# Model Construction of Hierarchical Polarization Characteristics Combined with Social E-Commerce Consumer Behavior

Authors: Quan Zhang; Jian Yang
Journal: Security and Communication Networks
 (2022)

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## Abstract

In order to analyze the consumer behavior of social e-commerce, this article attempts to explore the irrational consumer behavior factors that affect the audience in the live broadcast of e-commerce Internet celebrities. This paper predicts and analyzes the consumption behavior of social e-commerce and combines the characteristics of hierarchical planning to intelligently process the system to improve the effectiveness of the system. Moreover, this paper constructs a social e-commerce consumer behavior prediction model based on hierarchical polarization characteristics, researches and analyzes multiple factors and performance, and builds an intelligent simulation model. The analysis of the test results shows that the social e-commerce consumer behavior prediction model based on the hierarchical polarization characteristics proposed in this article is effective and can play an important role in the prediction of social consumer behavior.


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## Body

## 1. Introduction

Social networks can help social users maintain and expand personal connections. Its biggest feature is the “relationship” between people and spread through word of mouth to influence those around us who have a relationship with us. This relationship includes blood relationship, family relationship, friend relationship, neighbor relationship, colleague relationship, alumni relationship, fellow country relationship, and even netizen relationship. The essence of this “relationship” is trust, which means that the essence of social networks is the trust relationship between people. Because social networks successfully combine interpersonal relationships and word-of-mouth communication, users share product information or value-added services through social networks to create a word-of-mouth effect for corporate products or services [1].Whether it is socialized e-commerce using social networks or other social media, social attributes are key. Social e-commerce is still an emerging field; even in the world, there is no very successful social e-commerce website. Moreover, the proportion of users sharing shopping information through social applications in my country is still relatively small. However, due to the large number of Internet users using social media and the unique shopping experience of social e-commerce, social e-commerce will be the trend of future e-commerce development. With the rise of online celebrity live broadcasts, social e-commerce has become an important type of e-commerce [2].First of all, with the development of the Internet era, today’s mobile Internet era has entered a mature period, and the value of information needs to be driven by traffic. Internet celebrities are a newly born group in this new media era, such groups often have millions or even tens of millions of fans, and they have traffic characteristics [3].Nowadays, live broadcasting is becoming more and more common, and the transmission of information through live broadcasting can be more vivid and intuitive, and give the audience a sense of “3D interpretation.” Moreover, the live broadcast method is very simple, the operation is very easy, and the threshold for becoming a self-media is relatively low. As long as you have an idea, as long as you have a mobile phone or a computer, you can live webcast. This is a creative mode of completely user-generated content. This mode also breaks people’s understanding of traditional live broadcasts, and difference and TV shopping. Moreover, in the current live broadcast field of Internet celebrities, the two-way interaction between the anchor and the audience is also a feature born with the development of new media. It is not available in the traditional TV shopping marketing model. TV shopping is just the moderator conducts one-way information transmission. Internet celebrities are a type of group with great potential and liquidity. The influence of this type of group in the new media era cannot be ignored. Internet celebrities choose the marketing model of webcast to increase the popularity and influence of platforms, brands, or individuals, and then monetize through traffic to facilitate transactions and ultimately achieve their marketing goals. This behavior can be called e-commerce Internet celebrities live streaming. ① In the live broadcast of e-commerce Internet celebrities, the audience will have a strong desire to buy, and irrational consumption behaviors are endless.Based on the above analysis, this article conducts a predictive analysis of social e-commerce consumer behavior, combines the characteristics of hierarchical planning to intelligently process the system to improve the system’s work effect, and verifies the method proposed in this article through experiments.


