CN109009586B - A method for continuous decoding of electromyography based on the natural driving angle of artificial wrist joint - Google Patents

Abstract

The invention discloses a myoelectricity continuous decoding method for a man-machine natural driving angle of a prosthetic wrist joint, which enables a disabled person to imagine that a missing hand and a healthy hand of the disabled person do wrist joint movement with the same angle, and collects surface myoelectricity signals of the forearm of the disabled person and the movement angle of a healthy side wrist joint so as to establish a surface myoelectricity signal continuous decoding model for the man-machine natural driving angle of the prosthetic wrist joint. The invention has simple operation and high accuracy. The three-dimensional motion capture system can simultaneously realize high resolution and high capture frequency, and the joint angle calculated by the three-dimensional motion capture system has high accuracy; compared with the traditional wearable angle sensor, the wearable angle sensor has the advantages that compression interference on surface muscle electrical signals is avoided; the three-dimensional motion capture device is provided with an interface which is synchronously collected with an electromyograph, and can realize simultaneous collection of three-dimensional motion capture angles and surface electromyographic signals. In addition, the sampling frequency of the electromyograph is 2048Hz, and the change condition of the surface electromyogram signal can be collected in real time.

Description

A method for continuous decoding of electromyography based on the natural driving angle of artificial wrist joint

technical field

The invention belongs to the technical field of intelligent prosthetic hand and biomechanical integration, and relates to an electromyographic continuous decoding method for the natural driving angle of a prosthetic wrist joint of a human and a machine.

Background technique

According to the latest statistics from the China Disabled Persons' Federation, there are about 24.72 million people with physical disabilities in my country, including tens of millions of people with hand disabilities. The lack of hand function not only affects the life and work of the disabled, but also brings a heavy blow to their psychology. The traditional prosthetic hand only has the function of modification and cannot meet the needs of its daily life. The emergence of intelligent prosthetic hands makes up for the deficiencies of traditional prosthetic hands. Among them, myoelectric-controlled prosthetic hands have become a research hotspot because of their convenient wearing, accurate control and powerful functions.

Human surface EMG is a kind of bioelectric signal, which can objectively reflect the movement state of the human body and will be generated ahead of the actual action. It is predictable and can realize the perception of human movement intention. Most of the existing EMG prosthetic hands focus on the use of surface EMG signals to identify human hand movements and predict the grasping action of the prosthetic hand. However, during the prosthetic hand movement, the driving angle of the wrist joint largely determines the prosthetic hand. Therefore, in order to achieve better anthropomorphism of the prosthetic hand, it is extremely important to use the residual surface EMG signal of the arm to decode the natural driving angle of the artificial wrist joint. Based on this, it is the key point of current research to continuously decode the motion angle of the wrist joint by using the EMG signal on the arm surface to provide a suitable natural driving angle of the artificial wrist joint.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the above-mentioned shortcomings of the prior art, and to provide a method for continuous decoding of myoelectricity of a prosthetic wrist joint man-machine natural drive angle, which allows the disabled to imagine that his missing hand and his healthy hand make wrist joint movements of the same angle. , at this time, the surface EMG signal of the forearm of the disabled residual limb and the movement angle of the unaffected wrist joint are collected, so as to establish the surface EMG signal to continuously decode the human-machine natural driving angle model of the artificial wrist joint. Realize the continuous decoding of the human-machine natural driving angle of the artificial wrist joint by using the surface electromyographic signal of the residual limb forearm, so as to meet the daily needs of patients with hand disabilities.

To achieve the above object, the present invention adopts the following technical solutions to realize:

A method for continuously decoding the human-machine natural driving angle of a false wrist joint by an electromyogram signal on the surface of a human arm, comprising the following steps:

The first step: use the motion capture system to record the three-dimensional coordinates of the unaffected wrist joint movement, and calculate the wrist bending/extension angle through the kinematics modeling method of the human wrist joint.

In the above method, a reasonable wrist motion capture scheme is selected, a local coordinate system of the wrist joint is established, a wrist joint motion model is established, and a kinematic method is used to calculate the angle change of the wrist joint during the bending and extension process. Finally, the formula for the flexion and extension angle of the wrist joint is obtained as follows:

θ=arccos(T·i ₂ ·i ₁ )

In the formula, T is the transformation matrix from the local coordinate system of the wrist joint to the local coordinate system of the elbow joint, and i ₁ and i ₂ are the unit vectors of the sagittal axis direction of the elbow joint and the wrist joint, respectively.

