A maximum correlation coefficient method and system for measuring the correlation strength between variables

Abstract

The present invention belongs to the field of machine learning technology, and discloses a maximum correlation coefficient method and system for measuring the strength of association between variables. The idea of ​​piecewise linearity is realized through a partitioning method, and the Pearson correlation coefficient is used to measure the strength of association between variables, including linear correlation strength and nonlinear correlation strength. The Pearson correlation coefficient is used to calculate the correlation coefficient under each partitioning method, and the largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient between the variables, and this is proved by experiments. The present invention uses the idea of ​​piecewise linearity to describe the strength of association between variables through local linear correlation. The calculation is simple, the complexity is low, and it has universality and uniformity. The universality and uniformity of the present invention are verified through simulation data experiments. According to the experimental results of real data, it is shown that the measure can be used to measure the strength of association between variables. The use of this correlation strength information for feature analysis can well remove redundant features.

Description

Technical Field

[0001] The present invention belongs to the technical field of machine learning, and in particular relates to a maximum correlation coefficient method and system for measuring the correlation strength between variables. Background Art

[0002] In today's big data era, measuring the various forms of correlation between variables is a crucial issue, playing a crucial role in time series analysis and the construction of complex network systems, such as functional brain networks and gene interaction networks. Currently, a number of metrics exist that can quantitatively measure the strength of associations between variables. Traditional methods include the Pearson correlation coefficient, Spearman correlation coefficient, Kendall correlation coefficient, mutual information, and distance correlation coefficient. However, these methods each have drawbacks, such as measuring only linear relationships, low precision, requiring ordered variables, computational difficulties, and the fact that the distance between variables when independent is not necessarily zero.

[0003] To effectively measure the strength of association between variables, several improved methods have been proposed. For example, the Maximum Information Coefficient (MIC) is a widely used measure capable of detecting the strength of association between a wide range of correlations. However, it uses dynamic programming to find the optimal partitioning, resulting in high computational complexity. The R correlation coefficient, a measure based on mathematical statistics, is used to measure simple nonlinear relationships between variables. Its effectiveness is only demonstrated using a simple example, lacking experimental verification. The G-Squared coefficient, a piecewise linear regression method, tests the independence of two univariate random variables and measures the strength of their association. The G-Squared coefficient is difficult to estimate and requires certain regularity conditions to be met. A G-squared value of zero does not equate to independence between variables. The generalized Pearson correlation coefficient states that it can measure the strength of any nonlinear association if all possible maximum correlations are considered and an appropriate distance metric is used. However, this method primarily focuses on discrete variables.

[0004] Traditional metrics for measuring association strength include the Pearson correlation coefficient, Spearman correlation coefficient, Kendall correlation coefficient, mutual information, and distance correlation coefficient. Existing methods use improved traditional metrics to measure the strength of association between data. For example: 1) The maximum information coefficient calculates the strength of association between data using dynamic programming and mutual information; 2) The R correlation coefficient, a method based on mathematical statistics, can be used to measure the strength of association between data; 3) The G-Squared method, based on linear regression, is used to measure the independence of two random variables and the strength of their association; 4) The generalized Pearson correlation coefficient states that if all possible maximum correlations are considered and an appropriate distance metric is used, it can measure the strength of any nonlinear association. Therefore, how to reveal the strength of association between variables is an urgent problem that needs to be solved.

[0005] Through the above analysis, the problems and defects of the existing technology are as follows:

[0006] (1) The traditional linear correlation coefficient can only measure the linear correlation strength between variables; at the same time, the improved nonlinear correlation measure has a high computational complexity.

[0007] (2) Existing traditional measurement methods only measure linear relationships, have low accuracy, require ordered variables, are difficult to calculate, and the distance between variables is not necessarily 0 when the variables are independent.

[0008] (3) The maximum information coefficient uses a dynamic programming method to find the optimal partition, which has high computational complexity; the R correlation coefficient only uses a simple example to explain the effectiveness of the R correlation coefficient, and lacks experimental proof.

[0009] (4) The G-squared coefficient is difficult to estimate and requires some regularity conditions to be met. The value of G-squared is zero, which is not equivalent to the independence between variables. The generalized Pearson correlation coefficient mainly focuses on discrete variables.

[0010] The difficulty in solving the above problems and defects lies in how to use the linear correlation coefficient to measure the strength of nonlinear correlation; and how to simplify the calculation and reduce the computational complexity.

