# An Improved Online Folk Sports Culture Exchange Model Based on Multimedia Data Analysis and Edge Computing

Authors: Sheng-li Cui; Kalra Anurag
Journal: Mobile Information Systems
 (2022)

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## Abstract

In order to improve the effect of folk sports cultural exchange, this study proposes an improved online folk sports cultural exchange model based on multimedia data analysis and edge computing. Moreover, this study explores the factors that affect the local popularity of media content and establishes a relationship model between user request volume and edge node location characteristics. In addition, this study designs customized edge storage strategies under different conditions, which effectively increases the amount of user requests processed by edge nodes and enhances the agility of edge nodes to respond to user content requests. Finally, in order to improve the effectiveness of content crowdsourcing collection, the edge platform needs to select the optimal set of participants to complete the content collection task under a given task budget. The experimental research shows that the improved online folk sports culture exchange model based on multimedia data analysis and edge computing can realize the effective exchange of folk culture.


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## Body

## 1. Introduction

Culture belongs to the field of ideology and obeys the law that material determines consciousness, and changes at the level of material form will also lead to corresponding changes at the level of culture. The main source of folk culture is a cultural belief, and many folk sports activities are derived from belief worship. For example, the “Maogus” of the Tujia people in western Hunan originated from the worship of reproductive organs. The peacock dance of the Dai people in Yunnan originates from the fact that the local residents regard the peacock as the spiritual symbol of their own nation, thus imitating the dance of the peacock to express their ideals and wishes. Moreover, traditional folk sports activities transcend the closure and restrictions of primitive beliefs, transcend their own national and regional restrictions, and spread to a wider area and receive a higher degree of acceptance. For example, wrestling, which is prevalent in the life of the Yi nationality people, was originally a religious sacrifice for the Yi nationality people to entertain the gods in order to pray for good weather and prosperity of the six animals. With the development of society, people have a better understanding of nature, and the religious sacrificial color of wrestling activities of the Yi nationality gradually fades, but it still reflects strong cultural and folk customs.In addition to the influence from modern cultural civilization, Western sports culture, which is the dominant sports culture in the world today, has also had a great impact on the ecology of traditional folk sports culture. Comparing the natural ecosystem with the cultural ecosystem, the traditional folk sports culture is like the rice we often eat, while the western sports culture is like the corn that we are very common now. Corn originates from Central America and was introduced to China during the Ming Dynasty in the sixteenth century. Now China is the second largest corn producer in the world, and one of the main grains for the people in the wadi regions of northern and southwestern China. It is almost equal to rice, its economic value and use value are no less than that of rice, and it has more advantages than rice as feed for livestock. Compared with the local folk sports culture ecosystem, Western sports culture is a kind of foreign cultural species. It already has a mature and close cultural system, its adaptability and influence are greater than that of traditional folk sports culture, and its expansion is relatively stronger. It is undeniable that Western sports culture spreads rapidly in China like corn, and even its development level far exceeds that of traditional folk sports, and its acceptance is quite high. Moreover, under the trend of global economic integration, the invasion of foreign cultures is almost inevitable. In the face of this irreversible trend, we should not blindly reject it, but should “take what is long and make up for our shortcomings” and adjust together. And adapt to the new cultural ecosystem, strive to seek common ground while reserving differences, and achieve a win-win situation. Moreover, Western sports culture is not without merit. On the one hand, it brings a more advanced sports culture and a more active sports spirit, and also brings a sense of crisis and competition to folk sports culture, as well as opportunities and challenges., forcing folk sports out of the closed circle to cross geographical restrictions and spread to a wider area.This study proposes an improved online folk sports culture exchange model based on multimedia data analysis and edge computing to improve the effect of online folk sports culture exchange.