Step 2: Use the EMG acquisition instrument to simultaneously collect the surface EMG signals of the six muscles on the remaining side of the forearm. The six remaining muscles are extensor carpi radialis longus, flexor carpi radialis longus, extensor carpi ulnaris longus, flexor carpi ulnaris, extensor digitorum common, and flexor digitorum superficialis.

The third step: preprocessing and feature extraction on the collected six-channel surface EMG signals. Since the sampling frequency of the surface EMG is 2048Hz and the sampling frequency of the 3D motion capture system is 100Hz, the eigenvalues of the surface EMG signal are resampled to achieve the same sampling frequency of the surface EMG signal and the wrist kinematics data.

Step 4: Using the method of machine learning, a BP neural network is established to realize the continuous decoding of the bending/extending angle of the wrist joint by the surface EMG signal of the human arm. First set the network parameters of the BP neural network, secondly train the BP neural network, and finally test it.

In the above method, a three-layer BP neural network is constructed, the EMG activity intensity characteristic value of the surface EMG signal is extracted as the network input, the joint angle calculated by the wrist joint kinematics model is used as the network output, and 10 neurons are set in the middle layer. Each neuron uses a sigmoid action function.

Step 5: Collect the surface EMG signal of the residual forearm, and perform preprocessing and feature extraction on the collected surface EMG signal. Input the EMG activity intensity feature value into the wrist joint angle continuous decoding model, output the continuously changing wrist joint motion angle, and calculate the linear correlation coefficient between the joint angle predicted by the network and the joint angle calculated by kinematics, and determine the surface muscle of the human arm. Accuracy of electrical signals for continuous decoding of human-machine natural actuation angles of a prosthetic wrist joint.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention has simple operation and high precision. The three-dimensional motion capture system can achieve high resolution and high capture frequency at the same time, and the calculated joint angle has high accuracy; compared with traditional wearable angle sensors, it does not cause compressive interference to surface EMG signals; The interface for synchronous acquisition of electrical instruments can realize the simultaneous acquisition of three-dimensional motion capture angle and surface EMG signal acquisition. In addition, the sampling frequency of the EMG instrument is 2048Hz, which can collect the changes of surface EMG signals in real time.

The invention establishes a prediction model for continuously decoding the driving angle of the artificial wrist joint by the surface electromyography signal. The stretching and contraction of the skeletal muscle drives the movement of the wrist joint. During the muscle contraction process, the amplitude of the surface EMG signal corresponding to it will change differently, so the EMG activity intensity of the surface EMG signal can be used to continuously decode the artificial wrist. Joint man-machine natural drive angle. Let the disabled imagine the wrist joint of the missing hand and the healthy hand to perform the same movement synchronously. After the motor imagery training, the movement angle of the wrist joint on the sound side is used as the natural driving angle of the wrist joint of the prosthetic hand on the residual side. The input of the model is the surface EMG signal of the residual forearm, which avoids the individual differences caused by the modeling of the healthy person and the disabled person, so that the surface EMG signal can continuously decode the natural driving angle of the artificial wrist joint. It has potential application value in medical, ergonomics and other fields.

Description of drawings

Fig. 1 is a block diagram of the method for continuously decoding the natural driving angle of artificial wrist joint by the EMG signal on the arm surface;

Figure ₂ is _a schematic diagram of the position of the right upper limb marker point and the setting of the coordinate system; wherein P1 is the elbow joint, P2 is the radial side of the forearm, _P3 is the outer side of the wrist, _P4 is the inner side of the wrist, and _P5 is the middle finger of the right hand metacarpophalangeal joint;

Fig. 3 is the schematic diagram of the calculation result of wrist flexion and extension angle;

Figure 4 is the characteristic value of the EMG activity intensity of the arm's six-channel surface EMG signal;

Fig. 5 is the basic flow chart of BP neural network algorithm;

Figure 6 is the result of continuous decoding of the artificial wrist joint's natural driving angle of the artificial wrist joint by the EMG signal on the arm surface.