[0011] The significance of solving the above problems and defects is that it not only can use the linear correlation coefficient to measure the correlation strength between variables, including linear correlation strength and nonlinear correlation strength, but also simplifies the operation and reduces the computational complexity. Summary of the Invention

[0012] In response to the problems existing in the prior art, the present invention provides a maximum correlation coefficient method and system for measuring the correlation strength between variables, aiming to solve the technical problem that the linear correlation coefficient cannot measure the nonlinear correlation strength between variables and the problem that the prior art is inaccurate in measuring the nonlinear correlation strength.

[0013] The present invention is achieved as follows: a maximum correlation coefficient method for measuring the correlation strength between variables, wherein the maximum correlation coefficient method for measuring the correlation strength between variables realizes the piecewise linear idea through a division method, uses the Pearson correlation coefficient to measure the correlation strength between variables, and the correlation strength includes linear correlation strength and nonlinear correlation strength; uses the Pearson correlation coefficient to calculate the correlation coefficient under each division method, and the largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient between variables, and is proved by experiments.

[0014] Furthermore, the maximum correlation coefficient method for measuring the correlation strength between variables includes the following steps:

[0015] Step one: obtain data; the data given in the actual problem is the research object.

[0016] Step 2: Grid division: Grid division of the research object (data obtained in step 1) can achieve the purpose of piecewise linearity;

[0017] Step 3: Calculate the correlation coefficient. Calculate the correlation coefficient for each grid division in step 2. These correlation coefficients are used to measure the strength of the correlation between variables in each division.

[0018] Step 4: Calculate the maximum correlation coefficient. This maximum correlation coefficient can be used to measure the strength of the correlation between variables.

[0019] Furthermore, in step 1, for the data given in the actual problem, the variable x and the variable y are variables with a data size of n.

[0020] Furthermore, the grid division in step 2 includes:

[0021] For variables x and y in a dataset D with a data size of n, the K-means clustering method is used to implement variable grid partitioning. The K-means method divides the data of variables x and y in step 1 into different grids, where the K value determines the number of grids for each variable. Different K values ​​divide each variable space into different grids, and the two-dimensional data is divided into different grids, so that the data in the grid is piecewise linear. The maximum number of grids for grid partitioning is determined through experimental verification and analysis, and the maximum number of grids is MG = max{4, n α}, where n is the size of the data, α is a parameter and α∈[0,1]; the data of variable x is divided into s grids using the K-means clustering method; the data of variable y is divided into t grids using the K-means method, where The two-dimensional data is divided into s*t grids, and s is randomly selected on [2, MG / 2] to obtain various different grid divisions between variables.

[0022] Furthermore, the calculation of the correlation coefficient in step 3 includes:

[0023] Using the piecewise linear idea, the association strength under the division is measured by the weighted summation of the absolute value of the Pearson correlation coefficient of the data in each grid and the weight of each grid; the value of the Pearson correlation coefficient is between [-1, 1], and directly using the Pearson correlation coefficient for weighted summation will result in the cancellation of positive and negative values, and the result of the weighted summation cannot reflect the association between variables x and y; using the absolute value of the Pearson correlation coefficient for weighted summation can well reflect the association between variables x and y; according to step 2, different grid divisions between variables are obtained, and under each grid division, the correlation coefficient AC between variables x and y is calculated according to the following formula:

[0024] AC(x,y) (s，t) =∑ i w i |p i |;

[0025] Where i is the i-th grid containing data, w i is the weight of the i-th grid, p i is the Pearson correlation coefficient of the data in the i-th grid, w i Calculated according to the formula:

[0026]

[0027] Where s i is the area of ​​the i-th grid, ∑ j s j is the sum of the areas of all grids containing data; weight w i It is the process of normalizing the area so that the sum of the weights is 1, that is, ∑ i w i =1.

