the first data set to be classified is mapped to a fine lattice of the nested lattice system, and the following is performed:

[0026] Traversing the lattice system, respectively finding the lattice points with the smallest Euclidean distance to each simulation data in the first data set to be classified in the fine lattice of the nested lattice system, and taking them as the lattice points corresponding to the corresponding simulation data;

[0027] An index corresponding to each simulation data in the first data set to be classified and a lattice point in the fine lattice is established respectively, and each simulation data is mapped to a corresponding lattice point in the fine lattice to form corresponding second simulation data.

[0028] Further, the constructing of a nested lattice system matching the first data set to be classified is performed:

[0029] Analyzing characteristics of a first data set to be classified and determining matching basis vectors;

[0030] According to the selected basis vectors, a generator matrix is ​​constructed; using the generator matrix, a fine lattice and a coarse lattice are constructed; the fine lattice and the coarse lattice are combined to generate a nested lattice system.

[0031] Further, a fine lattice is constructed by:

[0032] Arrange the selected basis vectors in columns and construct The generator matrix ;

[0033] Defining a fine lattice , to generate dimensional lattice ;in, represents the lattice point, Represents fine lattice The data dimension, represents the scaling factor, express dimensional integer space.

[0034] Further, a coarse lattice is constructed by:

[0035] Adjust the generator matrix , in the generated matrix Multiply by , recorded as , is a positive integer;

[0036] Defining the coarse lattice , to generate Coarse lattice , and coarse lattice Fine lattice A subset of .

[0037] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0038] The data classification method based on probability limitation of discrete Gaussian distribution provided by the present invention aims at the problem that the probability distribution after the discrete Gaussian distribution modulus operation on the coarse lattice in the nested lattice system is difficult to accurately analyze. A new probability limitation calculation method is proposed, which can accurately calculate the probability distribution range of the discrete Gaussian distribution modulus coarse lattice. On this basis, a complete data classification method based on probability limitation of discrete Gaussian distribution is provided, which can well handle the relationship between fine lattices and coarse lattices, and can effectively solve the problem that the efficiency and accuracy of high-dimensional and large-scale data classification in the existing industrial design and virtual simulation service fields cannot meet the requirements.

[0039] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components;

[0041] Figure 1 A flowchart of a data classification method based on discrete Gaussian distribution probability limitation provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0043] A specific embodiment 1 of the present invention discloses a data classification method based on discrete Gaussian distribution probability limitation. The flowchart of the method is as follows: Figure 1 As shown, the method specifically includes the following steps.

[0044] Step S1: Acquire simulation data output by a simulation service platform to form a first data set to be classified; and construct a nested lattice system matching the first data set to be classified.

[0045] The simulation service platform in this embodiment may involve multiple fields such as general machinery, aerospace, automotive industry, and electronic appliances, and may also involve various forms of simulation such as fluid simulation and electromagnetic simulation. In simulation service platforms in different fields and in different forms, as long as there is a need for data classification for the first data set output by the simulation, this solution is applicable. By classifying the data, a large amount of simulation data can be effectively managed and analyzed, improving the accessibility and analysis efficiency of the data. At the same time, data classification can help discover potential patterns in the data, so as to better understand the distribution patterns of the data. By classifying the simulation data, data features of different categories can also be identified, and then resources can be reasonably allocated to improve the efficiency and effect of the simulation. For example, in the field of electromagnetic simulation, it is necessary to classify the electromagnetic field data at each simulated spatial position to determine how many different electromagnetic field distributions exist in the space.

[0046] Preferably, step S1 can be implemented in the following manner.

[0047] Step S11: Analyze the characteristics of the first data set to be classified and determine matching basis vectors.

