# A Data Acquisition and Processing Method for Edge Computing Robotic Arm Behavior Recognition

Authors: Yinhuan Zhang; Qinkun Xiao; Xing Liu; Yongquan Wei; Chaoqin Chu; Jingyun Xue
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Edge computing refers to the use of an open platform on the side close to the object or data source to integrate network, computing, storage, and core application functions to provide the latest nearby services. With the development of edge computing, the cost of data acquisition has been reduced, and the efficiency has been improved. However, at present, there is no in-depth research on edge computing for robot arm behavior recognition. This paper aims to study the data acquisition and processing methods of robotic arm behavior recognition through edge computing technology. A gesture recognition method based on Cauchy distribution and grey correlation threshold is proposed, which improves the efficiency of data processing and has great research significance. In edge computing, the use of Cauchy distribution processing is more impressive; compared with empirical distribution, the algorithm optimization can reach at least 10%. Experiments show that the static gesture recognition method used in this paper is simple and high in recognition and has good robustness and the accuracy rate can basically reach more than 90%. In the case of different threshold values, when the gray correlation threshold is 0.75, the MAE value reaches the minimum value, which means that the gap between the predicted score and the actual score is the smallest, which means that the predicted result is accurate, which can prove that the recommendation of the algorithm has relatively superior performance.


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## Body

## 1. Introduction

The society is gradually entering the era of “big data”, and with the advent of cloud computing, its ability to operate and use big data collection is also increasing. Cloud computing is actively supported by advantages including low operating costs, low weight, and ease of use and maintenance. The cloud computing industry is actively developing in China. Edge computing was initially the primary technology to address 5G latency, but has recently been introduced into new areas such as IoT and the Internet. The problem of cloud computing can also be solved with the help of modern information technology. The intelligent services provided by advanced computer technology meet key requirements such as flexible connection, real-time operation, data upgrade, software intelligence and security, and data basic processing. Robotic arms are the most widely used robots. It exists in the construction, industrial, healthcare, entertainment, military, electronics, manufacturing, and space exploration industries. Robotic arms come in many different forms, but they all share common characteristics. The ability to select a course of action and precisely point-and-shoot in three-dimensional (or two-dimensional) space. The traditional mechanical arm can only perform simple repetitive actions such as translation and grabbing, but when the mechanical arm is combined with the information system, it can complete complex operations such as cooking and wine mixing. At this time, it is necessary to identify and analyze the complex motion behavior of the manipulator. However, the traditional data acquisition and processing methods cannot analyze the data quickly, which leads to low efficiency. Therefore, it is necessary to collect and process the data of manipulator behavior recognition based on edge calculation.Aiming at the data acquisition and processing of the manipulator, this paper has made great innovations in data acquisition and uploading. We first select the optimal threshold value, fully considering the accuracy of the recommendation achieved by the threshold value and the time-consuming situation and also consider the role of the threshold value in the subsequent selection of the number of neighbors. The optimal threshold is selected to realize the clustering of gray projects, which makes the internal common features of the projects prominent, and the external differences of the projects are relatively large. Calculating the similarity of items on the obtained clusters, and according to the fixed number of neighbors, sort the calculated similarities from large to small in turn and select a fixed number of neighbors. The scoring prediction and recommendation of the item are completed, and the performance of the recommendation algorithm is verified experimentally. We have done in-depth research on static gesture recognition based on multiparameter features from image acquisition to gesture recognition. The RGB-D image information is obtained by using the Kinect depth sensor, and then the gesture image is segmented by the adaptive depth threshold fused with skin color, and the corresponding preprocessing is performed to extract the outline of the gesture.


## 2. Related Work

With the emergence and popularity of Internet of Things (IoT) cloud services, edge computing, a new technology that requires data processing over the Internet, has emerged. Chakraborty proposed a local pattern descriptor in higher-order derivative space for face recognition. His proposed descriptor significantly reduced the extraction and matching time, while the recognition rate of the descriptor is almost comparable to the existing state-of-the-art methods [1]. Taleb’s paper presented a survey of mobile edge computing (MEC), outlined current standardization activities, and further elaborated on the challenges of open research [2]. Jiang proposed a robust trajectory tracking control method for robotic arms based on H control theory, and the field operation test further verified the engineering practicability of the control method in macro and micro aspects [3]. For the rapid picking of lilies, Jiang designed a mechanical arm picking structure scheme, using a system consisting of an end effector, a manipulator, and a control system. The kinematics and picking experiments of the robotic arm were carried out in the experimental field in the natural environment through the robotic physics machine platform. The results show that the position error of the robot arm from the end of the arm is less than 12 mm, and the picking success rate is 83.33% [4]. The related research did not pay attention to saving the data of the manipulator, and even did not simulate the trajectory of the manipulator.Maffezzoni’s paper provided a realistic phase-domain modeling and simulation approach for oscillator arrays that is able to account for associated device non-idealities. This model was used to study the associative memory performance of an array consisting of resonant LC oscillators [5]. To practically implement brain-like computing in scalable physical systems, Kumar investigated a network of coupled micromachined oscillators. He performed numerical simulations of this all-pair fully coupled nonlinear oscillator array in the presence of randomness and demonstrated its ability to synchronize and store information with relative phase differences when synchronized [6]. Liu proposed an open-source face recognition method with deep representation called VIPLFaceNet, which is a 10-layer convolutional neural network consisting of 7 convolutional layers and 3 fully connected layers. Compared to the famous AlexNet, VIPLFaceNet only needed 20% training time and 60% testing time, but combined with actual LFW facial recognition metrics, it achieved a 40% error reduction. Their VIPLFaceNet achieved an average accuracy of 98.60% on LFW using a single network [7]. Biyani presented a new software package called Focus, which provided the functionality needed to remotely monitor the progress of data collection and data processing, and the rapid detection of any errors that may occur greatly increased the productivity of electron microscopy recording sessions [8]. However, none of them solve practical problems such as the redundancy of edge computing in data processing, and the following content will conduct in-depth research on these problems.


## 3. Edge Computing System Design and Data Sampling Method

### 3.1. Edge Computing System Design

The single-user scenario is shown in Figure1.Figure 1
Single-user scenario.Whether it is cloud, fog, or edge computing, it is only a method or mode to realize the computing technology needed by the Internet of Things, intelligent manufacturing, etc. On the basis of a single system, a reserved sensor interface is used to complete the realization of the sensor acquisition function. As shown in Figure2, by connecting the sensors that meet the requirements of the interface hardware with the edge device, the software is used to complete the preprocessing of the collected data, thereby forming the underlying data acquisition module. This can not only expand the scope of application of the sensor, but also ensure that the collected data is uploaded to the cloud in time, shortening the delay of data processing and feedback [9].Figure 2
Physical data acquisition system.The architecture of edge computing includes four domains: equipment, network, data, and application. Platform providers mainly provide hardware and software infrastructure in network interconnection (including bus), computing power, data storage, and application. In addition to the collection of actual physical data, with the continuous development of informatization today, a large amount of data existing on the Internet is also worthy of attention and utilization. Therefore, for the data that can be accessed on the network, especially those web page data presented in HTML and other formats, people will use various methods to download the web page codes and the data behind them and process them. As shown in Figure3, the system utilizes the characteristics of a large number of edge devices and low energy consumption and can establish a multi-threaded or long-term monitoring data capture system by providing it with a crawler program. For example, users can carry sensors through the edge device network to monitor the air quality of a certain area and at the same time use web crawler technology to query the indexes of various local social activities, such as factory operating conditions and regional weather. In this way, it is compared with the collected air parameters to analyze the factors that affect the local air quality.Figure 3
Network data capture system.The rapid development of global smart phones has promoted the development of mobile terminals and “edge computing.” The intelligent society with the internet of things and the perception of everything is accompanied by the development of the Internet of Things, and the edge computing system has emerged accordingly. In the edge computing system, the platform needs to be built by the cloud computing center and edge devices. The advantage of this architecture is that when the bottom layer needs to call the data analysis function, the edge device can complete the timely feedback, shorten the response time, and ensure the real-time response characteristics of edge computing [10]. For the Internet of Things, breakthroughs in edge computing technology mean that many controls will be implemented through local devices without being handed over to the cloud, and the processing will be completed at the local edge computing layer. This will undoubtedly greatly improve processing efficiency and reduce the load on the cloud. Due to being closer to the user, it can also provide users with a faster response and solve their needs at the edge.