[0028] Furthermore, the calculation of the maximum correlation coefficient in step 4 includes:

[0029] The correlation coefficients for each division between variables are calculated by the formula. The largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient MAC, which is obtained according to the following formula:

[0030]

[0031] Another object of the present invention is to provide a system for measuring the maximum correlation coefficient of the correlation strength between variables using the method for measuring the maximum correlation coefficient of the correlation strength between variables, wherein the system for measuring the maximum correlation coefficient of the correlation strength between variables comprises:

[0032] The data acquisition module is used for the data given in the actual problem, where the variables x and y are variables with a data size of n;

[0033] A grid partitioning module is used to implement variable grid partitioning using the K-means clustering method for variables x and y in a data set D with a data size of n;

[0034] A correlation coefficient calculation module is used to measure the correlation strength under the division situation by using the piecewise linear idea and the weighted sum of the absolute value of the Pearson correlation coefficient of the data in each grid and the weight of each grid;

[0035] The maximum correlation coefficient calculation module is used to calculate the correlation coefficient of each division between variables through a formula, and the largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient MAC.

[0036] Another object of the present invention is to provide a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the following steps:

[0037] The idea of ​​piecewise linearity is realized through the division method, and the Pearson correlation coefficient is used to measure the association strength between variables, which includes linear association strength and nonlinear association strength. The Pearson correlation coefficient is used to calculate the correlation coefficient under each division method. The largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient between variables, and this is proved by experiments.

[0038] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor performs the following steps:

[0039] The idea of ​​piecewise linearity is realized through the division method, and the Pearson correlation coefficient is used to measure the association strength between variables, which includes linear association strength and nonlinear association strength. The Pearson correlation coefficient is used to calculate the correlation coefficient under each division method. The largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient between variables, and this is proved by experiments.

[0040] Another object of the present invention is to provide an information data processing terminal, which is used to implement the system of maximum correlation coefficient for measuring the correlation strength between variables.

[0041] Combining all of the above technical solutions, the advantages and positive effects of the present invention are as follows: The present invention provides a maximum correlation coefficient method for measuring the strength of association between variables. Based on the idea that nonlinear associations can be viewed as piecewise linear associations, it proposes a new measure for measuring the strength of association between two variables—the maximum correlation coefficient (MAC)—using the traditional K-means clustering method and the Pearson correlation coefficient. This new measure is simple to calculate. Simulation data experiments have verified its universality and uniformity. Experimental results based on real data show that this measure can be used to measure the strength of association between variables. Using this correlation strength information for feature analysis can effectively remove redundant features.

[0042] The present invention technically utilizes the concept of piecewise linearity to describe the strength of association between variables through local linear correlation; the present invention technically uses the Pearson correlation coefficient to measure the strength of association between variables, including linear and nonlinear association strength; the present invention technically proposes a new measure for measuring the strength of association between two variables, which is simple to calculate, low in complexity, and has universality and uniformity. The present invention utilizes the concept of piecewise linearity to use the Pearson correlation coefficient to measure the strength of association between variables, including linear and nonlinear association strength; the present invention uses the Pearson correlation coefficient to calculate the maximum correlation coefficient between variables, simplifying the calculation and being verified by experiments.

[0043] The present invention uses the K-means clustering method to divide each variable space into different grids to achieve grid division between variables. For the grids containing data obtained after division, the weight of each grid is the area of ​​each grid divided by the sum of the areas of all grids containing data. The idea of ​​piecewise linearity is applied, and the Pearson correlation coefficient is used to measure the correlation strength of the data in each grid after division. The weighted sum of the absolute value of the Pearson correlation coefficient of the data in each grid and the weight is calculated to obtain the correlation coefficient under each division method. The correlation coefficients under all division methods are calculated, and the largest correlation coefficient is the maximum correlation coefficient. The present invention realizes the use of the Pearson correlation coefficient to measure the correlation strength between variables, including linear and nonlinear, and simplifies the operation and reduces the computational complexity. The feasibility, uniformity and extensiveness of the method are verified using simulation data, and the effectiveness of the method is further verified using real data. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0045] Figure 1 This is a flow chart of a maximum correlation coefficient method for measuring the correlation strength between variables provided by an embodiment of the present invention.

[0046] Figure 2 This is a schematic diagram of the principle of a maximum correlation coefficient method for measuring the correlation strength between variables provided by an embodiment of the present invention.

[0047] Figure 3 This is a system structure diagram of the maximum correlation coefficient for measuring the correlation strength between variables provided by an embodiment of the present invention;

[0048] In the figure: 1. Data acquisition module; 2. Grid division module; 3. Correlation coefficient calculation module; 4. Maximum correlation coefficient calculation module.