[0048] Specifically, the characteristics of the first data set to be classified include statistical characteristics and distribution patterns. The aggregation direction of the first data set is determined by analyzing the distribution pattern of the first data set to be classified; the aggregation degree of the first data set is determined by analyzing the statistical characteristics of the first data set to be classified; according to the aggregation direction and aggregation degree of the first data set, a plurality of different candidate basis vectors are designed, and the data dimension of each candidate basis vector is equal to the dimension of the simulation data; and a plurality of mutually orthogonal basis vectors matching the first data set to be classified are selected from the plurality of candidate basis vectors. In addition, methods such as principal component analysis (PCA) or independent component analysis (ICA) can also be used to assist in selecting basis vectors. That is, the first data set to be classified is subjected to feature extraction using principal component analysis or independent component analysis, and the extracted feature vectors are also used as candidate basis vectors to participate in the selection of basis vectors.

[0049] In the specific implementation process, the statistical characteristics of the first data set to be classified, such as mean, median, variance, standard deviation, skewness and kurtosis, and the distribution mode, such as normal distribution, uniform distribution or other distribution, can be used to analyze the central tendency and dispersion of the data. In addition, the statistical characteristics also include the covariance matrix of the data, which can be used to analyze the linear relationship between different features, which is crucial for selecting basis vectors and constructing lattice systems. The characteristics of the first data set to be classified can guide the selection of basis vectors to ensure that the basis vectors can better reflect the intrinsic structure of the data.

[0050] According to the above method, based on the characteristics of the first data set to be classified, combined with the principal component analysis method or the independent component analysis method, a set of appropriate basis vectors can be selected. , where the data dimension of each basis vector is , which is the same as the data dimension of each simulation data in the first data set. Since these basis vectors are orthogonal to each other and have the same data dimension, the redundancy and error of data representation can be effectively reduced.

[0051] Step S12: construct a generator matrix according to the selected basis vectors; construct a fine lattice and a coarse lattice using the generator matrix; and combine the fine lattice and the coarse lattice to generate a nested lattice system.

[0052] Arrange the selected basis vectors in columns and construct The generator matrix .make sure The column vectors of dimensional space basis. Using the generator matrix , defining the fine lattice , to generate dimensional lattice ,in, represents the lattice point, represents the scaling factor, express dimensional integer space, the appropriate scaling factor can be selected according to the actual situation of the first data set . Fine lattice Can cover the entire dimensional data space, and adjust its distribution and density in the space by selecting basis vectors.

[0053] Each lattice point has a unique coordinate representation on the fine lattice, and these coordinates are all integers. is a , which is defined by a set of linearly independent vector bases. For example, the fine lattice can be represented as the identity matrix [1 0; 0 1], whose vector bases are (1,0) and (0,1). Therefore, the fine lattice Each point on represents a potential location in the data space. Adjust the generator matrix , in the generated matrix Multiply by ( is a positive integer), denoted as , defining the coarse lattice , to generate Coarse lattice , and coarse lattice Fine lattice The fine lattice and the coarse lattice are combined to form a nested lattice system. In the nested lattice system, the fine lattice and coarse lattice There is an inclusion relationship between them, and the coarse lattice is strongly related to the fine lattice, that is, yes A subset of .

[0054] It should be noted that the discrete Gaussian distribution is a probability distribution defined on a lattice, and its properties are crucial to the performance of lattice-based algorithms. However, when the planar factor of the coarse lattice When the discrete Gaussian distribution on the fine lattice is small, it may show the characteristics of approximately uniform distribution after the coarse lattice operation, which increases the difficulty of accurately analyzing the probability distribution. To solve the above problem, this embodiment proposes a new probability-limited calculation method, which can calculate the probability of any given coarse lattice plane factor. , Standard Deviation and cluster centers , accurately calculate the discrete Gaussian distribution The specific process is as follows:

[0055] The nested lattice system is defined in the above manner. The fine lattice and the coarse lattice in the nested lattice system form a nested lattice pair, thereby determining dimensional nested lattice pair ,in For fine lattice, is a coarse lattice, and .