## 2. Related Work

Literature [4] equates irrational consumption behaviors with unplanned consumption behaviors and believes that consumers’ rational consumption behaviors should be planned purchases of goods. If the purchased goods are not in the original plan, you can say this irrational consumer behavior has occurred. Literature [5] believes that emotions can cause irrational consumer behaviors. When irrational consumer behaviors occur, their characteristics are often impulsive and reckless. In irrational consumer behavior, consumers’ emotions are considered uncontrollable. The literature [6] has great consistency in the definition of irrational consumption behaviors and believes that irrational consumption behaviors are purposeless and strongly impulsive. Literature [7] believes that individuals who make irrational consumer behaviors have a certain degree of vanity, and they want to highlight their own identity and status through their consumption power. There are also foreign researchers who believe that irrational consumption behavior has the characteristics of herding, which is manifested in the fact that consumers lack independent opinions and blindly follow the public’s choices when purchasing behaviors. Literature [8] believes that some consumers have a herd mentality and believe that following the masses to purchase goods can reduce the purchase risk, but these consumers do not know their true needs. Irrational consumption means that consumers fail to carefully examine their true needs and do not consider the maximum utility of commodities.For the research on audience users’ motivation, there are many related researches on the audience users’ motivation to watch the game live broadcast; of course, it is not limited to the related research on the game live broadcast field. These researches are based on various webcast platforms [9]. Research has found that users on these two social media-based webcasting platforms are often more inclined to watch the live broadcasts they follow on social media [10]. Aiming at the audience’s willingness to watch the game live broadcast, the literature [11] found that emotional motivation, cognitive motivation, individual integration, social integration, and stress release are the five viewer motivations that affect the audience’s watching game live broadcast. Literature [12] has conducted related research on the relationship between user needs and user viewing behavior, and the theory used is the theory of use and satisfaction. A large amount of data is collected and conducted in-depth analysis of the data, and established a model that can predict the number of barrage speeches based on the number of audiences. The research believes that analyzing user chat-related data can better understand the behavior of audience users.In recent years, a lot of related research on anchors has also appeared. Literature [13] studied the anchors’ motivation for live broadcasting. Based on the perspective of individual motivation and social capital, they found that self-expression and self-identification motivation, information propaganda motivation, and monetary gain motivation are the main factors that anchors are willing to live broadcast. There are also studies on the factors that affect the audience’s use of live broadcast from the perspective of the audience. Literature [14] studies the user’s willingness to use live broadcast from four perspectives, namely, the perspectives of immersion, entertainment, social interaction, and recognition. Based on the dual identity framework, relevant researches have been conducted on the factors that influence viewers’ choice to continue watching live broadcasts from the perspective of individual experience and common experience. There are also studies that have begun to pay attention to the behavior of users in the live broadcast situation. Literature [15] studied the influence of the motivation of the live broadcast viewers on the live broadcast conforming behavior of the viewers.Literature [16] found that customer fit in live broadcast can promote customers’ consumption of virtual gifts. Through literature reading, we have a deep understanding of the concept of customer fit. The literature [17] believes that customer fit is a dynamic psychological process in which attitude fit positively affects behavior fit. Literature [18] proposes that customer fit is a mental state, which refers to the mental state generated by interacting with core objects in the core service relationship and co-creating customer experience. Literature [19] found that users’ virtual interactive online communities have a positive impact on customer fit. Literature [20] proposes that the impact of this interaction on customer engagement is also applicable to online game scenarios.


## 3. Analysis of Hierarchical Plan Characteristics

The SCMA iterative decoding model of polarization code encoding is shown in Figure1. In this system, the external information output by the polarization code decoder needs to be fed back to the SCMA detector. However, the SCMA detector reuses this information as a priori information to perform iterative decoding until the preset maximum number of iterations is reached or the system converges.Figure 1
SCMA simplified system model encoded by polarization codes.This article will discuss the widely discussed and published SCMA system model in which 6 user data are carried on 4 resource points. The relationship between users and resource points is represented by the factor graph in Figure2.Figure 2
Factor graph corresponding to SCMA users and resource points.In SCMA modulation, each user selects a codeword in the codebook according to the encoded bits. For example, if the modulation order of the system isM, then the bit stream of the j-th user performs multi-dimensional codeword mapping for each group of Q=log2M bits. The relationship can be expressed as(1)fj:Blog2M⟶xj,xj∈χj.Among them,B=0,1 is a set of binary bits, χj is a codeword set of the j-th user, and xj=x1jx2j…xNjT is an N-dimensional complex codeword, and it is satisfied that the number of 0 elements in the codeword is greater than or equal to the number of nonzero elements. Each user maps the bit group to the same N resource points and then superimposes them on the channel to form a nonorthogonal transmission signal.According to the above modulation principle, the received signal of the SCMA system is(2)y=∑j=1Jdiaghj⋅xj+n.Among them,y=y1y2…yNT is the acceptance vector of the channel, hj=h1jh2j…hNjT is the channel gain between the j-th user and the base station, and n=n1n2…nNT is a complex Gaussian white noise signal with a zero mean variance of N0.SCMA’s MPA detection algorithm is also a belief propagation algorithm, similar to BP decoding, which is detected in an iterative manner. The main steps of the algorithm are as follows:


### 3.1. Joint Conditional Probability Calculation

According to the system model, the conditional probability of any resource noden can be obtained as(3)dnxi,xj,xk=−1N0yn−hnixni+hnjxnj+hnkxnk2,(4)Pyn|xi,xj,xk=expdnxi,xj,xk.Among them, usersi, j, and k are connected to the resource node n.