[0049] Figure 4 This is a schematic diagram of a division method between two variables provided by an embodiment of the present invention.

[0050] Figure 5 This is a schematic diagram of the maximum correlation coefficient for each relationship type with different data sizes provided by an embodiment of the present invention.

[0051] Figure 6 1 is a schematic diagram of the maximum correlation coefficient of each relationship type with different noise levels provided by an embodiment of the present invention.

[0052] Figure 7 It is a heat map of the maximum correlation coefficient between any two features among the 39 features in the neuroblastoma methylation dataset provided by an embodiment of the present invention.

[0053] Figure 8A and Figure 8B This is a schematic diagram of the correlation strength information between features before and after using MAC to remove redundant features, provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0055] In response to the problems existing in the prior art, the present invention provides a maximum correlation coefficient method and system for measuring the correlation strength between variables. The present invention is described in detail below with reference to the accompanying drawings.

[0056] like Figure 1 As shown, a maximum correlation coefficient method for measuring the correlation strength between variables provided by an embodiment of the present invention includes the following steps:

[0057] S101, data acquisition;

[0058] S102, performing grid division;

[0059] S103, calculating the correlation coefficient;

[0060] S104, calculating the maximum correlation coefficient.

[0061] The principle diagram of the maximum correlation coefficient method for measuring the correlation strength between variables provided by the embodiment of the present invention is as follows: Figure 2 shown.

[0062] like Figure 3 As shown, the system for measuring the maximum correlation coefficient of the correlation strength between variables provided by the embodiment of the present invention includes:

[0063] Data acquisition module 1 is used for the data given in the actual problem, where variable x and variable y are variables with data size n respectively;

[0064] Grid partitioning module 2 is used to implement variable grid partitioning using K-means clustering method for variables x and y in a data set D with a data size of n;

[0065] The correlation coefficient calculation module 3 is used to use the piecewise linear idea to measure the correlation strength under the division situation by using the weighted sum of the absolute value of the Pearson correlation coefficient of the data in each grid and the weight of each grid;

[0066] The maximum correlation coefficient calculation module 4 is used to calculate the correlation coefficient of each division between variables through a formula, and the largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient MAC.

[0067] The technical solution of the present invention is further described below in conjunction with specific embodiments.

[0068] In order to solve the technical problem that the linear correlation coefficient cannot measure the nonlinear association strength between variables and the problem that the existing technology is inaccurate in measuring the nonlinear association strength, the present invention proposes a method for measuring the association strength between variables based on the maximum correlation coefficient. The piecewise linear idea is realized by the division method, and then the Pearson correlation coefficient is used to calculate the correlation coefficient under each division method. The largest correlation coefficient among these correlation coefficients is the maximum correlation coefficient between the variables.

[0069] The present invention adopts the idea of ​​piecewise linearity and uses the Pearson correlation coefficient to measure the association strength between variables, including linear association strength and nonlinear association strength; the maximum association coefficient between variables is calculated using the Pearson correlation coefficient, which simplifies the calculation and has been verified by experiments.

[0070] The maximum correlation coefficient algorithm is a grid-based algorithm that measures the correlation strength between variables.

[0071] The most important concepts of the entire algorithm are the following five:

[0072] 1. Piecewise linearity: For variables x and y, use the clustering method to perform grid division on variables x and y, and divide the data into their respective grids. That is, through grid division, the data in the grid will show local linear characteristics.

[0073] 2. Grid weight: For a grid i (i∈N) containing data obtained after grid division, the weight w of grid i i It is the area of ​​grid cell i divided by the sum of the areas of all grid cells containing data points.

[0074] 3. Grid coefficient: For a grid i containing data obtained after grid division, the Pearson correlation coefficient p of the data in grid i i The absolute value of is the grid coefficient of grid i.

[0075] 4. Correlation coefficient: For a grid i containing data obtained after grid division, the weight of grid i is w i , the grid coefficient of grid i is p i The absolute value of the grid, the weighted sum of all grid weights and grid coefficients is the correlation coefficient under each grid division.

[0076] 5. Maximum correlation coefficient: A number of correlation coefficients are calculated for different grid divisions, and the largest correlation coefficient is the maximum correlation coefficient.

[0077] The technical route of the present invention is as follows Figure 2 shown.

[0078] Figure 2 The key steps in the research are detailed in the research plan.