[0056] Calculate the coarse lattice plane factor: For a given , calculate the planar factor of the coarse lattice , the plane factor describes the degree of inhomogeneity of the discrete Gaussian distribution on the fine lattice after the coarse lattice operation.

[0057] Discrete Gaussian distribution is defined on the fine lattice Λ_F, for any cluster center , calculate the discrete Gaussian distribution The probability distribution range of . The specific formula is:

[0058] (1)

[0059] Representation lattice Data points on Represents a coarse lattice , that is, for the coarse lattice Perform modular operations; represents the quotient between the fine lattice and the coarse lattice, that is, the number of different cosets, which is usually equal to the ratio of the fine lattice volume to the coarse lattice volume, that is, .

[0060] This formula gives the upper and lower bounds of the probability that the discrete Gaussian distribution falls into any coset after coarse lattice operation. Using the above probability limit formula, we can analyze the probability of the discrete Gaussian distribution falling into any coset. and The probability distribution characteristics of the discrete Gaussian distribution modulo the coarse lattice under the value of . This information has important guiding significance for designing compression algorithms and signal processing protocols based on nested lattices.

[0061] In addition, in this embodiment, the planar factor of the coarse lattice can be calculated as follows In the plane factor calculation process, for a given standard deviation , in the coarse lattice Gaussian distribution is defined above. Gaussian distribution can describe the probability distribution of data points in the lattice space and can be used as a key parameter to measure the distribution width of data points. Used to control the width of the distribution. Analyze the characteristics of the Gaussian distribution, especially its performance at different VNR (volume noise ratio). VNR is defined as a specific function of the volume V of the coarse lattice and The ratio of .in, is a setting function about V, such as .

[0062] In this embodiment, the plane factor can be calculated based on the nested lattice theory and mathematical derivation. , and the plane factor is used as the evaluation factor of the coarse lattice In a given The specific calculation process is as follows: First, the coarse lattice The volume V, and then use the function of V and Calculate the volume noise ratio VNR. Use VNR to evaluate the diffusion and shape of Gaussian distribution in the lattice space, which provides a basis for the subsequent plane factor calculation. The geometric properties of The specific steps may include:

[0063] Calculate the coarse lattice Volume (Lattice System The absolute value of the determinant).

[0064] Calculate volume noise ratio The VNR reflects the relative relationship between the lattice volume and the width of the Gaussian distribution.

[0065] Calculating Theta Series ,in , by traversing the coarse lattice All points in ,calculate Theta series is obtained by accumulating the values ​​of Represents coarse lattice lattice points in .

[0066] Finally, according to Calculate the plane factor.

[0067] In addition, in actual calculations, due to the complexity of the Theta series, it can be simplified and approximated as follows. Specifically, by defining a Related functions (such as in the example To approximate the value of the Theta series. At this time, according to the VNR, the approximate value of the Theta series and the mathematical formula, the plane factor is calculated. .

[0068] Next, for the discrete Gaussian distribution The application of the probability distribution range is explained in detail as follows.

[0069] Step S2: Map each simulation data in the first data set to be classified to the fine lattice of the nested lattice system respectively, and aggregate the obtained second simulation data to form a second data set to be classified.

[0070] In a specific implementation process, each simulation data in the first data set to be classified is mapped to a corresponding lattice point in the fine lattice to form corresponding second simulation data, and all second simulation data are aggregated to form the second data set to be classified.

[0071] During the specific implementation, the lattice system is traversed, and the lattice points with the smallest Euclidean distance with each simulation data in the first data set to be classified are found in the fine lattice of the nested lattice system, and are used as the lattice points corresponding to the corresponding simulation data; the index corresponding to each simulation data in the first data set to be classified and the lattice point in the fine lattice is established, and each simulation data is mapped to the corresponding lattice point in the fine lattice to form the corresponding second simulation data. It should be noted that mapping the simulation data to the fine lattice is equivalent to performing a coordinate system conversion, and the coordinate points (corresponding to the lattice points) corresponding to the simulation data after the coordinate system conversion in the fine lattice are described as the second simulation data. All second simulation data are aggregated to form the second data set to be classified.