### 3.2. Resource Node Update

According to the joint conditional probability obtained by the above steps, the edge condition probability can be calculated by the Bayes criterion, as shown below:(5)IFnVkxk=Pyn|xk=∑x′∈x′∑x′∈x′Pyn|xi,xj,xk⋅IViFnxi⋅IVjFnxj.Among them,xk∈χk,IViFnxi, and IVjEnxj represent the information delivered by users i and j to resource node n. In the first iteration, the probability of initializing variable nodes to resource nodes is(6)IVjFnxj=1M,∀n∈1,…,N,∀j∈1,…,J.Among them,M is the modulation order.


### 3.3. Variable Node Update

The update formula for the variable node of degree 2 is(7)IVkFnxk=IFmVkxk∑x^k∈xkIFmVkx^k.In fact, the symbol probability from resource nodem to variable node k is normalized.


### 3.4. Soft Information Calculation

When the iterative process is over, the soft information is calculated, and the soft information calculation formula for them-th bit of the j-th user is(8)LLRbqj=lnPbqj=0Pbqj=1=ln∑x′⋅jqj=0Qjxj−ln∑x′⋅kq=1Qjxj.Among them, there are(9)Qjxj=IFnVjxj⋅IFmVjxj.Among them,n and m are two resource nodes connected with variable node j.The MPA detection algorithm has the best detection performance. However, this algorithm involves a large number of divisions and multiplications, the computational complexity is extremely high, and it is difficult to apply to the actual mobile communication system. Therefore, an MPA detection algorithm based on the logarithmic domain is proposed, which simplifies the four major steps of MPA detection.


### 3.5. Channel Euclidean Distance Calculation

Since the entire calculation process has moved from the probability domain to the logarithmic domain, this step only needs to be calculated using formula (3), and the step of shifting to the probability domain is omitted.


### 3.6. Resource Node Update

The algorithm takes the natural logarithm of the probability information at the resource node and then uses the Jacobi approximation to simplify the formula as(10)IIF∗Vkxk=lnIFnVkxk,=ln∑x′∈xi∑x′∈x′Pyn|xi,xj,xk⋅IViFnxi⋅IVjFnxj=ln∑x′∈X′x′∈x′expdnxi,xj,xk+LIViFixi+LIVjFjxj≈maxx′∈X′,x′∈x′dnxi,xj,xk+LIViFFnxi+LIVjFnxj.


### 3.7. Variable Node Update

Same as the second step, the simplified formula is(11)LIVkFnxk=lnIVkFnxk,=LIFmVkxk−ln∑x^k∈xkIFmkVkx^k≈LIFmVkxk−maxx^k∈xkLIFmVkx^k.