Detailed ways

Below in conjunction with accompanying drawing, the present invention is described in further detail:

Referring to Fig. 1, the present invention uses a three-dimensional motion capture system to record the kinematic data of the unaffected wrist joint bending and stretching process, and calculates the angle of the wrist joint bending and stretching; the electromyography instrument synchronously collects the surface electromyographic signal of the residual side forearm muscle, and is preprocessed. and feature extraction to obtain the EMG activity intensity feature; the EMG activity intensity feature is used as the input of the BP neural network, and the wrist flexion and extension angle is used as the output of the BP neural network, and the BP neural network is trained, and the error range is set to meet the error conditions. After stopping the iteration, a stable arm decoding artificial wrist joint man-machine natural driving angle model was obtained; finally, the active strength of the tested residual surface EMG signal was input, and the predicted artificial wrist joint man-machine natural driving angle was output. The specific implementation is as follows:

Step 1: Calculate the flexion and extension angle of the wrist joint from the kinematic data. The specific method is as follows:

(1) Wrist joint motion capture mark position selection and joint local coordinate system establishment:

Figure 2 shows the sticking scheme of the mark points on the right upper limb. In order to ensure that the mark points are not blocked, the subjects took a sitting position, the right forearm and forearm were raised horizontally and kept still, and the wrist joint was bent and stretched with the back of the hand upward. According to the principle of kinematics, each rigid body has 6 degrees of freedom in the 3-dimensional space. To determine the pose of the moving rigid body in the 3-dimensional space, it is necessary to know the position coordinates of three non-collinear points on the rigid body. Therefore, set a mark point at the elbow joint, denoted as P ₁ , set a mark point on the radial side of the forearm, denoted as P ₂ , set a mark point at the outer and inner side of the wrist, denoted as P ₃ and P ₄ , A mark point is set at the metacarpophalangeal joint of the middle finger of the right hand, denoted as P ₅ .

The local coordinate system of the elbow joint is shown in Figure 2:

The local coordinate origin of the elbow joint is P ₁ , the line connecting P ₁ and P ₂ is the x-axis, and the direction points to P ₂ ; the normal line of the plane formed by the three points P ₁ , P ₂ and P ₃ is the y-axis, and the direction points to the inside of the body; It can be seen from the right-hand rule that the normal vector of the plane formed by the x-axis and the y-axis is the z-axis, and the direction is upward. The unit vector calculation formulas for the x, y, and z axes are:

k ₁ =i ₁ ×j ₁

The local coordinate system of the wrist joint is shown in Figure 2:

The origin of the local coordinates of the wrist joint is the midpoint of the line connecting _P3 and P4, the line connecting the origin and _P5 is the x _- axis, and the direction points to _P5 ; the normal vector of the plane formed by the _three points _P3 , P4, and _P5 is the z-axis , the direction is downward; according to the right-hand rule, the normal vector of the plane formed by the x-axis and the z-axis is the y-axis, and the direction points to the inside of the body. The unit vector calculation formula for the x, y, and z axes is:

k ₂ =i ₂ ×j ₂

(2) Calculation of wrist joint movement angle:

Based on the local coordinate system of the elbow joint and the wrist joint, the flexion/extension angle of the wrist joint in the sagittal plane of the human body is solved, and the flexion/extension angle of the wrist is represented by θ.

θ=arccos(T·i ₂ ·i ₁ )

In the formula, T is the transformation matrix from the local coordinate system of the wrist joint to the local coordinate system of the elbow joint, and i ₁ and i ₂ are the unit vectors of the sagittal axis direction of the elbow joint and the wrist joint, respectively.

Figure 3 presents the change in wrist flexion/extension angle calculated by this method. The palm-hand level position is defined as 0 degrees, the bending angle is positive, the extension angle is negative, and the wrist joint bending and extension range of motion is -60° to 75°. It can be seen that the wrist bending/extending angle calculated by this method is reasonable and consistent. within the human hand's range of motion in flexion/extension.