[0072] Step S3: clustering the second data set to be classified, and dynamically adjusting the clustering of each cluster according to the probability distribution range of the discrete Gaussian distribution of each second simulation data under each cluster in each round of iterative optimization process to achieve data classification.

[0073] The specific implementation process of step S3 is described below.

[0074] Step S31: Initialize the number of clusters to be classified, the cluster center and the standard deviation of each cluster. In the specific implementation process, the initial cluster center and the standard deviation can be selected randomly or according to a certain strategy.

[0075] Step S32: For each cluster, calculate the probability distribution range of the discrete Gaussian distribution of each second simulation data under the current cluster according to the standard deviation of the current cluster; assign each second simulation data to the cluster corresponding to the upper limit of the corresponding probability distribution range when it takes the maximum value, realize cluster update, and update the cluster center and standard deviation of each cluster.

[0076] In the specific implementation, the probability distribution range of the discrete Gaussian distribution of the second simulation data under the current cluster is calculated in the following manner: The lattice point of the fine lattice is represented by , according to the fine lattice With coarse lattice One-to-one correspondence between Corresponding to the coarse lattice The closest lattice point , to calculate the quotient in formula (1), that is, ; and according to the standard deviation of the current cluster, calculate the formula (1) , thus calculating the probability distribution range of the discrete Gaussian distribution of the second simulation data under the current cluster according to formula (1).

[0077] Step S33: Return to step S32 until the clustering termination condition is met (such as the intra-cluster variance reaches the minimum, the number of iterations reaches a preset upper limit, etc.), and the data classification result is obtained.

[0078] In addition, the quality and effect of clustering results can be evaluated by calculating clustering evaluation indicators (such as silhouette coefficient, Davies-Bouldin index, etc.).

[0079] In summary, the data classification method based on probability limitation of discrete Gaussian distribution provided in this embodiment aims at the problem that the probability distribution after the discrete Gaussian distribution modulus operation on the coarse lattice in the nested lattice system is difficult to accurately analyze. A new probability limitation calculation method is proposed, which can accurately calculate the probability distribution range of the discrete Gaussian distribution modulus coarse lattice. On this basis, a complete data classification method based on probability limitation of discrete Gaussian distribution is provided, which can well handle the relationship between fine lattices and coarse lattices, and can effectively solve the problem that the data classification method of the simulation service platform is difficult to adapt to complex, high-dimensional, large-scale data sets and the data classification accuracy is low.

[0080] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0081] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A data classification method based on discrete Gaussian distribution probability limitation, characterized in that: The method comprises: Acquire simulation data output by the simulation service platform to form a first data set to be classified; construct a nested lattice system matching the first data set to be classified; the nested lattice system is obtained by combining a coarse lattice and a fine lattice; Mapping each simulation data in the first data set to be classified to the fine lattice of the nested lattice system, respectively, and summarizing the obtained second simulation data to form a second data set to be classified; Data clustering is performed on the second data set to be classified, and in each round of iterative optimization, each second simulation data is respectively assigned to a cluster corresponding to the maximum value of the upper limit of the corresponding probability distribution range according to the probability distribution range of the discrete Gaussian distribution of each second simulation data under each cluster, and the clustering of each cluster is dynamically adjusted to achieve data classification; The probability distribution range of the discrete Gaussian distribution for each cluster is calculated as follows: (1) in, For fine lattice, is a coarse lattice, and ; Represents fine lattice Above As the cluster center, is the discrete Gaussian distribution with standard deviation; Representation lattice Data points on Represents a coarse lattice ; represents the quotient set between the fine lattice and the coarse lattice; represents the planar factor of the coarse lattice; Calculate the probability distribution range of the discrete Gaussian distribution of the second simulation data under each cluster and execute: The second simulation data The lattice point of the fine lattice is represented by , according to the fine lattice With coarse lattice One-to-one correspondence between Corresponding to the coarse lattice The closest lattice point ,calculate ; and based on the standard deviation of the current cluster, calculate , substitute into formula (1) and calculate the probability distribution range of the discrete Gaussian distribution of the current cluster.