### 3.2. Pattern Recognition Methods

#### 3.2.1. Host Component Analysis Method

Principal component analysis is a statistical method. Through orthogonal transformation, a group of variables that may be related are converted into a group of linearly unrelated variables, and the converted variables are called principal components. The traditional principal component analysis algorithm (PCA) is a method to minimize measurement features and is an important tool for measurement analysis. It has a predictable learning path [11]. Now PCA is continued to be derived for the mean least squares error of the object.
(1)λy=1n∑j=1nyj.(2)yj′=yj−λyThe sample matrix after zero mean processing is written asY′, and Y′=y1′,y2′,⋯,yn′. After the sample zero-mean centering, its autocorrelation function can be expressed as
(3)By=Y′Y′T.Let the optimal transformation vector beCd∈Rl, and find the eigenvalues and eigenvectors of By:
(4)Byd=ηd.The largest eigenvector obtained from this characteristic formula is the optimal PCA transform vector [12]. In the PCA dimensionality reduction process, it is usually necessary to manually adjust the reduced size [13]. The transformation matrix after dimensionality reduction can be written as
(5)D=d1,d2,⋯,dj,⋯,dk,dj∈Rl.


#### 3.2.2. Kernel Principal Component Analysis

If the purpose of PCA is to attenuate nonlinear correlations between a given data setY=y1,y1,⋯yj,⋯,yn,yi∈Rl, their covariances can be represented on a linear feature space F instead of the nonlinear representation in the original input space [14].
(6)BF=1n∑i=1nΦyiΦyiT.It is assumed that the mapping of the feature vector in the high-dimensional space is also zero-mean, that is,∑k=1nΦyk=0 and Φ• are nonlinear mapping functions that map the input feature vector to the high-dimensional space F. Then, diagonalize the covariance matrix:
(7)μν=BFν.Next, the eigenvalues and eigenvectors are solved by solving the characteristic formula. The specific content ofBFν can be deduced according to Formula (6):
(8)BFv=1n∑i=1nΦyiΦyiTv=1n∑i=1nΦyi,vΦyi.In the formula,u,v represents the inner product between u and v. The formula shows that all eigenvectors v of μ≠0 are composed of Φy1,⋯,Φyn, so we can use v=∑j=1n to represent the eigenvector, and Formula (7) can also be written as
(9)μΦyk,v=Φyk,BFv,k=1,2,⋯,n.Combining (8) and (9), we can get
(10)μ∑i=1nβiΦyk,Φyi=1n∑i=1nβiΦyk,∑j=1nΦyjΦyj,Φyi.Now, a matrixK of size n×n is assumed, where Kij=Φyi,Φyj; then, the left-hand side of Formula (10) can be written as
(11)μ∑i=1nβiΦyk,Φyi=μ∑i=1nβiKki=μKβ.The right-hand side of the formula can be written as(12)1n∑i=1nβiΦyk,∑j=1nΦyjΦyj,Φyi=1n∑i=1nβi∑j=1nKkjKji=1nK2β.Combining Formulas (11) and (12), we get
(13)μnβ=Kβ.


### 3.3. Cauchy Distribution Function Data Sampling and Processing

The distribution is estimated from the sample using the Cauchy distribution function, mainly the estimation of the parameters of the Cauchy distribution, and then the inverse cumulative distribution function is used for sampling [15]. A description of the Cauchy distribution function and parameter estimation and sampling methods is first given [16].The Cauchy distribution, also known as the Cauchy-Lorentz distribution, is a continuous distribution function. If the probability density function of random variableξ is
(14)fy,y0,γ=1πγ1+y−y0/γ2=1πγy−y02+γ2.Among them,γ,y0 are constants, and γ>0, then ξ is said to obey the Cauchy distribution with parameters γ,y0 and denoted as ξ~Cγ,y0. The cumulative distribution function of ξ~Cγ,y0 is
(15)Fy,y0,γ=1πarctany−y0γ+12.In the formula,y0 is the position parameter that defines the location of the peak of the distribution, and γ is the scale parameter that is half width at half the maximum value. And Fξy0=1/2, and Fξγ+y0=3/4, the former formula states that y0 is the median of Cγ,y0, while the latter formula states that γ+y0 is the 3/4 quantile of Cγ,y0.In particular, the Cauchy distribution with parametery0=0,γ=1 is called the standard Cauchy distribution, denoted by ξ~Cγ,y0. Its probability density function is
(16)fy;0,1=1π1+y2.Its cumulative distribution function is(17)expy0it−γt.The properties of the Cauchy distribution: the expectation and variance are undefined, the median or mode isy0, the entropy value is ln4πx, and the eigenfunction is expy0it−γt.It can be seen from the characteristics of the Cauchy distribution that the Cauchy distribution is a continuous distribution function with neither expectation nor variance. Therefore, the classical parameter estimation method cannot be used to estimate the parameters of the Cauchy distribution [17].For continuous distribution functions, the inverse cumulative distribution function can be used for sampling. Supposing the distribution function of the sample random variable X isFX, and the function FX is continuous. Its inverse cumulative distribution function is also its inverse function, denoted as F−1z,0≤z≤1.In Theorem 1, if the random variableR is uniformly distributed on (0,1), that is, R~U0,1, then Y=F−1R is the inverse function of FY.From the cumulative distribution function formula of the Cauchy distribution, its inverse cumulative distribution function can be obtained as(18)F−1q;y0,η=y0+ηtanπq−12.It can be known from Theorem 1 that if people want to generate a random variable number that obeysFY, first generate a random variable number u that obeys U(0,1) uniform distribution, and finally calculate F−1u.


## 3.1. Edge Computing System Design

The single-user scenario is shown in Figure1.Figure 1
Single-user scenario.Whether it is cloud, fog, or edge computing, it is only a method or mode to realize the computing technology needed by the Internet of Things, intelligent manufacturing, etc. On the basis of a single system, a reserved sensor interface is used to complete the realization of the sensor acquisition function. As shown in Figure2, by connecting the sensors that meet the requirements of the interface hardware with the edge device, the software is used to complete the preprocessing of the collected data, thereby forming the underlying data acquisition module. This can not only expand the scope of application of the sensor, but also ensure that the collected data is uploaded to the cloud in time, shortening the delay of data processing and feedback [9].Figure 2
Physical data acquisition system.The architecture of edge computing includes four domains: equipment, network, data, and application. Platform providers mainly provide hardware and software infrastructure in network interconnection (including bus), computing power, data storage, and application. In addition to the collection of actual physical data, with the continuous development of informatization today, a large amount of data existing on the Internet is also worthy of attention and utilization. Therefore, for the data that can be accessed on the network, especially those web page data presented in HTML and other formats, people will use various methods to download the web page codes and the data behind them and process them. As shown in Figure3, the system utilizes the characteristics of a large number of edge devices and low energy consumption and can establish a multi-threaded or long-term monitoring data capture system by providing it with a crawler program. For example, users can carry sensors through the edge device network to monitor the air quality of a certain area and at the same time use web crawler technology to query the indexes of various local social activities, such as factory operating conditions and regional weather. In this way, it is compared with the collected air parameters to analyze the factors that affect the local air quality.Figure 3
Network data capture system.The rapid development of global smart phones has promoted the development of mobile terminals and “edge computing.” The intelligent society with the internet of things and the perception of everything is accompanied by the development of the Internet of Things, and the edge computing system has emerged accordingly. In the edge computing system, the platform needs to be built by the cloud computing center and edge devices. The advantage of this architecture is that when the bottom layer needs to call the data analysis function, the edge device can complete the timely feedback, shorten the response time, and ensure the real-time response characteristics of edge computing [10]. For the Internet of Things, breakthroughs in edge computing technology mean that many controls will be implemented through local devices without being handed over to the cloud, and the processing will be completed at the local edge computing layer. This will undoubtedly greatly improve processing efficiency and reduce the load on the cloud. Due to being closer to the user, it can also provide users with a faster response and solve their needs at the edge.