## 2. Related Work

Regarding the definition of the concept of folk sports, scholars use different disciplinary theories to define it from different angles. Literature [1] believes that “folk sports is a collection of diverse sports and games”. The common element of this collection is the formation of customs among the people and is related to folk culture. Folk sports include traditional sports, National sports, indigenous sports, and games also include new sports activities based on traditional behaviors, such as bar games, and noncompetitive walks. Folk sports correspond to modern sports and are closer to all sports for the public [2]. Literature [3] pointed out according to the connotation of “custom” of folklore: “The ontology attribute of folklore sports lies in the ontology attribute of folklore. Folklore sports are created by certain people, inherited and enjoyed by certain people, and integrated into and attached to it. A collective, patterned, traditional, and daily sports activity in the customs and habits of people’s daily life (such as festivals, etiquette, etc.) is not only a sports culture but also a life culture. Literature [4] defines folk sports from the perspective of cultural forms as: “The sports form spread in folk customs or folk culture and folk way of life is a special kind of sports that is produced and developed to meet and meet the various needs of the people cultural form”. Literature [5] believes that from the perspective of life mode: “Folk sports refers to the sports life mode that the people (the common people) have inherited from generation to generation in social life, and it is a social group in sports language, behavior, and psychology.” Literature [6] believes that: “Folk sports is a form of activity related to fitness, entertainment, competition, and performance that is produced in folk activities, depends on the development of folk festivals, and spreads in a certain time and space.” “Folk custom sports is a kind of physical exercise cultural habit that a nation slowly co-creates and forms a tradition in the place where it lives.” It has a common national outlook on life, long-standing living habits, and typical behavior patterns. The physical exercise of this nation’s culture must use gross muscle activity as a way to increase health and use the educational opportunities of physical activity to cultivate the ability of social life and achieve the purpose of education for the balanced development of body and mind [7]. In addition to the folk sports in the school sports, the more important thing is the activities in the social and folk welcome games and festivals.Regarding the research on the characteristics of folk sports, the literature pointed out that folk sports have internal characteristics such as competition, entertainment, dependence, ethnic differences, and commonality of all human beings, while external characteristics include historical, regional, inheritance, Variability and ornamental. Literature [9] pointed out that the characteristics of folk sports are: people’s ideas and intentions to participate in folk sports activities are relatively clear, mainly from beliefs and tendencies of passion; there is a considerable time and space span of tradition; relatively strict normative, participants can consciously respect and maintain; have a certain universality; focus on mass activities, with very competitive characteristics; obvious social benefits; most projects have more or less religious colors. It is believed that the characteristics of sports folklore are the embodiment of the internal form of folklore events, which are mainly nationality, regionality, inheritance, variability, collectivity, and program. In the research on the characteristics of folk sports, most scholars are based on the essential attribute of folk sports, and by grasping the characteristics of folk sports, they summarize the universal characteristics of folk sports [10]. Most of the studies on the characteristics of these folk sports are macroscopic and general studies, and there are few studies on the characteristics of regional folk sports from a microscopic perspective. “Commonality resides in individuality”, the research on the characteristics of regional folk sports is an important guarantee for the general research on the characteristics of folk sports, and the research on the characteristics of regional folk sports needs to be further improved [11]. Regarding the classification of folk sports, folk sports are divided into: running, jumping, throwing, gymnastics, ball, water, shooting, riding, wrestling, martial arts, dance, and games according to the form and content of sports and others [12]. Literature [13] divides folk sports into Han folk sports and ethnic minority folk sports according to nationality and physical education. Literature [14] divides folk sports into: playful entertainment, competition, and festival customs according to the application of folk sports in physical education courses. Literature [15] is divided into traditional labor production, folk sports in daily life, Chinese marriage custom culture, folk sports in festivals, flower fairs, temple fairs, and folk sports in sacrificial rituals. Literature [16] classifies the folk sports culture in traditional festivals and divides them into the sports of gambling and competition in festivals and the sports of entertainment and viewing in festivals according to the nature of the activities. Due to the different research perspectives and classification standards chosen by different scholars, the classification of folk sports is also different. The above classification of folk sports will provide a certain literature for the classification of traditional festival folk sports in this study.