### 3.8. Soft Information Calculation

In the MPA algorithm, the calculation of soft information is carried out in the logarithmic domain, and then, the Jacobi approximate simplified formula is also used as(12)LLRbmj=ln∑x′:bm=0Qjxj−ln∑x′:bmj=1Qjxj=maxx′,jm′=0LQjxj−maxx′,bm′=1LQjxj.Among them, there are(13)LQjxj=LIFnVjxj+LIFmVjxj.Polar codes use probability domain BP decoding algorithm, while SCMA uses MPA algorithm, and the whole system has the best decoding performance.Due to the addition of prior information, the MPA detection algorithm needs to correct the steps at the variable node update, as shown below:(14)IVkFnxk=Paxk⋅IFmVkxk∑x^k∈xkPax^k⋅IFmVkx^k.Among them, the prior information of thepaxk detector is calculated from the external information output by the decoder, and the calculation formula is(15)Paxk=∏i=1i=QPebik,bk=f−1xk.Among them,pebik cannot be obtained directly from the output of the polarization code decoder. Due to the polarization characteristics of the polarization code channel, it needs to be processed before it can be used for the calculation of a priori information. Using the generator matrix G in the encoder, when G(I, j) = 1, it can be calculated by the following formula:(16)Pebk=0.5⋅1−∏G,j=11−2PPolarbk.After the iteration of the SCMA detection part is completed, the soft information calculation steps are rewritten as(17)P^bqj=i=∑xj:bqj=iQjxj,i∈0,1.Then, it is normalized, and you can get(18)Pbqj=0=P^bqj=0P^bqj=0+P^bqj=1.The probability value output by the detector is passed as the channel probability to the polarization code decoder for iterative decoding. The algorithm details are shown in Table1. Among them, the code length of the polarization code is L,xlk represents the l-th SCMA symbol of the k-th user, and I,ISCMA, and IPoar represent the number of system iterations, the number of SCMA iterations, and the number of iterations of the polarization code, respectively. f⋅ and g⋅ have been introduced in the BP decoding algorithm of the probability domain polarization code in chapter 2.Table 1
Evaluation of the performance improvement effect of the consumption behavior prediction model.
NumberPerformance improvementNumberPerformance improvement183.501678.31268.521767.43374.921875.57465.411968.46572.932074.46674.542171.99770.082272.24881.102365.99982.522464.411068.182581.581179.592683.301282.702784.811378.202867.081472.172969.601570.003064.32Iterative decoding in the logarithmic domain means that the polarization code uses the original BP or min-sum-based BP decoding algorithm, while the SCMA uses the max log-MPA algorithm. In this algorithm, the variable node update formula is(19)LIViFixk=LIFmVkxk−ln∑x^i∈XkPax^k⋅IFmVkx^k≈Laxk+LIFmVkxk−maxx^k∈xxLax^k+LIFmVkx^k.Among them,Laxk is the logarithm and prior probability of the SCMA symbol. Through the external information output by the polarization code decoder, we get(20)Laxk=∑i=1QLeTbik,bk=f−1xk.Among them,LeTbik represents the prior information of the i-th bit of the k-th user, which is obtained by processing the external information output by the decoder:(21)LLRbk=minG,j=1LLRPolarbk∏G,j=1signLLRPolarbk.The soft information output by the SCMA detector is consistent with the calculation in the previous section. In summary, the iterative decoding process in the logarithmic domain is consistent with the iterative decoding process, and the difference lies in some calculation formulas.The MIMO system based on the joint detection and decoding algorithm can effectively improve the decoding performance of the system. Due to the similarity between SCMA and MIMO, this paper proposes a combination of the factor graph in the polarization code BP decoding algorithm and the SCMA factor graph to form a joint factor graph, as shown in Figure3. Based on the factor graph, the optimal joint detection and decoding algorithm and the log-domain joint detection and decoding algorithm are proposed.Figure 3
Joint factor graph.In iterative detection and decoding, the whole process can be divided into several steps. First, SCMA completes detection based on channel information. Then, the detector inputs the information to the polarization code decoder as the channel information of the decoder for decoding. Then, the polarization code decoder transmits the output external information to the detector as a priori information of the SCMA detector to perform detection again. Subsequently, the detector outputs new information and then passes it to the decoder. In this way, the algorithm iterates until the maximum number of iterations or meets a certain stopping criterion.Different from iterative detection and decoding, in joint detection and decoding, the message is passed directly on the joint factor graph, and the whole detection and decoding process is decoded through joint detection and decoding. The process is as follows.


#### 3.8.1. SCMA Resource Node Update

The update formula of the SCMA resource node in the joint factor graph is(22)IFnVkxlk=Pynl|xlk=∑xii∈Xixi∈xjPyn|xli,xlj,xlk⋅IViFnxli⋅IVjFnxlj,1≤l≤LQ.


#### 3.8.2. Polarization Code Factor Graph Update

In this step, the probability domain BP decoding iteration of the polarization code is completed once, and the iteration formula is(23)Li,jt=fLi+1,2j−1t−1,gLi+1,2jt−1,Ri,j+N/2t−1,Li,j+N/2t=gfRi,jt−1,Li+1,2j−1t−1,Li+1,2jt−1,Ri+1,2j−1t=fRi,jt−1,gLi+1,2jt−1,Ri,j+N/2t−1,Ri+1,2jt=gfRi,jt−1,Li+1,2j−1t−1,Ri,j+N/2t−1.Among them,f• and g• are the calculation formulas of the probability domain BP. During the initial iteration, the probability of the joint variable node being transmitted to the polarization code is set to 0.5.


#### 3.8.3. Joint Variable Node Update

In this step, the information of the leftmost node of the polarization code factor graph is converted from bit probability to symbol probability, as shown below:(24)Pebk=0.5⋅1−∏Gi,j=11−2PPolarbk,Paxlk=∏i=1i=QPebik,l,bk,l=f−1xlk,xlk∈χk.The algorithm passes it to the SCMA variable node for update. The formula is(25)IVkFnxlk=PaxlkIFmVkxlk∑x^i∈xkPax^lk⋅IFmVkx^lk.The symbol probability that the algorithm passes to the rightmost node of the polarization code factor graph is(26)Qjxlj=IFnVjxlj⋅IFmVjxlj,n,m∈ζjThe algorithm converts the symbol probability to the bit probability required by the polarization code factor graph.(27)P^VNObqj,l=i=∑xi,bqj,i=iQjxlj,i∈0,1,n,m∈ζjPVNObqj,l=0=P^VNObqj,l=0P^VNObqj,l=0+P^VNObqj,l=1.The above steps are the entire process of one iteration of joint detection and decoding. The algorithm repeats the above steps until the maximum number of iterations is reached or a certain stopping criterion is met.


## 3.1. Joint Conditional Probability Calculation

According to the system model, the conditional probability of any resource noden can be obtained as(3)dnxi,xj,xk=−1N0yn−hnixni+hnjxnj+hnkxnk2,(4)Pyn|xi,xj,xk=expdnxi,xj,xk.Among them, usersi, j, and k are connected to the resource node n.