[0079] The technical solutions of the present invention are as follows:

[0080] (1) Data

[0081] For the data given in the actual problem, variable x and variable y are variables with data size n.

[0082] (2) Grid division

[0083] For variables x and y in a data set D with a data size of n, a simple K-means clustering method is used to implement grid division between variables.

[0084] The data in (1) is gridded and a simple K-means clustering method is used to implement variable grid division. The K-means method is used to divide the data of variables x and y in (1) into different grids, where the K value determines the number of grids for each variable. Different K values ​​divide each variable space into different grids, so that the two-dimensional data is divided into different grids, and the data in the grid is piecewise linear. The maximum number of grids for grid division is determined through experimental verification and analysis. The maximum number of grids (MG) is MG = max{4, n α}, where n is the size of the data, α is a parameter and α∈[0,1]. Use the K-means clustering method to divide the data of variable x into s grids. Use the K-means method to divide the data of variable y into t grids, where The two-dimensional data is divided into s*t grids. By randomly selecting s on [2, MG / 2], a variety of different grid divisions between variables can be obtained.

[0085] (3) Calculation of correlation coefficient

[0086] Using the piecewise linear idea, the association strength under this division is measured by the weighted summation of the absolute value of the Pearson correlation coefficient of the data in each grid and the weight of each grid. The reason why the Pearson correlation coefficient is not directly used for weighted summation is that the value of the Pearson correlation coefficient is between [-1, 1]. Therefore, directly using the Pearson correlation coefficient for weighted summation will result in the cancellation of positive and negative values. Therefore, the result of weighted summation cannot reflect the association between variables x and y. However, using the absolute value of the Pearson correlation coefficient for weighted summation can well reflect the association between variables x and y. According to (2), different grid divisions between variables can be obtained. Under each grid division, the association coefficient (AC) between variables x and y is calculated according to the following formula (1).

[0087] AC(x,y) (s，t) =∑ i w i |p i | (1)

[0088] In formula (1), i is the i-th grid containing data, w i is the weight of the i-th grid, p i is the Pearson correlation coefficient of the data in the i-th grid, w i It can be calculated according to formula (2).

[0089]

[0090] In formula (2), s i is the area of ​​the i-th grid, ∑ j s j is the sum of the areas of all grids containing data. In fact, in formula (2), the weight w i It is the process of normalizing the area so that the sum of the weights is 1, that is, ∑ i w i =1.

[0091] (4) Maximum correlation coefficient

[0092] The correlation coefficients of each partition between variables are calculated by formula (1). The largest correlation coefficient among these correlation coefficients is the maximum association coefficient (MAC), which is abbreviated as MAC. According to formula (3), it is obtained as follows:

[0093]

[0094] If a measure can measure the strength of associations across a wide range of data with a sufficient sample size, it is said to be universal; if it can give similar scores for different types of data relationships under the same noise, it is said to be uniform. Experiments have verified that MAC is both universal and uniform.

[0095] The technical effects of the present invention are further described below in conjunction with simulation experiments.

[0096] For a set of simulation data, the data in the variable x is 200 data generated between the domain [0,1]. There is a functional relationship between the variable y and the variable x, namely: y = sin(1.5πx 2 ), one way of grid division between variables is as follows Figure 4 As shown, and in Figure 4 Under the division method, the maximum correlation coefficient between variables can be obtained.

[0097] In order to further verify whether the MAC measurement method is uniform and universal, a simulation experiment is conducted using 10 specific relationship types as shown in Table 1. The corresponding relationship expressions are given in the table. i (where i is 1, 2, ..., n) is randomly generated between the domain [0, 1], and the data y in the variable y i (where i is 1, 2, ..., n) is derived from the equations given in Table 1, where n is the data size. If MAC can capture the strength of associations across a wide range of variables with a sufficient sample size, it is considered extensive. If MAC can give similar scores for different types of relationships with the same noise level, it is considered uniform. The data for different relationship types in Table 1 were used to verify the extensiveness and uniformity of MAC.