## 3. Multimedia Content Storage Strategy Based on Location Characteristics of Edge Nodes

The d-dimensional vectorxf,n∈ℝd represents the parameter vector of file f at edge node n. Taking video content as an example, this parameter can describe the video’s definition, style, theme, length, and historical data requested at an edge node (Figure 1). We assume that df,n represents the request volume of file f at the edge node n, and we assume that the following linear model exists:(1)df,n=xf,nTθn∗+wn.Figure 1
Edge storage system model.Among them,θn∗∈ℝd is the position feature vector of the edge node n to be predicted. In the actual scene, the position feature vector will change with time. wn is the random noise associated with edge node n. It is affected by many factors, including the social function of the node’s location, the number of users served, and the frequency of stored content updates.We assume that the setℱ=1,2,…,F is the set of all storable files, and denote the storage capacity at each edge node by c < F. The model divides time into a series of time slots T=1,2,…,T, and sets ℱn,t to be the set of files stored at edge node n in time slot t, while setting df,n,t to be the amount of requests for file f at edge node n in time slot t. The goal of formulating the storage strategy in this study is to maximize the average number of requests processed locally within each time slot. Its mathematical description is as follows:(2)max1T∑t∈T∑n∈N∑f∈ℱn,tdf,n,t,(3)Subject toℱn,t≤c,∀n∈N,t∈T.Since the user’s request volume is unknown, the setℱn,t of stored files is also unknown, and the above optimization problem cannot be solved directly. To this end, we solve the above optimization problem by approaching the optimal storage strategy. We assume that ℱn,t∗ represents the optimal set of timeslot t stored at node n, then for ∀n∈N,t∈T, we have(4)ℱn,t∗=argmaxℱn,t≤c∑f∈ℱn,tdf,n,t.For any given storage strategy, the time-averaged storage utility loss functionR (t) is defined as follows:(5)RT=1TE∑t∈T∑n∈N∑f∈ℱn,ttdf,n,t−∑f∈ℱn,tdf,n,t.Then, the problem of maximizing content requests described in formula (2) can be transformed into the following problem:(6)minℱn,t,∀n∈N,t∈TRT.Considering that the noise process described by the linear model 1 is an ideal zero-mean scene, at this time, the influence of various uncertain factors at the edge noden on the user’s request volume has a mean value of zero. That is, Ewn=0. From formula (1), we can obtain:(7)Edf,n|xf,n=xf,nTθn∗.Specifically, least squares estimation is the solution to the following problems:(8)θn∗=argminθnyf,n−Φf,nθn2.Among them,yf,n∈ℝm is the historical request vector of the file f at the edge node n, and Φf,n∈ℝm×d is the parameter matrix composed of the corresponding historical parameter vector. Accordingly, the unbiased estimate of θn∗ can be obtained as θn∗=Φf,nTΦf,n−1Φf,nTyf,n.Compared with the unbiased estimation of least squares, ridge regression can solve the problem of $3.8$ and get a biased but more stable estimation. Specifically, ridge regression adds a penalty term when solving the minimization problem of (8), as follows:(9)θn∗=argminθnyf,n−Φf,nθn2+μθn2.Among them,μ>0 is a constant, which controls the size of the estimator. The larger the μ, the smaller the magnitude of θn. Thus, a more stable estimation of θn∗ can be obtained, and the explicit expression of the estimation result is(10)θn∗=Φf,nTΦf,n+μId−1Φf,nTyf,n.Among them,Id is a D-dimensional unit matrix. To simplify the formula symbol, Vf,n=Φf,nTΦf,n+μId is defined, and the error of the ridge regression estimate is analyzed.We assumehf,n=Φf,nTyf,n, and the ridge regression estimation error can be rewritten as:(11)xf,nTθ∼n−xf,nTθn∗=xf,nTVf,n−1hf,n−xf,nTVf,n−1Φf,nTΦf,n+μIdθn∗.(12)=xf,nTVf,n−1Φf,nTyf,n−Φf,nθn∗−μxf,nTVf,n−1θn∗.Due toθn∗≤ζ, according to Hölder inequality μxf,nTVf,n−1θn∗≤ζμxf,nTVf,n−1 is established. Then, the estimated error in the formula (12) can be further written as(13)xf,nTθ∼n−xf,nTθn∗≤xf,nTVf,n−1Φf,nTyf,n−Φf,nθn∗+ζμxf,nTVf,n−1.Two nonequivalent right sides are variance (Variance) and deviation (Bias) in the ridge regression estimation error, respectively.It can be seen from the formula (7) Eyf,n−Φf,nθn∗=0. If the requests of each content are independent of each other, the McDiarmid inequality of the Azuma inequality can be obtained by the following variance probability:(14)ℙxf,nTVf,n−1Φf,nTyf,n−Φf,nθn∗>δxf,nVf,n−1≤2exp−2δ2xf,nVf,n−12xf,nTVf,n−1Φf,nT2≤2e−2δ2.Among them, the last inequality is:(15)xf,nVf,n−12=xf,nTVf,n−1Φf,nTΦf,n+μIdVf,n−1xf,n≥xf,nTVf,n−1Φf,nTΦf,nVf,n−1xf,n=xf,nTVf,n−1Φf,nT2.It can be seen from formula (14) that the probability that the upper boundary of the variance term of the estimation error is δxf,nVf,n−1 is not lower than 1−2e−2δ2. For the bias term, its upper bound can be directly given by the following formula:(16)xf,nTVf,n−1=xf,nTVf,n−1IdVf,n−1xf,n≤xf,nTVf,n−1Φf,nTΦf,n+μIdVf,n−1xf,n=xf,nVf,n−1.Substituting formulas (14) and (16) into (13), the following lemma holds.Lemma 1.