## 3.2. Resource Node Update

According to the joint conditional probability obtained by the above steps, the edge condition probability can be calculated by the Bayes criterion, as shown below:(5)IFnVkxk=Pyn|xk=∑x′∈x′∑x′∈x′Pyn|xi,xj,xk⋅IViFnxi⋅IVjFnxj.Among them,xk∈χk,IViFnxi, and IVjEnxj represent the information delivered by users i and j to resource node n. In the first iteration, the probability of initializing variable nodes to resource nodes is(6)IVjFnxj=1M,∀n∈1,…,N,∀j∈1,…,J.Among them,M is the modulation order.


## 3.3. Variable Node Update

The update formula for the variable node of degree 2 is(7)IVkFnxk=IFmVkxk∑x^k∈xkIFmVkx^k.In fact, the symbol probability from resource nodem to variable node k is normalized.


## 3.4. Soft Information Calculation

When the iterative process is over, the soft information is calculated, and the soft information calculation formula for them-th bit of the j-th user is(8)LLRbqj=lnPbqj=0Pbqj=1=ln∑x′⋅jqj=0Qjxj−ln∑x′⋅kq=1Qjxj.Among them, there are(9)Qjxj=IFnVjxj⋅IFmVjxj.Among them,n and m are two resource nodes connected with variable node j.The MPA detection algorithm has the best detection performance. However, this algorithm involves a large number of divisions and multiplications, the computational complexity is extremely high, and it is difficult to apply to the actual mobile communication system. Therefore, an MPA detection algorithm based on the logarithmic domain is proposed, which simplifies the four major steps of MPA detection.


## 3.5. Channel Euclidean Distance Calculation

Since the entire calculation process has moved from the probability domain to the logarithmic domain, this step only needs to be calculated using formula (3), and the step of shifting to the probability domain is omitted.


## 3.6. Resource Node Update

The algorithm takes the natural logarithm of the probability information at the resource node and then uses the Jacobi approximation to simplify the formula as(10)IIF∗Vkxk=lnIFnVkxk,=ln∑x′∈xi∑x′∈x′Pyn|xi,xj,xk⋅IViFnxi⋅IVjFnxj=ln∑x′∈X′x′∈x′expdnxi,xj,xk+LIViFixi+LIVjFjxj≈maxx′∈X′,x′∈x′dnxi,xj,xk+LIViFFnxi+LIVjFnxj.


## 3.7. Variable Node Update

Same as the second step, the simplified formula is(11)LIVkFnxk=lnIVkFnxk,=LIFmVkxk−ln∑x^k∈xkIFmkVkx^k≈LIFmVkxk−maxx^k∈xkLIFmVkx^k.