## 3.2. Pattern Recognition Methods

### 3.2.1. Host Component Analysis Method

Principal component analysis is a statistical method. Through orthogonal transformation, a group of variables that may be related are converted into a group of linearly unrelated variables, and the converted variables are called principal components. The traditional principal component analysis algorithm (PCA) is a method to minimize measurement features and is an important tool for measurement analysis. It has a predictable learning path [11]. Now PCA is continued to be derived for the mean least squares error of the object.
(1)λy=1n∑j=1nyj.(2)yj′=yj−λyThe sample matrix after zero mean processing is written asY′, and Y′=y1′,y2′,⋯,yn′. After the sample zero-mean centering, its autocorrelation function can be expressed as
(3)By=Y′Y′T.Let the optimal transformation vector beCd∈Rl, and find the eigenvalues and eigenvectors of By:
(4)Byd=ηd.The largest eigenvector obtained from this characteristic formula is the optimal PCA transform vector [12]. In the PCA dimensionality reduction process, it is usually necessary to manually adjust the reduced size [13]. The transformation matrix after dimensionality reduction can be written as
(5)D=d1,d2,⋯,dj,⋯,dk,dj∈Rl.


### 3.2.2. Kernel Principal Component Analysis

If the purpose of PCA is to attenuate nonlinear correlations between a given data setY=y1,y1,⋯yj,⋯,yn,yi∈Rl, their covariances can be represented on a linear feature space F instead of the nonlinear representation in the original input space [14].
(6)BF=1n∑i=1nΦyiΦyiT.It is assumed that the mapping of the feature vector in the high-dimensional space is also zero-mean, that is,∑k=1nΦyk=0 and Φ• are nonlinear mapping functions that map the input feature vector to the high-dimensional space F. Then, diagonalize the covariance matrix:
(7)μν=BFν.Next, the eigenvalues and eigenvectors are solved by solving the characteristic formula. The specific content ofBFν can be deduced according to Formula (6):
(8)BFv=1n∑i=1nΦyiΦyiTv=1n∑i=1nΦyi,vΦyi.In the formula,u,v represents the inner product between u and v. The formula shows that all eigenvectors v of μ≠0 are composed of Φy1,⋯,Φyn, so we can use v=∑j=1n to represent the eigenvector, and Formula (7) can also be written as
(9)μΦyk,v=Φyk,BFv,k=1,2,⋯,n.Combining (8) and (9), we can get
(10)μ∑i=1nβiΦyk,Φyi=1n∑i=1nβiΦyk,∑j=1nΦyjΦyj,Φyi.Now, a matrixK of size n×n is assumed, where Kij=Φyi,Φyj; then, the left-hand side of Formula (10) can be written as
(11)μ∑i=1nβiΦyk,Φyi=μ∑i=1nβiKki=μKβ.The right-hand side of the formula can be written as(12)1n∑i=1nβiΦyk,∑j=1nΦyjΦyj,Φyi=1n∑i=1nβi∑j=1nKkjKji=1nK2β.Combining Formulas (11) and (12), we get
(13)μnβ=Kβ.


## 3.2.1. Host Component Analysis Method

Principal component analysis is a statistical method. Through orthogonal transformation, a group of variables that may be related are converted into a group of linearly unrelated variables, and the converted variables are called principal components. The traditional principal component analysis algorithm (PCA) is a method to minimize measurement features and is an important tool for measurement analysis. It has a predictable learning path [11]. Now PCA is continued to be derived for the mean least squares error of the object.
(1)λy=1n∑j=1nyj.(2)yj′=yj−λyThe sample matrix after zero mean processing is written asY′, and Y′=y1′,y2′,⋯,yn′. After the sample zero-mean centering, its autocorrelation function can be expressed as
(3)By=Y′Y′T.Let the optimal transformation vector beCd∈Rl, and find the eigenvalues and eigenvectors of By:
(4)Byd=ηd.The largest eigenvector obtained from this characteristic formula is the optimal PCA transform vector [12]. In the PCA dimensionality reduction process, it is usually necessary to manually adjust the reduced size [13]. The transformation matrix after dimensionality reduction can be written as
(5)D=d1,d2,⋯,dj,⋯,dk,dj∈Rl.


## 3.2.2. Kernel Principal Component Analysis

If the purpose of PCA is to attenuate nonlinear correlations between a given data setY=y1,y1,⋯yj,⋯,yn,yi∈Rl, their covariances can be represented on a linear feature space F instead of the nonlinear representation in the original input space [14].
(6)BF=1n∑i=1nΦyiΦyiT.It is assumed that the mapping of the feature vector in the high-dimensional space is also zero-mean, that is,∑k=1nΦyk=0 and Φ• are nonlinear mapping functions that map the input feature vector to the high-dimensional space F. Then, diagonalize the covariance matrix:
(7)μν=BFν.Next, the eigenvalues and eigenvectors are solved by solving the characteristic formula. The specific content ofBFν can be deduced according to Formula (6):
(8)BFv=1n∑i=1nΦyiΦyiTv=1n∑i=1nΦyi,vΦyi.In the formula,u,v represents the inner product between u and v. The formula shows that all eigenvectors v of μ≠0 are composed of Φy1,⋯,Φyn, so we can use v=∑j=1n to represent the eigenvector, and Formula (7) can also be written as
(9)μΦyk,v=Φyk,BFv,k=1,2,⋯,n.Combining (8) and (9), we can get
(10)μ∑i=1nβiΦyk,Φyi=1n∑i=1nβiΦyk,∑j=1nΦyjΦyj,Φyi.Now, a matrixK of size n×n is assumed, where Kij=Φyi,Φyj; then, the left-hand side of Formula (10) can be written as
(11)μ∑i=1nβiΦyk,Φyi=μ∑i=1nβiKki=μKβ.The right-hand side of the formula can be written as(12)1n∑i=1nβiΦyk,∑j=1nΦyjΦyj,Φyi=1n∑i=1nβi∑j=1nKkjKji=1nK2β.Combining Formulas (11) and (12), we get
(13)μnβ=Kβ.


## 3.3. Cauchy Distribution Function Data Sampling and Processing

The distribution is estimated from the sample using the Cauchy distribution function, mainly the estimation of the parameters of the Cauchy distribution, and then the inverse cumulative distribution function is used for sampling [15]. A description of the Cauchy distribution function and parameter estimation and sampling methods is first given [16].The Cauchy distribution, also known as the Cauchy-Lorentz distribution, is a continuous distribution function. If the probability density function of random variableξ is
(14)fy,y0,γ=1πγ1+y−y0/γ2=1πγy−y02+γ2.Among them,γ,y0 are constants, and γ>0, then ξ is said to obey the Cauchy distribution with parameters γ,y0 and denoted as ξ~Cγ,y0. The cumulative distribution function of ξ~Cγ,y0 is
(15)Fy,y0,γ=1πarctany−y0γ+12.In the formula,y0 is the position parameter that defines the location of the peak of the distribution, and γ is the scale parameter that is half width at half the maximum value. And Fξy0=1/2, and Fξγ+y0=3/4, the former formula states that y0 is the median of Cγ,y0, while the latter formula states that γ+y0 is the 3/4 quantile of Cγ,y0.In particular, the Cauchy distribution with parametery0=0,γ=1 is called the standard Cauchy distribution, denoted by ξ~Cγ,y0. Its probability density function is
(16)fy;0,1=1π1+y2.Its cumulative distribution function is(17)expy0it−γt.The properties of the Cauchy distribution: the expectation and variance are undefined, the median or mode isy0, the entropy value is ln4πx, and the eigenfunction is expy0it−γt.It can be seen from the characteristics of the Cauchy distribution that the Cauchy distribution is a continuous distribution function with neither expectation nor variance. Therefore, the classical parameter estimation method cannot be used to estimate the parameters of the Cauchy distribution [17].For continuous distribution functions, the inverse cumulative distribution function can be used for sampling. Supposing the distribution function of the sample random variable X isFX, and the function FX is continuous. Its inverse cumulative distribution function is also its inverse function, denoted as F−1z,0≤z≤1.In Theorem 1, if the random variableR is uniformly distributed on (0,1), that is, R~U0,1, then Y=F−1R is the inverse function of FY.From the cumulative distribution function formula of the Cauchy distribution, its inverse cumulative distribution function can be obtained as(18)F−1q;y0,η=y0+ηtanπq−12.It can be known from Theorem 1 that if people want to generate a random variable number that obeysFY, first generate a random variable number u that obeys U(0,1) uniform distribution, and finally calculate F−1u.