2. The data classification method based on discrete Gaussian distribution probability limitation according to claim 1 is characterized in that: Planarity factor of coarse lattice It is expressed as: (2) Where VNR represents the coarse lattice The volume noise ratio is coarse lattice The volume V is a function of The ratio of The data dimension representing the coarse lattice; represents the Theta series, ; By traversing the coarse lattice All lattice points in ,calculate Theta series is obtained by adding up the values ​​of .

3. The data classification method based on discrete Gaussian distribution probability limitation according to claim 1 is characterized in that: Planarity factor of coarse lattice It can be expressed approximately as: (3) in, ; VNR represents coarse lattice The volume noise ratio is coarse lattice The volume V is a function of The ratio of The data dimension representing the coarse lattice.

4. The data classification method based on discrete Gaussian distribution probability limitation according to any one of claims 1 to 3, characterized in that: The second data set to be classified is clustered by executing: Initialize the number of clusters to be classified, the cluster center and standard deviation of each cluster; For each cluster, according to the standard deviation of the current cluster, the probability distribution range of the discrete Gaussian distribution of each second simulation data under the current cluster is calculated respectively; each second simulation data is respectively assigned to the cluster corresponding to the maximum value of the upper limit of the corresponding probability distribution range, so as to realize the cluster update, and update the cluster center and standard deviation of each cluster; Jump to the step of respectively calculating the probability distribution range of the discrete Gaussian distribution of each second simulation data under the current cluster until the clustering termination condition is reached to obtain the data classification result.

5. The data classification method based on discrete Gaussian distribution probability limitation according to claim 4 is characterized in that: The clustering termination condition is that the intra-cluster variance reaches a minimum, or the number of iterations reaches a preset upper limit.

6. The data classification method based on discrete Gaussian distribution probability limitation according to claim 5 is characterized in that: The step of mapping each simulation data in the first data set to be classified to the fine lattice of the nested lattice system is performed: Traversing the lattice system, respectively finding the lattice points with the smallest Euclidean distance to each simulation data in the first data set to be classified in the fine lattice of the nested lattice system, and taking them as the lattice points corresponding to the corresponding simulation data; An index corresponding to each simulation data in the first data set to be classified and a lattice point in the fine lattice is established respectively, and each simulation data is mapped to a corresponding lattice point in the fine lattice to form corresponding second simulation data.

7. The data classification method based on discrete Gaussian distribution probability limitation according to claim 6 is characterized in that: The constructing of a nested lattice system matching the first data set to be classified comprises: Analyzing characteristics of a first data set to be classified and determining matching basis vectors; According to the selected basis vectors, a generator matrix is ​​constructed; using the generator matrix, a fine lattice and a coarse lattice are constructed; the fine lattice and the coarse lattice are combined to generate a nested lattice system.

8. The data classification method based on discrete Gaussian distribution probability limitation according to claim 7 is characterized in that: The fine lattice is constructed by: Arrange the selected basis vectors in columns and construct The generator matrix ; Defining a fine lattice , to generate dimensional lattice ;in, represents the lattice point, Represents fine lattice The data dimension, represents the scaling factor, express dimensional integer space.

9. The data classification method based on discrete Gaussian distribution probability limitation according to claim 8, characterized in that: The coarse lattice is constructed by: Adjust the generator matrix , in the generated matrix Multiply by , recorded as , is a positive integer; Defining the coarse lattice , to generate Coarse lattice , and coarse lattice Fine lattice A subset of .

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