## 3.8. Soft Information Calculation

In the MPA algorithm, the calculation of soft information is carried out in the logarithmic domain, and then, the Jacobi approximate simplified formula is also used as(12)LLRbmj=ln∑x′:bm=0Qjxj−ln∑x′:bmj=1Qjxj=maxx′,jm′=0LQjxj−maxx′,bm′=1LQjxj.Among them, there are(13)LQjxj=LIFnVjxj+LIFmVjxj.Polar codes use probability domain BP decoding algorithm, while SCMA uses MPA algorithm, and the whole system has the best decoding performance.Due to the addition of prior information, the MPA detection algorithm needs to correct the steps at the variable node update, as shown below:(14)IVkFnxk=Paxk⋅IFmVkxk∑x^k∈xkPax^k⋅IFmVkx^k.Among them, the prior information of thepaxk detector is calculated from the external information output by the decoder, and the calculation formula is(15)Paxk=∏i=1i=QPebik,bk=f−1xk.Among them,pebik cannot be obtained directly from the output of the polarization code decoder. Due to the polarization characteristics of the polarization code channel, it needs to be processed before it can be used for the calculation of a priori information. Using the generator matrix G in the encoder, when G(I, j) = 1, it can be calculated by the following formula:(16)Pebk=0.5⋅1−∏G,j=11−2PPolarbk.After the iteration of the SCMA detection part is completed, the soft information calculation steps are rewritten as(17)P^bqj=i=∑xj:bqj=iQjxj,i∈0,1.Then, it is normalized, and you can get(18)Pbqj=0=P^bqj=0P^bqj=0+P^bqj=1.The probability value output by the detector is passed as the channel probability to the polarization code decoder for iterative decoding. The algorithm details are shown in Table1. Among them, the code length of the polarization code is L,xlk represents the l-th SCMA symbol of the k-th user, and I,ISCMA, and IPoar represent the number of system iterations, the number of SCMA iterations, and the number of iterations of the polarization code, respectively. f⋅ and g⋅ have been introduced in the BP decoding algorithm of the probability domain polarization code in chapter 2.Table 1
Evaluation of the performance improvement effect of the consumption behavior prediction model.
NumberPerformance improvementNumberPerformance improvement183.501678.31268.521767.43374.921875.57465.411968.46572.932074.46674.542171.99770.082272.24881.102365.99982.522464.411068.182581.581179.592683.301282.702784.811378.202867.081472.172969.601570.003064.32Iterative decoding in the logarithmic domain means that the polarization code uses the original BP or min-sum-based BP decoding algorithm, while the SCMA uses the max log-MPA algorithm. In this algorithm, the variable node update formula is(19)LIViFixk=LIFmVkxk−ln∑x^i∈XkPax^k⋅IFmVkx^k≈Laxk+LIFmVkxk−maxx^k∈xxLax^k+LIFmVkx^k.Among them,Laxk is the logarithm and prior probability of the SCMA symbol. Through the external information output by the polarization code decoder, we get(20)Laxk=∑i=1QLeTbik,bk=f−1xk.Among them,LeTbik represents the prior information of the i-th bit of the k-th user, which is obtained by processing the external information output by the decoder:(21)LLRbk=minG,j=1LLRPolarbk∏G,j=1signLLRPolarbk.The soft information output by the SCMA detector is consistent with the calculation in the previous section. In summary, the iterative decoding process in the logarithmic domain is consistent with the iterative decoding process, and the difference lies in some calculation formulas.The MIMO system based on the joint detection and decoding algorithm can effectively improve the decoding performance of the system. Due to the similarity between SCMA and MIMO, this paper proposes a combination of the factor graph in the polarization code BP decoding algorithm and the SCMA factor graph to form a joint factor graph, as shown in Figure3. Based on the factor graph, the optimal joint detection and decoding algorithm and the log-domain joint detection and decoding algorithm are proposed.Figure 3
Joint factor graph.In iterative detection and decoding, the whole process can be divided into several steps. First, SCMA completes detection based on channel information. Then, the detector inputs the information to the polarization code decoder as the channel information of the decoder for decoding. Then, the polarization code decoder transmits the output external information to the detector as a priori information of the SCMA detector to perform detection again. Subsequently, the detector outputs new information and then passes it to the decoder. In this way, the algorithm iterates until the maximum number of iterations or meets a certain stopping criterion.Different from iterative detection and decoding, in joint detection and decoding, the message is passed directly on the joint factor graph, and the whole detection and decoding process is decoded through joint detection and decoding. The process is as follows.


### 3.8.1. SCMA Resource Node Update

The update formula of the SCMA resource node in the joint factor graph is(22)IFnVkxlk=Pynl|xlk=∑xii∈Xixi∈xjPyn|xli,xlj,xlk⋅IViFnxli⋅IVjFnxlj,1≤l≤LQ.


### 3.8.2. Polarization Code Factor Graph Update

In this step, the probability domain BP decoding iteration of the polarization code is completed once, and the iteration formula is(23)Li,jt=fLi+1,2j−1t−1,gLi+1,2jt−1,Ri,j+N/2t−1,Li,j+N/2t=gfRi,jt−1,Li+1,2j−1t−1,Li+1,2jt−1,Ri+1,2j−1t=fRi,jt−1,gLi+1,2jt−1,Ri,j+N/2t−1,Ri+1,2jt=gfRi,jt−1,Li+1,2j−1t−1,Ri,j+N/2t−1.Among them,f• and g• are the calculation formulas of the probability domain BP. During the initial iteration, the probability of the joint variable node being transmitted to the polarization code is set to 0.5.


### 3.8.3. Joint Variable Node Update

In this step, the information of the leftmost node of the polarization code factor graph is converted from bit probability to symbol probability, as shown below:(24)Pebk=0.5⋅1−∏Gi,j=11−2PPolarbk,Paxlk=∏i=1i=QPebik,l,bk,l=f−1xlk,xlk∈χk.The algorithm passes it to the SCMA variable node for update. The formula is(25)IVkFnxlk=PaxlkIFmVkxlk∑x^i∈xkPax^lk⋅IFmVkx^lk.The symbol probability that the algorithm passes to the rightmost node of the polarization code factor graph is(26)Qjxlj=IFnVjxlj⋅IFmVjxlj,n,m∈ζjThe algorithm converts the symbol probability to the bit probability required by the polarization code factor graph.(27)P^VNObqj,l=i=∑xi,bqj,i=iQjxlj,i∈0,1,n,m∈ζjPVNObqj,l=0=P^VNObqj,l=0P^VNObqj,l=0+P^VNObqj,l=1.The above steps are the entire process of one iteration of joint detection and decoding. The algorithm repeats the above steps until the maximum number of iterations is reached or a certain stopping criterion is met.