## 4. Edge Algorithm Simulation Test Experiment and Data Processing Analysis

### 4.1. Edge Algorithm Simulation Test Experiment

To test the performance of the algorithm, experiments were performed using the following four test functions:Rosenbrock:(19)gy=∑i=1m100yi+1−yi22+yi−12.In the formula,‐10≤yi≤10,ming=g1,⋯,1=0.SumCan:(20)gy=−105+∑i=1nxi−1.In the formula,xi=yi,xi=xi−1+yi,i=2,⋯,d,−0.16≤yi≤0.16,ming=g0,⋯,0=−105.Sphere:(21)gy=∑i=1nyi2.In the formula,‐100≤yi≤100,ming=g0,⋯,0=0.Schwefel2.22:(22)gy=∑i=1nyi+∏i=1nyi.In the formula,‐10≤yi≤10,ming=g0,⋯,0=0.The test function Rosenbrock is a classical function, and it is a complex optimization problem. Its shape is parabolic and narrow, but the position of the global optimal solution is in the smoothest flat valley of this parabolic shape, and most of the algorithms can search this parabolic canyon, but it is difficult to find the global optimal solution [18]. The test function SumCan is shaped like an inverted spire, and the optimal position is at this inverted spire, and other positions are relatively flat. Therefore, the position of the global optimal solution searched by many algorithms during optimization is very close to the optimal position of the test function, but it is very different from the optimal fitness value, which is ‐105.The test function Sphere is a unimodal function with simple relationships between variables. The function test Schwefel is a multimodal function, and its local optimum position is far away from its global optimum position because its local optimum value is also very small. Thus, when it converges to the local optimum, it is easy to mistakenly think that it has converged to the global optimum. At the same time, it is difficult for the algorithm to get rid of the local optimum that has been trapped, and it is difficult to achieve the level of global optimization. Therefore, this test function is often used to analyze the execution performance of algorithms out of local optima. The test function Rastrigin is a multimodal function. Similar to the test function Schwefel, it is used to test the execution ability of the algorithm to get rid of the local optimum. The difference is that its local optimum is located near the global optimum. So it is easy to fall into local optimum. The test function Griewank is a multimodal function with many local optimal points, and each dimension variable has a strong interaction relationship. Due to the strong interaction and influence of each dimension variable, the number of local optimal points will increase with the increase of dimensions and increase sharply, thus making it extremely easy for the algorithm to fall into local optimum points and not easily get out of it. Therefore, the test function is often used to test the ability of the algorithm to get rid of local optima and the performance of the optimization problem for high-dimensional variables. The optimal solution and optimal value of the test function are shown in Table1.Table 1
Optimal solution and optimal value of test function.
Test functionOptimal solutionThe optimal valueRosenbrocky=1,⋯,10SumCany=1,⋯,1−105Spherey=0,⋯,00Schwefel2.22y=0,⋯,00The simulation results of the test function in the marginal distribution are shown in Figure4.Figure 4
Simulation results of the test function in the marginal distribution.The population size is 2000, the dimension is 10, and the selection rate is 0.5. Some individuals are selected as part of the new population by truncation selection and roulette selection. The mutation operator is used in the algorithm, and the mutation rate is 0.05. The algorithm stops when any of the following conditions are met. The conditions are as follows: ① The difference between the optimal values of the evolution of the adjacent two generations of the algorithm within 25 consecutive generations is less than 1e-6; ② the optimal value is found; and ③ the maximum fitness evaluation times are 300,000. Each function was run 50 times independently in different test environments. In addition, in the copula distribution estimation algorithm of the Cauchy distribution probability model, the parameter estimation adopts the quantile estimation method for simulation experiments.From the experimental results in Table2, it can be seen that for the four test functions, the copulaEDA whose marginal distribution is a Cauchy distribution function is better than the copulaEDA with an empirical distribution function. For the test function Rosenbrock, it can be seen from Table 2 that whether the empirical distribution function is used as the marginal distribution or the Cauchy distribution function is used as the marginal distribution function, the simulation results show that the optimization effect of the copula distribution estimation algorithm is relatively poor. Relatively speaking, the copula distribution estimation algorithm of the Cauchy distribution probability model is relatively better than the copula distribution estimation algorithm of the empirical distribution probability model in terms of optimization performance and tending to stability [19].Table 2
Comparison of copulaEDA simulation results of two marginal distribution functions.
Test functionMarginal distributionAverage valueVarianceMinimum valueMaximum valueRosenbrockEmpirical distribution6.55340.37465.94528.1534Cauchy distribution5.43240.26344.45625.1256SumCanEmpirical distribution−8.3573e+049.4638e+03−9.7832e+04−5.5346e+04Cauchy distribution−8.9805e+041.0372e+04−9.3278e+04−5.5527e+04SphereEmpirical distribution4.6734e-082.7839e-087.9452e-091.4627e-07Cauchy distribution2.4537e-081.9875e-081.5848e-099.7462e-08Schwefel2.22Empirical distribution4.6738e-061.7839e-061.4268e-068.4528e-06Cauchy distribution7.3279e-073.0945e-072.4837e-071.5371e-06For the test function SumCan, it is also a difficult problem in the distribution estimation algorithm to continue to optimize. From the results in Table2, it can be seen that the optimization results of the two algorithms are not good and the difference is not large. For the test function Sphere, it can be seen from the experimental results that the optimization result of the copula distribution estimation algorithm of the Cauchy distribution probability model on this function is better than the copula distribution estimation algorithm of the empirical distribution probability model. For the test function Schwefel, the copula distribution estimation algorithm of the Cauchy probability model is obviously superior to the Clayton copula distribution estimation algorithm of the empirical distribution probability model in terms of mean, variance, minimum and maximum values during optimization. After careful calculation, the optimization rate of the Cauchy model has reached more than 10%.


### 4.2. Gesture Recognition Robustness Verification

In the current vision-based gesture recognition, most of them use color cameras to obtain image information, while the color camera-based visual gesture recognition system has high requirements on the environment. And it is easily affected by changes in illumination, resulting in the inability to accurately segment gestures part, which ultimately affects the result of gesture recognition; in skin-color-based gesture detection, it is unavoidable that it will be affected by the skin-like environment and its own skin color and gestures cannot be extracted from complex backgrounds. This paper uses the Kinect depth camera to obtain RGB-D image information. The infrared camera group it contains can project and receive infrared light to obtain depth data within the visible environment. Changes in ambient lighting will not affect the acquisition of depth data, and depth information can be used for gesture recognition even in dark environments [20]. Through the depth threshold gesture segmentation fused with skin color information, the interference of non-skin color environmental factors in the effective gesture area can be excluded, thereby improving the accuracy of gesture segmentation. In the calculation of the gesture feature parameters, the judgment of the effective convex defect and the ratio of the gesture area to the minimum circumscribed circle area are all in the form of ratio, which makes the gesture recognition have good adaptability; the effective convex defect feature angle and the effective vertex itself have scaling and rotation invariance, correct recognition of gesture rotation, and scaling. In order to verify the robustness of the static gesture recognition method, gesture recognition experiments are carried out under strong light, weak light, and complex backgrounds. The experimental results are shown in Table 3.Table 3
Gesture recognition results in different environments.
Serial numberGlareLow lightBackground distractionRecognitionAccuracy rate/%RecognitionAccuracy rate/%RecognitionAccuracy rate/%1499/50099.8499/50099.8498/50099.62499/50099.8489/50097.8494/50098.83489/50097.8479/50095.8496/50099.24469/50093.8469/50093.8490/50098.05499/50099.8459/50091.8459/50091.86498/50099.6449/50089.8498/50099.67489/50097.8439/50087.8459/50091.88479/50095.8459/50091.8497/50099.4The static gesture recognition method adopted in this paper can well overcome the influence of different light intensities and can also correctly recognize gestures in the presence of background interference [21]. The experimental results of gesture recognition under different operators and gesture rotation and zoom conditions are shown in Table 4. Although different operators have differences in expressing gestures, or excessive zooming in the process of gesture changes weakens gesture features, it will eventually lead to identify the wrong situation, but can get a good recognition effect within the effective recognition range.Table 4
Recognition results of different operators and gesture changes.
Serial numberDifferent operatorsGesture rotationGesture zoomRecognitionAccuracy rate/%RecognitionAccuracy rate/%RecognitionAccuracy rate/%1498/50099.6499/50099.8498/50099.62499/50099.8489/50097.8494/50098.83489/50097.8479/50095.8496/50099.24469/50093.8469/50093.8490/50098.05499/50099.8459/50091.8458/50091.66498/50099.6459/50091.8498/50099.67489/50097.8459/50091.8459/50091.88479/50095.8459/50091.8497/50099.4An in-depth study on static gesture recognition based on multiparameter features from image acquisition to gesture recognition have been done [22]. The RGB-D image information is obtained by using the Kinect depth sensor, and then the gesture image is segmented by the adaptive depth threshold fused with skin color, and the corresponding preprocessing is performed to extract the outline of the gesture. Experiments show that the static gesture recognition method used in this paper is simple and high in recognition and has good robustness, and the accuracy rate can basically reach more than 90%.