The second step: use the electromyography instrument to simultaneously collect the surface electromyography signals of the six muscles related to the forearm stump. The specific method is as follows:

Analyzing the muscles of the forearm of the human hand, it was found that the extensor carpi radialis longus longus, the extensor carpi ulnaris longus and the extensor digitorum generalis were closely related to the wrist extension, and the flexor carpi radialis, flexor carpi ulnaris and flexor digitorum superficialis were closely related to the wrist joint. The bending action is closely related, so the above six muscles are selected as the surface EMG signal source. First, the subject's forearm was disinfected with alcohol to reduce the interference of the skin surface oil on the surface EMG signal; secondly, the differential electrodes were pasted on the surface of the six muscles along the direction of the muscle fibers, and the EMG signal zero point was set at the elbow joint; Finally, the trigger is used to realize the synchronous acquisition of the EMG and the 3D motion capture system.

Step 3: Preprocess the collected six-channel arm surface EMG signal, extract the EMG activity intensity feature, and finally resample the arm surface EMG signal activity intensity to unify the surface EMG signal and wrist joint angle value sampling frequency. The specific method is as follows:

(1) Preprocessing of the EMG signal on the arm surface:

The collected EMG signals on the arm surface are usually mixed with noise and interference, including inherent noise of the device, surrounding noise interference, 50Hz power frequency interference, and artifact noise. The effective frequency range of the surface EMG signal is 20-500Hz. In order to reduce the interference of the noise signal, a 4th-order Butterworth filter is used to perform 20-500Hz band-pass filtering on the surface EMG signal, and then the notch filter is used to remove the 50Hz power frequency interference. .

(2) Feature extraction of arm surface EMG signal:

In order to continuously decode the natural driving angle of the artificial wrist joint by the surface EMG signal of the arm, it is necessary to find the relationship between the strength of the surface EMG signal of the arm and the natural driving joint angle of the artificial hand, and the EMG activity intensity feature of the surface EMG signal can be extracted. . Using the envelope method, the filtered surface EMG signal is subjected to full-wave sorting, and then low-pass filtering is performed.

The fourth step: adopt the method of machine learning, establish a BP neural network, and realize the continuous decoding of the human-machine natural driving angle of the artificial wrist joint by the EMG signal on the surface of the arm. The specific method is as follows:

(1) Construction of BP neural network:

Usually, a three-layer BP neural network can solve most pattern recognition problems, so a three-layer BP neural network is constructed here. The input layer is the characteristic value of surface EMG, where b=6, that is, the input layer has 6 neuron nodes; the output layer is the wrist bending and stretching angle, that is, the output layer has 1 neuron node; the middle layer has 1 neuron node The number is determined by the following empirical publicity:

Among them, g is the number of nodes in the middle layer, b is the number of nodes in the input layer, c is the number of nodes in the output layer, and d=1-10 is an adjustment constant. Here, d=8 is taken, that is, g=10.

(2) Training of BP neural network:

In Figure 5, let the network input vector be X=[x ₁ x ₂ x ₃ x ₄ x ₅ x ₆ ] ^T , the network output vector be Y=[y] ^T , and the neuron output of the middle layer network is:

The output layer output is:

Among them, the neuron action function is:

Define the error function:

in,

N is the number of samples, m is the number of sample points in each sample, d _pi is the bending and extending angle of the wrist joint calculated from the kinematic data, y _pi is the bending and extending angle of the wrist joint estimated by the BP neural network, and q is the network layer. number.

Using the gradient descent method to find the local minimum of E, each connection weight needs to be corrected along the opposite direction of the derivative of E to the connection weight. If the error function is within the ideal range, stop the iteration, otherwise continue to correct the connection weights until the error is small enough.

(3) Test of BP neural network:

Input 3 sets of arm surface EMG eigenvalues to the trained BP neural network, and output 3 sets of predicted values of wrist flexion and extension angle. Calculate the correlation coefficient between the wrist flexion and extension angle input by BP neural network and the angle calculated by the real kinematic data captured by the 3D motion capture system to reflect the degree of linear correlation between the two. The formula for calculating the correlation coefficient is as follows:

Among them, Cov(X, Y) is the covariance of X and Y, and Var[X] and Var[Y] are the variances of X and Y, respectively. The correlation coefficient |ρ _xy |≤1, the closer |ρ _xy | is to 1, the higher the correlation between X and Y, the closer |ρ _xy | is to 0, the lower the correlation between X and Y.

Extracting the EMG activity intensity feature of the surface EMG signal of the arm, and using the BP neural network method to predict the decoding result of the natural driving angle of the artificial wrist joint is shown in Figure 6. It can be seen from the figure that this method can stably and effectively realize the continuous decoding of the wrist flexion and extension angle by the EMG signal on the arm surface, which can be used for the natural human-machine drive control of the EMG intelligent prosthetic hand.