## 3.8.1. SCMA Resource Node Update

The update formula of the SCMA resource node in the joint factor graph is(22)IFnVkxlk=Pynl|xlk=∑xii∈Xixi∈xjPyn|xli,xlj,xlk⋅IViFnxli⋅IVjFnxlj,1≤l≤LQ.


## 3.8.2. Polarization Code Factor Graph Update

In this step, the probability domain BP decoding iteration of the polarization code is completed once, and the iteration formula is(23)Li,jt=fLi+1,2j−1t−1,gLi+1,2jt−1,Ri,j+N/2t−1,Li,j+N/2t=gfRi,jt−1,Li+1,2j−1t−1,Li+1,2jt−1,Ri+1,2j−1t=fRi,jt−1,gLi+1,2jt−1,Ri,j+N/2t−1,Ri+1,2jt=gfRi,jt−1,Li+1,2j−1t−1,Ri,j+N/2t−1.Among them,f• and g• are the calculation formulas of the probability domain BP. During the initial iteration, the probability of the joint variable node being transmitted to the polarization code is set to 0.5.


## 3.8.3. Joint Variable Node Update

In this step, the information of the leftmost node of the polarization code factor graph is converted from bit probability to symbol probability, as shown below:(24)Pebk=0.5⋅1−∏Gi,j=11−2PPolarbk,Paxlk=∏i=1i=QPebik,l,bk,l=f−1xlk,xlk∈χk.The algorithm passes it to the SCMA variable node for update. The formula is(25)IVkFnxlk=PaxlkIFmVkxlk∑x^i∈xkPax^lk⋅IFmVkx^lk.The symbol probability that the algorithm passes to the rightmost node of the polarization code factor graph is(26)Qjxlj=IFnVjxlj⋅IFmVjxlj,n,m∈ζjThe algorithm converts the symbol probability to the bit probability required by the polarization code factor graph.(27)P^VNObqj,l=i=∑xi,bqj,i=iQjxlj,i∈0,1,n,m∈ζjPVNObqj,l=0=P^VNObqj,l=0P^VNObqj,l=0+P^VNObqj,l=1.The above steps are the entire process of one iteration of joint detection and decoding. The algorithm repeats the above steps until the maximum number of iterations is reached or a certain stopping criterion is met.