### 4.3. Data Processing Experimental Analysis

#### 4.3.1. Experimental Process

The experimental flow chart in Figure5 clearly describes the entire experimental process.Figure 5
Experimental flow chart.First, selecting the optimal threshold value, fully consider the accuracy of the recommendation achieved by the threshold value and the time-consuming situation, and considering the effect of the threshold value in the subsequent selection of the number of neighbors. Selecting the optimal threshold to achieve gray project clustering makes the internal common features of the project prominent, and the external differences between the projects are large [23]. Calculating the similarity of items on the obtained clusters, and according to the fixed number of neighbors, sort the calculated similarities from large to small in turn, and select a fixed number of neighbors. The scoring prediction and recommendation of the item are completed, and the performance of the recommendation algorithm is verified experimentally.


#### 4.3.2. Performance Evaluation Criteria

The performance of the algorithm is verified by experimental simulation. During the experiment, other recommendation algorithms are used to compare and analyze the algorithm. The movie data set is used, and the recommendation algorithm is used to operate the data set. And the obtained simulation results can test the efficiency and accuracy of the algorithm we study.The evaluation method of the pros and cons of the recommendation algorithm has also been under exploration. Nowadays, the commonly used evaluation schemes are as follows: decision support accuracy and statistical accuracy. The most commonly used is the mean absolute difference measurement method among the statistical accuracy measurement methods. Therefore, this paper uses the MAE algorithm to evaluate the recommendation system. The MAE value represents the value of the degree of deviation between the predicted user score calculated by the algorithm and the actual score, so when the obtained value is smaller, it means that the difference between the predicted value and the actual value is smaller, so it also proves that the accuracy of the recommendation algorithm is higher, which also clarifies the effectiveness of the recommendation algorithm [24].The calculation formula of the MAE evaluation scheme is as follows:(23)MAE=∑j=1MGj−AjT.In Formula (23), Gj represents the predicted value of the user’s rating, Aj represents the actual value of the known user’s rating, and T represents the total number of rating items.


#### 4.3.3. Selection of Optimal Threshold for Grey Clustering

Given a known movie data set, the classification situation has been clarified, and the original data set is subjected to the gray theory to realize the project clustering process, and a new data set classification situation will be obtained, and the gray project clustering algorithm is based on thresholds are used to classify categories. Therefore, in the experimental process, the known classification situation is compared with the clustering results obtained by the gray clustering algorithm when the threshold values are different so that it can be clear that the highest accuracy obtained under a certain clustering threshold can be obtained the classification result. During the experiment, the threshold value is from 0.1 to 0.9, and the obtained clustering result is shown in Figure6, which vividly describes the change trend of the clustering accuracy curve under the condition of different threshold selection [25].Figure 6
Clustering accuracy analysis.It can be clearly seen from Figure6 that in the process of obtaining the threshold from 0.1 to 0.7, the accuracy of the item clustering division of the gray correlation algorithm is a monotonically increasing function, and the accuracy is known to improve; when the threshold value is obtained from 0.7 to 0.9, it can be clearly seen from the vertical coordinate of the accuracy in Figure 6 that the accuracy has a downward trend. It can be seen that when the grey relational clustering threshold is 0.7, the highest clustering accuracy can be obtained, that is, the divided item clusters are the least different from the actual known item clusters [26]. Therefore, the optimal threshold of the grey relational clustering algorithm obtained is 0.7.Table5 describes the number of samples of clustering errors generated under each threshold and the corresponding clustering accuracy when different clustering thresholds are selected. And the number of categories generated by clustering has made a specific numerical elaboration and comparison.Table 5
Item clustering result analysis.
Threshold value0.10.20.30.40.50.60.70.80.9Number of clustering error samples366830772561234118451598117812342323Clustering accuracy7.32430.940.853.559.873.368.940.9Number of categories2046476475110121145321It can be seen from Table5 that when the optimal threshold for grey relational clustering is 0.7, the accuracy of the clustering algorithm reaches 73.3%, and a total of 121 categories of movie clusters are generated. In order to further optimize the selection of the threshold, the experimental range of the threshold is selected between 0.6 and 0.8, and the obtained clustering accuracy is shown in Figure 7.Figure 7
Clustering accuracy refinement analysis.From Figure7, we can see that the accuracy of clustering shows a clear upward trend in the process of changing the threshold from 0.60 to 0.75, while the accuracy decreases significantly when the threshold changes from 0.75 to 0.8. Tables 6 and 7 describe the clustering accuracy obtained with further refinement of the clustering threshold selection. Table 6 describes the clustering accuracy analysis when the threshold range is between 0.61 and 0.69, and Table 7 describes the accuracy when the clustering threshold is selected between 0.71 and 0.79. The number of samples corresponding to clustering errors under each threshold and the corresponding clustering accuracy can be used to determine the optimal threshold more accurately [27].Table 6
Analysis of the clustering results of items with a threshold in the range of 0.61-0.69.
Threshold value0.610.620.630.640.650.660.670.680.69Number of clustering error samples156715341500146314221376132712811234Clustering accuracy (%)60.261.162.163.164.265.066.567.568.7Error (%)1.22.11.42.33.12.22.22.22.3Table 7
Analysis of item clustering results with thresholds in the range of 0.71-0.79.
Threshold value0.710.720.730.740.750.760.770.780.79Number of clustering error samples113610981065106310381028103310551111Clustering accuracy (%)70.271.172.173.174.273.071.571.070.5Error (%)2.33.33.33.43.13.02.52.62.3Table7 is an analysis of the clustering results of items with a threshold in the range of 0.71-0.79.It can be seen from Tables6 and 7 that when the gray correlation clustering threshold is 0.75, the highest clustering accuracy can be obtained, that is, the difference between the divided item clusters and the actual known item clusters is the least, so the optimal threshold of the obtained grey relational clustering algorithm is 0.75.In the grey relational clustering algorithm in this paper, the clustering based on user items is completed, so in the process of comparing recommendation algorithms, it cannot be compared with the commonly used classical clustering methods that use item attributes as a reference. Therefore, in order to better study the performance of the recommendation algorithm, we introduce a gray-based collaborative filtering recommendation algorithm for comparison to verify the effectiveness of gray clustering. The ratio of the test set to the training set is 1 : 4 randomly divided, 20% of the test set and 80% of the training set are selected, and the number of neighbors is 40. Under different gray clustering thresholds, the item scores are predicted and the MAE value is obtained.It can be seen from Figure8 that under different threshold values, when the gray correlation threshold is 0.75, the MAE value reaches the minimum value, which means that the gap between the predicted score and the actual score is the smallest, which means that the predicted result is very accurate, so it can be proved that the recommendation algorithm has relatively superior performance. Therefore, choosing the optimal threshold value as 0.75 can achieve the best user recommendation effect.Figure 8
MAE values under different clustering thresholds.