The invention is a method for continuously decoding the natural driving angle of artificial wrist joint by the electromyographic signal on the arm surface, so as to realize the recognition of the bending and stretching driving angle of the artificial wrist joint through the amplitude change of the electromyographic signal on the surface of the forearm, and increase the anthropomorphic nature of the intelligent artificial hand. operate. This method extracts the superficial muscles of the six muscles of the extensor carpi radialis longus, flexor carpi radialis longus, extensor carpi ulnaris longus, flexor carpi ulnaris, extensor digitorum common, and flexor digitorum superficialis in the process of wrist flexion and extension The electrical signal, combined with the angle change value during the bending and extension process of the wrist joint, uses the BP neural network to establish a nonlinear mapping model to achieve the purpose of continuously decoding the natural driving angle of the artificial wrist joint by the EMG signal on the arm surface and flexibly controlling the motion of the artificial wrist joint. The model established by the invention is reliable and has a high accuracy rate of angle prediction, which is beneficial for patients with hand disabilities to better use the intelligent prosthetic hand for natural operation, meets the functional requirements of the prosthetic hand in their life and work, and has good social and economic benefits.

The above content is only to illustrate the technical idea of the present invention, and cannot limit the protection scope of the present invention. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention all fall within the scope of the claims of the present invention. within the scope of protection.

Claims (4)

1. A myoelectric continuous decoding method for man-machine natural driving angles of artificial wrist joints is characterized by comprising the following steps:

step 1: the motion capture system is used for recording the three-dimensional coordinates of the movement of the wrist joint at the exercise side, and the wrist bending/stretching angle is calculated by a wrist joint kinematics modeling method, wherein the method comprises the following specific steps:

1-1) selecting mark positions of wrist joint motion capture mark points and establishing a joint local coordinate system:

setting a mark point at the elbow joint, and marking the mark point as P₁The radial side of the forearm is provided with a mark point marked as P₂A mark point is respectively arranged at the outer side and the inner side of the wrist and is marked as P₃And P₄Then, a mark point is arranged at the middle finger metacarpophalangeal joint of the right hand and is marked as P₅；

The local coordinate origin of the elbow joint is P₁，P₁And P₂The line is the x-axis and the direction is towards P₂(ii) a From P₁、P₂、P₃The normal line of the plane formed by the three points is the y axis, and the direction points to the inner side of the body; the vector is obtained by a right hand rule, a normal vector of a plane formed by the x axis and the y axis is a z axis, and the direction is upward; the unit vector calculation formulas of the x axis, the y axis and the z axis are respectively as follows:

k₁＝i₁×j₁

the origin of local coordinates of the wrist joint is P₃And P₄Midpoint of line, origin and P₅The line is the x-axis and the direction is towards P₅(ii) a From P₃、P₄、P₅The normal vector of the plane formed by the three points is the z axis, and the direction is downward; the right hand rule shows that the normal vector of a plane formed by the x axis and the z axis is the y axis, and the direction points to the inner side of the body; the unit vector calculation formula of the x, y and z axes is as follows:

k₂＝i₂×j₂

1-2) calculating the wrist joint motion angle:

solving the bending/stretching angle of the wrist joint in the human sagittal plane on the basis of the elbow joint and wrist joint local coordinate system, and expressing the bending/stretching angle of the wrist by theta;

θ＝arccos(T·i₂·i₁)

where T is the transformation matrix from the local coordinate system of the wrist joint to the local coordinate system of the elbow joint, i₁、i₂Respectively are unit vectors in sagittal axis directions of the elbow joint and the wrist joint;

step 2: synchronously acquiring surface electromyographic signals of six muscles on the residual side of the forearm by using an electromyographic acquisition instrument; the six residual muscles are extensor carpi radialis longus, flexor carpi radialis longus, extensor carpi ulnaris, flexor carpi ulnaris, extensor digitorum communis and flexor digitorum superficialis respectively;

and step 3: preprocessing and extracting characteristics of the collected six-channel surface electromyographic signals; resampling the surface electromyographic signal characteristic value to realize that the surface electromyographic signal and the wrist joint kinematic data have the same sampling frequency;