[0098] Table 1 Various types of relationships between two variables

[0099]

[0100]

[0101] Verify the universality. For each relationship type in Table 1, a simulation dataset with data size n of 10, 20, 40, 80, 100, 200, 400, 800, 1000, 2000, 4000, 8000, and 10000 is generated. The parameter α in the maximum number of grids is set to 0.5, that is, MG = max{4, n 0.5}, n is the data size. Repeat the calculation of the MAC between variables under each data scale under different relationship types 50 times, and take the average as the MAC between variables. The purpose of this is to reduce the influence of random factors on the experiment. The first nine categories in Table 1 are non-random relationship types, and the tenth category is a random relationship type. As the data size increases, the MAC between two variables under each relationship type is as follows: Figure 5 As shown, according to Figure 5 As can be seen from the legend, different types of polylines are used to represent different relationship types.

[0102] from Figure 5 It can be seen that for the first five simple relationship types, a smaller amount of data can accurately detect the strength of the association between them, that is, MAC tends to or is equal to 1. For the last four complex relationship types, a larger amount of data is required to effectively detect the strength of the association between them, and at this time, MAC tends to or is greater than 0.9. When the association between two variables is random, MAC will decrease as the data size increases until it tends to zero. Therefore, simple relationship types require a smaller amount of data or a smaller α value, while complex relationship types require a larger amount of data or a larger α value. In short, when the amount of data is larger (or smaller), the value of α can be smaller (or larger).

[0103] Depend on Figure 5 It can be seen that the MAC between two deterministic variables increases with increasing data size, while the MAC between two random variables decreases with increasing data size. Except for random relationship types, when the actual data size is much larger than 10,000, the maximum correlation coefficient (MAC) between two variables is infinitely close to 1. The MAC measurement method can be used to detect the strength of association between data under various relationship types, and therefore has good versatility.

[0104] Verify uniformity. As shown in Table 1, the data generated using the first nine relation types are used to demonstrate the uniformity of MAC. The data in variable x is uniformly generated between [0, 1]. Then, the data in variable y is obtained according to the relational expressions under each relation type in Table 1. This results in nine noise-free data sets, where the data size n is set to 4000. Uniform vertical noise is added to the data in variable y, thus generating some noisy data sets. 2 is the square of the Pearson correlation coefficient between the perturbed y-values ​​and the true y-values, in other words, 1-R 2is the noise added to the true y value. Then, noise levels of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90% and 100% are added to the above 9 noise-free datasets respectively. Considering the noise-free dataset, 11 datasets with different noise levels for each relationship type are obtained. The size of α determines the maximum number of grids. For different relationship types, the α value taken when measuring their association strength is different. Here, for simple relationship types such as linear, exponential and triangle composite function, α is set to 0.2. For slightly more complex relationship types such as parabolic and sine, α is set to 0.3. For more complex relationship types such as Periodic plus Linear, Sinusoidal, Sinusoidal and Sinusoidal, α is set to 0.5.

[0105] Applying the MAC measurement method to the datasets with different noise levels under these 9 relationship types, the MAC between two variables can be obtained. Repeat this step 50 times and take the average of the 50 MACs as the MAC between two variables with different noise levels under each relationship type. The purpose of taking the average is to reduce the influence of random factors on the experiment. As the noise level increases, the MAC between two variables under each relationship type is as follows. Figure 6 As shown, according to Figure 6 As can be seen from the legend, different types of broken lines are used to represent different types of relationships. Figure 6 As shown in the figure, under the same relationship type, the calculated MAC between two variables gradually decreases as the noise level increases. When the added noise level is the same, the MAC between two variables calculated under different relationship types is not much different. Therefore, the MAC measurement method has good uniformity.

[0106] By exploring the MAC between two variables of various relation types and data sizes, we found that as the data size increases, the corresponding MAC gradually increases to 1 or approaches 1 infinitely, indicating that the MAC measure has good universality. By exploring the MAC between two variables of the same relation type and different noise levels, we found that the MAC between two variables of the same relation type decreases with increasing noise level. However, the MAC between variables of different relation types with the same noise level is generally consistent, indicating that the MAC measure has good uniformity. Therefore, the MAC measure has good universality and uniformity.

[0107] The above simulation experiments prove that the MAC measurement method can be used to measure the association strength between variables and that the MAC measurement method is extensive and uniform. Below, we select a set of real data sets for experimental verification to illustrate the ability of MAC to measure the association strength between variables and how to use the association strength information between variables for feature analysis, thereby effectively achieving the purpose of removing redundant features.