## 4.1. Edge Algorithm Simulation Test Experiment

To test the performance of the algorithm, experiments were performed using the following four test functions:Rosenbrock:(19)gy=∑i=1m100yi+1−yi22+yi−12.In the formula,‐10≤yi≤10,ming=g1,⋯,1=0.SumCan:(20)gy=−105+∑i=1nxi−1.In the formula,xi=yi,xi=xi−1+yi,i=2,⋯,d,−0.16≤yi≤0.16,ming=g0,⋯,0=−105.Sphere:(21)gy=∑i=1nyi2.In the formula,‐100≤yi≤100,ming=g0,⋯,0=0.Schwefel2.22:(22)gy=∑i=1nyi+∏i=1nyi.In the formula,‐10≤yi≤10,ming=g0,⋯,0=0.The test function Rosenbrock is a classical function, and it is a complex optimization problem. Its shape is parabolic and narrow, but the position of the global optimal solution is in the smoothest flat valley of this parabolic shape, and most of the algorithms can search this parabolic canyon, but it is difficult to find the global optimal solution [18]. The test function SumCan is shaped like an inverted spire, and the optimal position is at this inverted spire, and other positions are relatively flat. Therefore, the position of the global optimal solution searched by many algorithms during optimization is very close to the optimal position of the test function, but it is very different from the optimal fitness value, which is ‐105.The test function Sphere is a unimodal function with simple relationships between variables. The function test Schwefel is a multimodal function, and its local optimum position is far away from its global optimum position because its local optimum value is also very small. Thus, when it converges to the local optimum, it is easy to mistakenly think that it has converged to the global optimum. At the same time, it is difficult for the algorithm to get rid of the local optimum that has been trapped, and it is difficult to achieve the level of global optimization. Therefore, this test function is often used to analyze the execution performance of algorithms out of local optima. The test function Rastrigin is a multimodal function. Similar to the test function Schwefel, it is used to test the execution ability of the algorithm to get rid of the local optimum. The difference is that its local optimum is located near the global optimum. So it is easy to fall into local optimum. The test function Griewank is a multimodal function with many local optimal points, and each dimension variable has a strong interaction relationship. Due to the strong interaction and influence of each dimension variable, the number of local optimal points will increase with the increase of dimensions and increase sharply, thus making it extremely easy for the algorithm to fall into local optimum points and not easily get out of it. Therefore, the test function is often used to test the ability of the algorithm to get rid of local optima and the performance of the optimization problem for high-dimensional variables. The optimal solution and optimal value of the test function are shown in Table1.Table 1
Optimal solution and optimal value of test function.
Test functionOptimal solutionThe optimal valueRosenbrocky=1,⋯,10SumCany=1,⋯,1−105Spherey=0,⋯,00Schwefel2.22y=0,⋯,00The simulation results of the test function in the marginal distribution are shown in Figure4.Figure 4
Simulation results of the test function in the marginal distribution.The population size is 2000, the dimension is 10, and the selection rate is 0.5. Some individuals are selected as part of the new population by truncation selection and roulette selection. The mutation operator is used in the algorithm, and the mutation rate is 0.05. The algorithm stops when any of the following conditions are met. The conditions are as follows: ① The difference between the optimal values of the evolution of the adjacent two generations of the algorithm within 25 consecutive generations is less than 1e-6; ② the optimal value is found; and ③ the maximum fitness evaluation times are 300,000. Each function was run 50 times independently in different test environments. In addition, in the copula distribution estimation algorithm of the Cauchy distribution probability model, the parameter estimation adopts the quantile estimation method for simulation experiments.From the experimental results in Table2, it can be seen that for the four test functions, the copulaEDA whose marginal distribution is a Cauchy distribution function is better than the copulaEDA with an empirical distribution function. For the test function Rosenbrock, it can be seen from Table 2 that whether the empirical distribution function is used as the marginal distribution or the Cauchy distribution function is used as the marginal distribution function, the simulation results show that the optimization effect of the copula distribution estimation algorithm is relatively poor. Relatively speaking, the copula distribution estimation algorithm of the Cauchy distribution probability model is relatively better than the copula distribution estimation algorithm of the empirical distribution probability model in terms of optimization performance and tending to stability [19].Table 2
Comparison of copulaEDA simulation results of two marginal distribution functions.
Test functionMarginal distributionAverage valueVarianceMinimum valueMaximum valueRosenbrockEmpirical distribution6.55340.37465.94528.1534Cauchy distribution5.43240.26344.45625.1256SumCanEmpirical distribution−8.3573e+049.4638e+03−9.7832e+04−5.5346e+04Cauchy distribution−8.9805e+041.0372e+04−9.3278e+04−5.5527e+04SphereEmpirical distribution4.6734e-082.7839e-087.9452e-091.4627e-07Cauchy distribution2.4537e-081.9875e-081.5848e-099.7462e-08Schwefel2.22Empirical distribution4.6738e-061.7839e-061.4268e-068.4528e-06Cauchy distribution7.3279e-073.0945e-072.4837e-071.5371e-06For the test function SumCan, it is also a difficult problem in the distribution estimation algorithm to continue to optimize. From the results in Table2, it can be seen that the optimization results of the two algorithms are not good and the difference is not large. For the test function Sphere, it can be seen from the experimental results that the optimization result of the copula distribution estimation algorithm of the Cauchy distribution probability model on this function is better than the copula distribution estimation algorithm of the empirical distribution probability model. For the test function Schwefel, the copula distribution estimation algorithm of the Cauchy probability model is obviously superior to the Clayton copula distribution estimation algorithm of the empirical distribution probability model in terms of mean, variance, minimum and maximum values during optimization. After careful calculation, the optimization rate of the Cauchy model has reached more than 10%.


## 4.2. Gesture Recognition Robustness Verification

In the current vision-based gesture recognition, most of them use color cameras to obtain image information, while the color camera-based visual gesture recognition system has high requirements on the environment. And it is easily affected by changes in illumination, resulting in the inability to accurately segment gestures part, which ultimately affects the result of gesture recognition; in skin-color-based gesture detection, it is unavoidable that it will be affected by the skin-like environment and its own skin color and gestures cannot be extracted from complex backgrounds. This paper uses the Kinect depth camera to obtain RGB-D image information. The infrared camera group it contains can project and receive infrared light to obtain depth data within the visible environment. Changes in ambient lighting will not affect the acquisition of depth data, and depth information can be used for gesture recognition even in dark environments [20]. Through the depth threshold gesture segmentation fused with skin color information, the interference of non-skin color environmental factors in the effective gesture area can be excluded, thereby improving the accuracy of gesture segmentation. In the calculation of the gesture feature parameters, the judgment of the effective convex defect and the ratio of the gesture area to the minimum circumscribed circle area are all in the form of ratio, which makes the gesture recognition have good adaptability; the effective convex defect feature angle and the effective vertex itself have scaling and rotation invariance, correct recognition of gesture rotation, and scaling. In order to verify the robustness of the static gesture recognition method, gesture recognition experiments are carried out under strong light, weak light, and complex backgrounds. The experimental results are shown in Table 3.Table 3
Gesture recognition results in different environments.
Serial numberGlareLow lightBackground distractionRecognitionAccuracy rate/%RecognitionAccuracy rate/%RecognitionAccuracy rate/%1499/50099.8499/50099.8498/50099.62499/50099.8489/50097.8494/50098.83489/50097.8479/50095.8496/50099.24469/50093.8469/50093.8490/50098.05499/50099.8459/50091.8459/50091.86498/50099.6449/50089.8498/50099.67489/50097.8439/50087.8459/50091.88479/50095.8459/50091.8497/50099.4The static gesture recognition method adopted in this paper can well overcome the influence of different light intensities and can also correctly recognize gestures in the presence of background interference [21]. The experimental results of gesture recognition under different operators and gesture rotation and zoom conditions are shown in Table 4. Although different operators have differences in expressing gestures, or excessive zooming in the process of gesture changes weakens gesture features, it will eventually lead to identify the wrong situation, but can get a good recognition effect within the effective recognition range.Table 4
Recognition results of different operators and gesture changes.
Serial numberDifferent operatorsGesture rotationGesture zoomRecognitionAccuracy rate/%RecognitionAccuracy rate/%RecognitionAccuracy rate/%1498/50099.6499/50099.8498/50099.62499/50099.8489/50097.8494/50098.83489/50097.8479/50095.8496/50099.24469/50093.8469/50093.8490/50098.05499/50099.8459/50091.8458/50091.66498/50099.6459/50091.8498/50099.67489/50097.8459/50091.8459/50091.88479/50095.8459/50091.8497/50099.4An in-depth study on static gesture recognition based on multiparameter features from image acquisition to gesture recognition have been done [22]. The RGB-D image information is obtained by using the Kinect depth sensor, and then the gesture image is segmented by the adaptive depth threshold fused with skin color, and the corresponding preprocessing is performed to extract the outline of the gesture. Experiments show that the static gesture recognition method used in this paper is simple and high in recognition and has good robustness, and the accuracy rate can basically reach more than 90%.