and 4, step 4: establishing a BP neural network by adopting a machine learning method to realize the continuous decoding of the wrist joint bending/stretching angle of the arm surface electromyographic signals; firstly, setting network parameters of a BP neural network, secondly training the BP neural network, and finally testing the BP neural network;

and 5: collecting surface electromyographic signals of the forearm of the disabled side, and preprocessing and extracting characteristics of the collected surface electromyographic signals; inputting the characteristic value of the myoelectricity activity intensity into a wrist joint angle continuous decoding model, outputting continuously changed wrist joint motion angles, calculating a linear correlation coefficient between a network prediction joint angle and a joint angle calculated by kinematics, and judging the accuracy of the human-computer natural driving angle of the artificial wrist joint continuously decoded by the myoelectricity signal on the surface of the arm.

2. The myoelectric continuous decoding method of the man-machine natural driving angle of the artificial wrist joint according to claim 1, characterized in that the specific method of step 3 is as follows:

3-1) preprocessing the myoelectric signal of the surface of the arm:

performing 20-500Hz band-pass filtering on the surface myoelectric signal by adopting a 4-order Butterworth filter, and removing 50Hz power frequency interference by utilizing notch filtering;

3-2) extracting the electromyographic signal characteristics of the surface of the arm:

and performing full-wave finishing on the filtered surface electromyogram signal by adopting an envelope curve method, performing low-pass filtering, and selecting a cutoff frequency of 4-10 Hz to obtain the peak value change of the surface electromyogram signal.

3. The method for continuously decoding the myoelectricity of the artificial wrist joint man-machine natural driving angle according to claim 1, wherein in step 4, a three-layer BP neural network is constructed, the myoelectricity activity intensity characteristic value of the surface myoelectricity signal is extracted as the network input, the joint angle calculated by a wrist joint kinematics model is used as the network output, 10 neurons are arranged in the middle layer, and each neuron adopts a Sigmoid action function.

4. The myoelectric continuous decoding method of man-machine natural driving angles of the artificial wrist joint according to claim 1 or 3, characterized in that the specific method of step 4 is as follows:

4-1) construction of BP neural network:

constructing a three-layer BP neural network; the input layer is a surface myoelectricity intensity characteristic value, and b is 6, namely the input layer has 6 neuron nodes; the output layer is at a wrist bending and stretching angle, namely the output layer is provided with 1 neuron node; the number of intermediate layer neuron nodes is determined by the following empirical disclosure:

g is the number of intermediate layer nodes, b is the number of input layer nodes, c is the number of output layer nodes, and d is 1-10 and is an adjusting constant; taking d as 8, namely g as 10;

4-2) training of BP neural network:

let the network input vector be X ═ X₁x₂x₃x₄x₅x₆]^TThe network output vector is Y ═ Y]^TThe neuron output of the intermediate layer network is:

the output of the output layer is:

wherein the neuron action function is:

defining an error function:

wherein,

n is the number of samples, m is the number of samples in each sample, d_piFor the wrist flexion-extension angle, y, calculated from kinematic data_piThe wrist joint bending and stretching angle estimated by the BP neural network, and q is the number of network layers;

searching a local minimum value of E by using a gradient descent method, wherein each connection weight needs to be corrected along the reverse direction of the derivative of the connection weight of E; if the error function is in the ideal range, stopping iteration, otherwise, continuously correcting the connection weight until the error is small enough;

4-3) testing of BP neural network:

inputting 3 groups of arm surface electromyographic signal characteristic values to a trained BP neural network, and outputting 3 groups of predicted values of wrist bending and stretching angles; calculating a correlation coefficient between a wrist bending and stretching angle input by the BP neural network and an angle obtained by real kinematics data calculation captured by a three-dimensional motion capture system to reflect the linear correlation degree between the wrist bending and stretching angle and the angle; the correlation coefficient calculation formula is as follows:

wherein Cov (X, Y) is the covariance of X and Y, Var [ X ]]And Var [ Y]The variances of X and Y, respectively; correlation coefficient | ρ_xy|≤1，|ρ_xyA closer | to 1 indicates a higher degree of correlation of X with Y, and | ρ_xyA closer | to 0 indicates a lower degree of correlation of X with Y.

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