[0108] The real data set selected in the present invention is a neuroblastoma methylation data set provided by Therapeutic Applicable Research To Generate Effective Treatments (TARGET, see: https: / / ocg.cancer.gov / programs / target). This methylation data set has 88 samples, labeled as the 5-year survival of neuroblastoma patients, where positive samples are marked as 1 and negative samples are marked as 0. In order to select those features that are effective for classification and recognition from a large number of features, the methylation data is first subjected to feature selection processing using the Fisher feature selection method. The Fisher score of each feature can be obtained. If the Fisher score of a feature is equal to or greater than 0.07, the feature is selected. Finally, 39 features were selected. The MAC measure is then used to measure the correlation strength between any two features among these 39 features. Feature analysis is performed based on the correlation strength information between the features, ultimately achieving the purpose of removing redundant features.

[0109] The MAC algorithm with α set to 0.45 is used to measure the association strength between any two of the 39 features. The results are as follows Figure 7 As shown. Figure 7 In the heat map, the value in the grid is the maximum correlation coefficient between the two features. The correlation strength between any two features among the 39 selected features can be expressed as Figure 8A Indicates that the node represents a feature, the number on the node represents which of the 39 features the feature is, and the edge represents that the MAC between them is equal to or greater than 0.5. When the MAC between two features is equal to or greater than 0.5, one of the features is considered redundant. If the degree of a node is equal to or greater than 4, it means that this node has a strong correlation with other nodes connected to this node, indicating that this node (i.e., feature) is a redundant node (i.e., redundant feature) of other nodes (i.e., other features). Delete these nodes (i.e., redundant features), and the remaining 6 nodes (i.e., features) are as follows Figure 8B As shown, there are no redundant features in the selected feature subset.

[0110] To verify that the MAC measure can effectively measure the strength of association between variables, an SVM classifier was trained using the six features selected using the MAC measure. Meanwhile, all 39 features selected were used to train the SVM classifier as a control experiment. To verify the MAC measure's ability to measure the strength of association between variables, another comparative experiment used the MIC measure to measure the strength of association between any two of the 39 features. Ultimately, 12 features were selected for training the SVM classifier. The MAC and MIC measures were used to measure the strength of association between features, and feature analysis was performed using the strength of association information between features. The classification results before and after removing redundant features are shown in Table 2. In Table 2, ACC is the accuracy, and AUC is the area under the ROC curve. Table 2 shows the following results: When the MAC measure is used to measure the strength of association between features, redundant features are removed based on the strength of association information between features, which not only reduces the number of features used to construct the SVM classification model but also improves the ACC and AUC of the model. When using the MIC metric to measure the strength of association between features, although the number of features used to build the SVM classification model is reduced and the model's ACC and AUC are improved, the ACC and AUC of the model using the MIC metric are still lower than those obtained using the MAC metric. Therefore, the MAC metric can effectively measure the strength of association between variables. Feature analysis based on the strength of association between variables achieves the goal of removing redundant features. The MAC metric performs better than the MIC metric in measuring the strength of association between features.

[0111] Table 2 Evaluation results of SVM classifiers before and after MAC and MIC redundancy removal

[0112]

[0113] Based on the idea that nonlinear associations can be viewed as piecewise linear associations, this paper proposes a new measure, the Maximum Correlation Coefficient (MAC), to measure the strength of association between two variables using the traditional K-means clustering method and the Pearson correlation coefficient. This new measure is computationally simple. Simulation data experiments validate its universality and uniformity. Experimental results with real data demonstrate its applicability to measuring the strength of associations between variables. Using this association strength information for feature analysis effectively removes redundant features.

[0114] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware, or any combination thereof. When implemented in whole or in part in the form of a computer program product, the computer program product includes one or more computer instructions. When the computer program instructions are loaded or executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)) method. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)).