## 4. Social E-Commerce Consumer Behavior Prediction Model Based on Hierarchical Polarization Characteristics

The third part proposes the hierarchical planning feature method, and with the support of this method, the social e-commerce consumer behavior prediction model based on the hierarchical polarization feature is constructed.This research mainly discusses the influence of the characteristics of e-commerce network anchors on consumer attitudes. According to the previous article, the following model is constructed, as shown in Figure4.Figure 4
The influence of the characteristics of e-commerce network anchors on consumer attitudes.This article combines the above analysis to construct a social e-commerce consumer behavior prediction framework, as shown in Figure5.Figure 5
Social e-commerce consumer behavior prediction framework.Irrational consumer behavior is a phenomenon in which consumer behavior is alienated. This phenomenon causes consumption to become the focus of people’s lives and triggers the bad social atmosphere of hedonism and money worship. In the daily life of the general public, irrational consumer behavior is common, but the degree is different. Among irrational consumption behaviors, comparison consumption and herd consumption are the most serious. Moreover, sub-healthy consumption patterns are now subtly affecting people’s daily lives, but many people do not have a clear understanding of irrational consumption behaviors.Irrational consumer behavior is an unhealthy consumer behavior that is diametrically opposed to rational consumer behavior. According to the definition of rational consumption behavior, we can understand irrational consumption behavior as an individual’s purchase behavior that lacks consideration of the maximization of commodity utility under unhealthy consumption concepts and is only for satisfying their own timely enjoyment psychology. People who make irrational consumption usually lack a serious review of their real needs, have no clear specific purchase goals, are easily stimulated and disturbed by the external environment, have no long-term plans for the future, and only focus on short-term psychological experiences. Irrational consumption behavior can be divided into common ones: impulsive consumption, conspicuous consumption, and blind consumption. Such irrational consumer behavior has prompted the emergence of many “shopaholics” who would rather max out dozens of credit cards and buy some things that they basically do not use. This kind of consumption is really a mental illness. The development of e-commerce platforms now allows consumption without leaving the house, which is much more convenient than shopping in the past, which makes this phenomenon even more serious. In fact, this is a kind of psychological abnormality caused by psychological backlog. What this group of people pursue is to get a certain degree of pleasure after consumption.The Internet celebrity economy is to attract fans through the packaging of Internet celebrities derived from the self-media era through their own unique personality charm and superior skills, and then maintain fan stickiness through regular communication and exchanges with fans. Finally, it uses the fan effect to monetize the traffic, thus forming a complete economic situation of the net celebrity profit chain. Internet celebrities are no longer synonymous with “nonmainstream,” and such groups have begun to have their own commercial value in the era of the Internet celebrity economy. The consumption behavior process of Internet celebrity social e-commerce is shown in Figure6.Figure 6
The consumption behavior process of Internet celebrity social e-commerce.Perceived attraction is the subjective feelings of individual consumers about brand community attraction, and it is also the source of self-awareness and classification. Under the “Internet celebrity + live broadcast + e-commerce” model, there are three dimensions including the attraction of Internet celebrities, the attraction of live broadcasts, and the attraction of products. Brand community recognition is the psychological manifestation of self-recognition and classification after perceptual attraction. The repeat purchase intention is the dependent behavior tendency oriented by the brand community identification. This article believes that the attracting source of online celebrity live broadcast e-commerce, that is, perceptual attraction (influencer attraction, live broadcast attraction, product attraction), will lead to consumers’ self-recognition and classification (identification of the online celebrity live broadcast e-commerce community), and then generate a corresponding tendency of dependence (repurchase willingness). At the same time, this study also selected age and gender as control variables. The research model is shown in Figure7.Figure 7
Research model.In this study, SmartPLS2.0 is used for SEM analysis, and the bootstrapping method is used to repeatedly sample 5000 times to test the significance of the path coefficient. The model test results are as follows (see Figure8).Figure 8
Model test results.According to the model test results in Figure8, first, consumer-brand community identification has a significant impact on consumers’ repurchase intentions and explains 67.636% of the variance of repeat purchase intentions. Secondly, the three types of consumer perception (Internet celebrity attraction, live broadcast attraction, and product attraction) under the “Internet celebrity + live broadcast + e-commerce” model have a significant impact on brand community recognition and explain the 72.616% variance of brand community recognition. At the same time, among the three types of perceptual attraction, both live broadcast attraction and product attraction can significantly affect consumers’ repurchase intentions, while online celebrity attraction cannot directly and significantly affect customers’ repurchase intentions, which is inconsistent with the hypothesis.After constructing the above model, the effect of the social e-commerce consumer behavior prediction model proposed in this paper is verified. First of all, this article verifies the hierarchical characteristics of the system constructed in this article, calculates the performance improvement effect of the system, and validates it through the simulation platform. The results are shown in Table1 and Figure 9.Figure 9
Statistical diagram of system performance improvement evaluation.From the above research, we can see that the hierarchical characteristics can effectively improve the performance of the system model. On this basis, the social e-commerce consumer behavior prediction model is verified, and data are collected from many current live delivery platforms for experimental analysis. The statistical test results are shown in Table2 and Figure 10.Table 2
Effectiveness verification of social e-commerce consumer behavior prediction model based on hierarchical polarization characteristics.
NumberConsumption forecastNumberConsumption forecast173.91588.0285.11686.6382.71781.0477.71885.0586.01986.8672.62081.8784.12188.7885.52277.0986.22378.31082.42487.61188.32577.21277.22687.61383.22776.51490.22884.31588.02987.01686.63085.0Figure 10
Statistical diagram of the effect of social e-commerce consumer behavior prediction model based on hierarchical polarization characteristics.From the above research, it can be seen that the social e-commerce consumer behavior prediction model based on the hierarchical polarization characteristics proposed in this paper is effective and can play an important role in the prediction of social consumer behavior.


## 5. Conclusion

Social e-commerce can help many offline companies and traditional e-commerce companies to learn the current “net celebrity economy” model. Moreover, it promotes these companies to keep pace with the times in the era of new media. In addition, it encourages them to improve their competitiveness while maintaining their own state in this era of extremely high penetration rate of online shopping, and to obtain better returns, so that they will not be slowly banned. Secondly, this article focuses on the influence factors of e-commerce Internet celebrity live broadcast on the audience’s irrational consumption and deeply analyzes the characteristics of e-commerce Internet celebrity live broadcast platform and the consumer psychology of the audience. This can help the Internet celebrity group to understand consumers’ psychology in depth, help the Internet celebrity group to better establish a communication bridge with consumers to form a more mature and good interaction mechanism, and better use new media to promote sales activities. This article predicts and analyzes the consumption behavior of social e-commerce and combines the characteristics of hierarchical planning to intelligently process the system to improve the effectiveness of the system. The experimental analysis shows that the social e-commerce consumer behavior prediction model based on the layered polarization characteristics proposed in this article is effective and can play an important role in the prediction of social consumer behavior.



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*Source: 9666677-2022-05-29.xml*