## 4.3. Data Processing Experimental Analysis

### 4.3.1. Experimental Process

The experimental flow chart in Figure5 clearly describes the entire experimental process.Figure 5
Experimental flow chart.First, selecting the optimal threshold value, fully consider the accuracy of the recommendation achieved by the threshold value and the time-consuming situation, and considering the effect of the threshold value in the subsequent selection of the number of neighbors. Selecting the optimal threshold to achieve gray project clustering makes the internal common features of the project prominent, and the external differences between the projects are large [23]. Calculating the similarity of items on the obtained clusters, and according to the fixed number of neighbors, sort the calculated similarities from large to small in turn, and select a fixed number of neighbors. The scoring prediction and recommendation of the item are completed, and the performance of the recommendation algorithm is verified experimentally.


### 4.3.2. Performance Evaluation Criteria

The performance of the algorithm is verified by experimental simulation. During the experiment, other recommendation algorithms are used to compare and analyze the algorithm. The movie data set is used, and the recommendation algorithm is used to operate the data set. And the obtained simulation results can test the efficiency and accuracy of the algorithm we study.The evaluation method of the pros and cons of the recommendation algorithm has also been under exploration. Nowadays, the commonly used evaluation schemes are as follows: decision support accuracy and statistical accuracy. The most commonly used is the mean absolute difference measurement method among the statistical accuracy measurement methods. Therefore, this paper uses the MAE algorithm to evaluate the recommendation system. The MAE value represents the value of the degree of deviation between the predicted user score calculated by the algorithm and the actual score, so when the obtained value is smaller, it means that the difference between the predicted value and the actual value is smaller, so it also proves that the accuracy of the recommendation algorithm is higher, which also clarifies the effectiveness of the recommendation algorithm [24].The calculation formula of the MAE evaluation scheme is as follows:(23)MAE=∑j=1MGj−AjT.In Formula (23), Gj represents the predicted value of the user’s rating, Aj represents the actual value of the known user’s rating, and T represents the total number of rating items.


### 4.3.3. Selection of Optimal Threshold for Grey Clustering

Given a known movie data set, the classification situation has been clarified, and the original data set is subjected to the gray theory to realize the project clustering process, and a new data set classification situation will be obtained, and the gray project clustering algorithm is based on thresholds are used to classify categories. Therefore, in the experimental process, the known classification situation is compared with the clustering results obtained by the gray clustering algorithm when the threshold values are different so that it can be clear that the highest accuracy obtained under a certain clustering threshold can be obtained the classification result. During the experiment, the threshold value is from 0.1 to 0.9, and the obtained clustering result is shown in Figure6, which vividly describes the change trend of the clustering accuracy curve under the condition of different threshold selection [25].Figure 6
Clustering accuracy analysis.It can be clearly seen from Figure6 that in the process of obtaining the threshold from 0.1 to 0.7, the accuracy of the item clustering division of the gray correlation algorithm is a monotonically increasing function, and the accuracy is known to improve; when the threshold value is obtained from 0.7 to 0.9, it can be clearly seen from the vertical coordinate of the accuracy in Figure 6 that the accuracy has a downward trend. It can be seen that when the grey relational clustering threshold is 0.7, the highest clustering accuracy can be obtained, that is, the divided item clusters are the least different from the actual known item clusters [26]. Therefore, the optimal threshold of the grey relational clustering algorithm obtained is 0.7.Table5 describes the number of samples of clustering errors generated under each threshold and the corresponding clustering accuracy when different clustering thresholds are selected. And the number of categories generated by clustering has made a specific numerical elaboration and comparison.Table 5
Item clustering result analysis.
Threshold value0.10.20.30.40.50.60.70.80.9Number of clustering error samples366830772561234118451598117812342323Clustering accuracy7.32430.940.853.559.873.368.940.9Number of categories2046476475110121145321It can be seen from Table5 that when the optimal threshold for grey relational clustering is 0.7, the accuracy of the clustering algorithm reaches 73.3%, and a total of 121 categories of movie clusters are generated. In order to further optimize the selection of the threshold, the experimental range of the threshold is selected between 0.6 and 0.8, and the obtained clustering accuracy is shown in Figure 7.Figure 7
Clustering accuracy refinement analysis.From Figure7, we can see that the accuracy of clustering shows a clear upward trend in the process of changing the threshold from 0.60 to 0.75, while the accuracy decreases significantly when the threshold changes from 0.75 to 0.8. Tables 6 and 7 describe the clustering accuracy obtained with further refinement of the clustering threshold selection. Table 6 describes the clustering accuracy analysis when the threshold range is between 0.61 and 0.69, and Table 7 describes the accuracy when the clustering threshold is selected between 0.71 and 0.79. The number of samples corresponding to clustering errors under each threshold and the corresponding clustering accuracy can be used to determine the optimal threshold more accurately [27].Table 6
Analysis of the clustering results of items with a threshold in the range of 0.61-0.69.
Threshold value0.610.620.630.640.650.660.670.680.69Number of clustering error samples156715341500146314221376132712811234Clustering accuracy (%)60.261.162.163.164.265.066.567.568.7Error (%)1.22.11.42.33.12.22.22.22.3Table 7
Analysis of item clustering results with thresholds in the range of 0.71-0.79.
Threshold value0.710.720.730.740.750.760.770.780.79Number of clustering error samples113610981065106310381028103310551111Clustering accuracy (%)70.271.172.173.174.273.071.571.070.5Error (%)2.33.33.33.43.13.02.52.62.3Table7 is an analysis of the clustering results of items with a threshold in the range of 0.71-0.79.It can be seen from Tables6 and 7 that when the gray correlation clustering threshold is 0.75, the highest clustering accuracy can be obtained, that is, the difference between the divided item clusters and the actual known item clusters is the least, so the optimal threshold of the obtained grey relational clustering algorithm is 0.75.In the grey relational clustering algorithm in this paper, the clustering based on user items is completed, so in the process of comparing recommendation algorithms, it cannot be compared with the commonly used classical clustering methods that use item attributes as a reference. Therefore, in order to better study the performance of the recommendation algorithm, we introduce a gray-based collaborative filtering recommendation algorithm for comparison to verify the effectiveness of gray clustering. The ratio of the test set to the training set is 1 : 4 randomly divided, 20% of the test set and 80% of the training set are selected, and the number of neighbors is 40. Under different gray clustering thresholds, the item scores are predicted and the MAE value is obtained.It can be seen from Figure8 that under different threshold values, when the gray correlation threshold is 0.75, the MAE value reaches the minimum value, which means that the gap between the predicted score and the actual score is the smallest, which means that the predicted result is very accurate, so it can be proved that the recommendation algorithm has relatively superior performance. Therefore, choosing the optimal threshold value as 0.75 can achieve the best user recommendation effect.Figure 8
MAE values under different clustering thresholds.