[0115] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A maximum correlation coefficient method for measuring the strength of correlation between variables, characterized in that: The maximum correlation coefficient method for measuring the correlation strength between variables includes the following steps: Step 1: Acquire data; Step 2: Perform grid division; realize piecewise linear idea through division method; Step 3: Calculate the correlation coefficient; use the Pearson correlation coefficient to measure the correlation strength between variables, which includes linear correlation strength and nonlinear correlation strength; use the Pearson correlation coefficient to calculate the correlation coefficient under each division method; Step 4: Calculate the maximum correlation coefficient; the maximum correlation coefficient among the correlation coefficients is the maximum correlation coefficient between the variables, and prove it through experiments; The real dataset we chose is a neuroblastoma methylation dataset provided by Therapeutical Applicable Research To Generate Effective Treatments. This methylation dataset contains 88 samples, labeled as the 5-year survival of neuroblastoma patients, with positive samples marked as 1 and negative samples marked as 0. To select features that are effective for classification and recognition from a large number of features, we first used the Fisher feature selection method to perform feature selection on the methylation data to obtain the Fisher score of each feature. If the Fisher score of a feature is equal to or greater than 0.07, then the feature is selected. Finally, 39 features were selected. The MAC measure was then used to measure the correlation strength between any two features among these 39 features. Feature analysis was performed based on the correlation strength information between the features, ultimately achieving the goal of removing redundant features. The correlation coefficient AC in step 3 is calculated according to the following formula: AC(x,y) (s，t) =∑ i w i | p i |; In the formula, for the data given in the actual problem, variables x and y are variables with data size n; i is the i-th grid containing data, w i is the weight of the i-th grid, p i is the Pearson correlation coefficient of the data in the i-th grid, w i Calculated according to the formula: Where s i is the area of ​​the i-th grid, ∑ j s j is the sum of the areas of all grids containing data; weight w i It is the process of normalizing the area so that the sum of the weights is 1, ∑ i w i =1; The calculation of the maximum correlation coefficient in step 4 includes: calculating the correlation coefficients under each division between the variables by formula, and the largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient MAC, which is obtained according to the following formula:

2. The maximum correlation coefficient method for measuring the correlation strength between variables according to claim 1, characterized in that: The grid division in step 2 includes: for variables x and y in a data set D with a data size of n, using the K-means clustering method to implement variable grid division; the K-means method divides the data of variables x and y in step 1 into different grids, wherein the K value determines the number of grids for each variable division, and different K values ​​cause each variable space to be divided into different grids, and the two-dimensional data is divided into different grids, so that the data in the grid is piecewise linear; the maximum number of grids for grid division is determined through experimental verification and analysis, and the maximum number of grids is MG=max{4, n α }, where n is the size of the data, α is a parameter and α∈[0,1]; the data of variable x is divided into s grids using the K-means clustering method; the data of variable y is divided into t grids using the K-means method, where The two-dimensional data is divided into s*t grids, and s is randomly selected on [2, MG / 2] to obtain various different grid divisions between variables.

3. The maximum correlation coefficient method for measuring the correlation strength between variables according to claim 1, characterized in that: The calculation of the correlation coefficient in step three includes: using the piecewise linear idea, using the result of weighted summation of the absolute value of the Pearson correlation coefficient of the data in each grid and the weight of each grid to measure the correlation strength under the division situation; the value of the Pearson correlation coefficient is between [-1, 1], and directly using the Pearson correlation coefficient for weighted summation will result in the cancellation of positive and negative values, and the result of the weighted summation cannot reflect the correlation between variable x and variable y; using the absolute value of the Pearson correlation coefficient for weighted summation can well reflect the correlation between variable x and variable y; according to step two, different grid divisions between variables are obtained, and under each grid division, the correlation coefficient AC between variable x and variable y is calculated.

4. A system for implementing the maximum correlation coefficient of the method according to any one of claims 1 to 3 to measure the correlation strength between variables, characterized in that: include: The data acquisition module is used for the data given in the actual problem, where the variables x and y are variables with a data size of n; A grid partitioning module is used to implement variable grid partitioning using the K-means clustering method for variables x and y in a data set D with a data size of n; A correlation coefficient calculation module is used to measure the correlation strength under the division situation by using the piecewise linear idea and the weighted sum of the absolute value of the Pearson correlation coefficient of the data in each grid and the weight of each grid; The maximum correlation coefficient calculation module is used to calculate the correlation coefficient of each division between variables through a formula, and the largest correlation coefficient among the correlation coefficients is the maximum correlation coefficient MAC.

5. A computer device, characterized in that: The computer device includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the maximum correlation coefficient method for measuring the correlation strength between variables as claimed in any one of claims 1 to 3.

6. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor executes the maximum correlation coefficient method for measuring the correlation strength between variables according to any one of claims 1 to 3.

7. An information data processing terminal, characterized in that: The information data processing terminal is used to implement the system for measuring the maximum correlation coefficient of the correlation strength between variables as claimed in claim 4.

Images