## 4.3.1. Experimental Process

The experimental flow chart in Figure5 clearly describes the entire experimental process.Figure 5
Experimental flow chart.First, selecting the optimal threshold value, fully consider the accuracy of the recommendation achieved by the threshold value and the time-consuming situation, and considering the effect of the threshold value in the subsequent selection of the number of neighbors. Selecting the optimal threshold to achieve gray project clustering makes the internal common features of the project prominent, and the external differences between the projects are large [23]. Calculating the similarity of items on the obtained clusters, and according to the fixed number of neighbors, sort the calculated similarities from large to small in turn, and select a fixed number of neighbors. The scoring prediction and recommendation of the item are completed, and the performance of the recommendation algorithm is verified experimentally.


## 4.3.2. Performance Evaluation Criteria

The performance of the algorithm is verified by experimental simulation. During the experiment, other recommendation algorithms are used to compare and analyze the algorithm. The movie data set is used, and the recommendation algorithm is used to operate the data set. And the obtained simulation results can test the efficiency and accuracy of the algorithm we study.The evaluation method of the pros and cons of the recommendation algorithm has also been under exploration. Nowadays, the commonly used evaluation schemes are as follows: decision support accuracy and statistical accuracy. The most commonly used is the mean absolute difference measurement method among the statistical accuracy measurement methods. Therefore, this paper uses the MAE algorithm to evaluate the recommendation system. The MAE value represents the value of the degree of deviation between the predicted user score calculated by the algorithm and the actual score, so when the obtained value is smaller, it means that the difference between the predicted value and the actual value is smaller, so it also proves that the accuracy of the recommendation algorithm is higher, which also clarifies the effectiveness of the recommendation algorithm [24].The calculation formula of the MAE evaluation scheme is as follows:(23)MAE=∑j=1MGj−AjT.In Formula (23), Gj represents the predicted value of the user’s rating, Aj represents the actual value of the known user’s rating, and T represents the total number of rating items.


## 4.3.3. Selection of Optimal Threshold for Grey Clustering

Given a known movie data set, the classification situation has been clarified, and the original data set is subjected to the gray theory to realize the project clustering process, and a new data set classification situation will be obtained, and the gray project clustering algorithm is based on thresholds are used to classify categories. Therefore, in the experimental process, the known classification situation is compared with the clustering results obtained by the gray clustering algorithm when the threshold values are different so that it can be clear that the highest accuracy obtained under a certain clustering threshold can be obtained the classification result. During the experiment, the threshold value is from 0.1 to 0.9, and the obtained clustering result is shown in Figure6, which vividly describes the change trend of the clustering accuracy curve under the condition of different threshold selection [25].Figure 6
Clustering accuracy analysis.It can be clearly seen from Figure6 that in the process of obtaining the threshold from 0.1 to 0.7, the accuracy of the item clustering division of the gray correlation algorithm is a monotonically increasing function, and the accuracy is known to improve; when the threshold value is obtained from 0.7 to 0.9, it can be clearly seen from the vertical coordinate of the accuracy in Figure 6 that the accuracy has a downward trend. It can be seen that when the grey relational clustering threshold is 0.7, the highest clustering accuracy can be obtained, that is, the divided item clusters are the least different from the actual known item clusters [26]. Therefore, the optimal threshold of the grey relational clustering algorithm obtained is 0.7.Table5 describes the number of samples of clustering errors generated under each threshold and the corresponding clustering accuracy when different clustering thresholds are selected. And the number of categories generated by clustering has made a specific numerical elaboration and comparison.Table 5
Item clustering result analysis.
Threshold value0.10.20.30.40.50.60.70.80.9Number of clustering error samples366830772561234118451598117812342323Clustering accuracy7.32430.940.853.559.873.368.940.9Number of categories2046476475110121145321It can be seen from Table5 that when the optimal threshold for grey relational clustering is 0.7, the accuracy of the clustering algorithm reaches 73.3%, and a total of 121 categories of movie clusters are generated. In order to further optimize the selection of the threshold, the experimental range of the threshold is selected between 0.6 and 0.8, and the obtained clustering accuracy is shown in Figure 7.Figure 7
Clustering accuracy refinement analysis.From Figure7, we can see that the accuracy of clustering shows a clear upward trend in the process of changing the threshold from 0.60 to 0.75, while the accuracy decreases significantly when the threshold changes from 0.75 to 0.8. Tables 6 and 7 describe the clustering accuracy obtained with further refinement of the clustering threshold selection. Table 6 describes the clustering accuracy analysis when the threshold range is between 0.61 and 0.69, and Table 7 describes the accuracy when the clustering threshold is selected between 0.71 and 0.79. The number of samples corresponding to clustering errors under each threshold and the corresponding clustering accuracy can be used to determine the optimal threshold more accurately [27].Table 6
Analysis of the clustering results of items with a threshold in the range of 0.61-0.69.
Threshold value0.610.620.630.640.650.660.670.680.69Number of clustering error samples156715341500146314221376132712811234Clustering accuracy (%)60.261.162.163.164.265.066.567.568.7Error (%)1.22.11.42.33.12.22.22.22.3Table 7
Analysis of item clustering results with thresholds in the range of 0.71-0.79.
Threshold value0.710.720.730.740.750.760.770.780.79Number of clustering error samples113610981065106310381028103310551111Clustering accuracy (%)70.271.172.173.174.273.071.571.070.5Error (%)2.33.33.33.43.13.02.52.62.3Table7 is an analysis of the clustering results of items with a threshold in the range of 0.71-0.79.It can be seen from Tables6 and 7 that when the gray correlation clustering threshold is 0.75, the highest clustering accuracy can be obtained, that is, the difference between the divided item clusters and the actual known item clusters is the least, so the optimal threshold of the obtained grey relational clustering algorithm is 0.75.In the grey relational clustering algorithm in this paper, the clustering based on user items is completed, so in the process of comparing recommendation algorithms, it cannot be compared with the commonly used classical clustering methods that use item attributes as a reference. Therefore, in order to better study the performance of the recommendation algorithm, we introduce a gray-based collaborative filtering recommendation algorithm for comparison to verify the effectiveness of gray clustering. The ratio of the test set to the training set is 1 : 4 randomly divided, 20% of the test set and 80% of the training set are selected, and the number of neighbors is 40. Under different gray clustering thresholds, the item scores are predicted and the MAE value is obtained.It can be seen from Figure8 that under different threshold values, when the gray correlation threshold is 0.75, the MAE value reaches the minimum value, which means that the gap between the predicted score and the actual score is the smallest, which means that the predicted result is very accurate, so it can be proved that the recommendation algorithm has relatively superior performance. Therefore, choosing the optimal threshold value as 0.75 can achieve the best user recommendation effect.Figure 8
MAE values under different clustering thresholds.


## 5. Discussion

Although the method in this paper reduces the complexity of the system to a certain extent, if the system is applied in an embedded platform, the running speed is still relatively slow. How to further improve the recognition efficiency of the whole system is the focus of future research. In the process of threshold selection for grey item clustering, several experiments are carried out in this paper to obtain a fixed optimal threshold. In the future, the dynamic adaptive algorithm of item clustering threshold can be studied. In the process of finding the optimal threshold, the optimal threshold is used to achieve the highest accuracy of gray item clustering and to alleviate the influence of the number of neighbors on the selection of neighbors and the final recommendation effect.


## 6. Conclusions

In edge computing, the use of Cauchy distribution processing is more impressive; compared with empirical distribution, the algorithm optimization can reach at least 10%. Experiments show that the static gesture recognition method used in this paper is simple and high in recognition and has good robustness and the accuracy rate can basically reach more than 90%. In the case of different threshold values, when the gray correlation threshold is 0.75, the MAE value reaches the minimum value, which means that the gap between the predicted score and the actual score is the smallest, which means that the predicted result is accurate, which can prove that the recommendation of the algorithm has relatively superior performance. Therefore, the optimal threshold value is selected as 0.75, which can achieve the best effect. Moreover, aiming at the behavior of the manipulator, we will have a deeper understanding of computer-related technologies and simulate a better behavior of the manipulator.



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*Source: 1170373-2022-08-09.xml*