If∀n∈N, and θn∗≤ζ is established, then ∀δ>0, and the upper bound of the ridge regression estimation error is:(17)xf,nTθ∼n−xf,nTθn∗≤δ+ζμxf,nVf,n−1.
The probability of the above formula is not lower than1−2e−2δ2.
The above lemma shows that the actual valuexf,nTθn∗ of the user request quantity falls within the high probability confidence interval xf,nTθ∼n−δ+ζμxf,nVf,n−1,xf,nTθ∼n+δ+ζμxf,nVf,n−1 of the estimated value xf,nTθ∼n, and the size of the interval is determined by the parameters δ,ζ,μ and the video content parameter matrix.
Specifically, the operation of each part is as follows.
In each time slott, the edge node $n$ firstly updates the estimated θ∼n,t of its location feature vector based on the user’s observation of the amount of storage content requested at the previous moment. Then, according to the linear prediction model 7, the edge node makes a prediction d˜f,n,t for the content f requested by users in this time slot. Considering the influence of zero-mean noise, we add the perturbation term pf,n,t to the estimate of the request volume of each file and obtain the upper boundary of its request volume d^f,n,t=d˜f,n,t+pf,n,t. Among them, there are(18)pf,n,t=αtxf,n,tVf,n−1.
Furthermore, there isαt=lntF1/21/2+ζμ°.
It is worth noting that the value ofαt is formally consistent with the upper bound of the error given by formula (11). The value form of αt is consistent with the upper bound of the probability of Lemma 1, and there is αt=lntF1/21/2. Further, the probability that the upper bound of the estimated error holds is 1−2F−1t−2. With the increase of time t, the value of the above tail probability rapidly approaches 1.
The theoretical analysis of the storage strategy is now carried out, and the specific form of the time-averaged storage utility loss function is solved. By Lemma1, the high-probability confidence interval for the estimation error of the RPUC algorithm for the user request volume is defined as:(19)Jf,n,t=xf,nTθ∼n−pf,n,t,xf,nTθ∼n+pf,n,t.
We assume that eventxn,t=∃f∈ℱ:df,n,t−d˜f,n,t≥pf,n,t means that there is at least one content whose estimated value of the request volume falls outside the corresponding confidence interval, and X¯n,t is the complementary event of event xn,t, that is, the estimated value of the request volume of all content falls within the corresponding confidence interval. Further, rn,t is set to be the instantaneous storage utility loss of edge node n in time slot t. It can be seen from formula (5) that the immediate storage utility loss of edge nodes is positively related to the difference between the storage content set ℱn,t and the optimal storage set ℱn,t∗ selected by the RPUC algorithm, that is,(20)rn,t=∑f∈ℱn,t∗df,n,t−∑f∈ℱn,tdf,n,t.
Moreover, the statistical mean of storage loss utility is:(21)RT=1T∑t∈T∑n∈Nrn,t=1T∑t∈T∑n∈N1xn,trn,t+1T∑t∈T∑n∈N1x¯n,trn,t.
Among them,1xn,t indicates the truth value function of the event. When the event Xn,t occurs, its value is 1, otherwise, it is 0. The discussion of the estimation error of the user’s request amount in formula (21) is divided into two cases according to whether the event xn,t occurs or not, and its influence on the average storage utility is discussed accordingly.
When the eventXn,t occurs, the value of αt indicates that ∀n∈N,t∈T,f∈ℱ, and ℙdf,n,t−d˜f,n,t≥pf,n,t≤2F−1t−2 is established. Therefore, the upper bound on the occurrence frequency of event Xn,t on the full-time scale is:(22)∑t∈T∑n∈N1xn,t≤∑t∈T∑n∈N∑f∈ℱℙdf,n,t−d˜f,n,t≥pf,n,t≤∑t∈T∑n∈N∑f∈ℱ2F−1t−2=2N∑t∈Tt−2≤2N∑t=1∞t−2≤π23N.
Since the user request quantitydf,n,t≤γ. According to formula (20), the upper bound of the immediate storage loss can be roughly written as rn,t≤cγ, where c=ℱn,t∗ represents the storage capacity of the edge node. Accordingly, the first term on the right side of formula (21), that is, the loss of storage utility when the event Xn,t occurs, satisfies the following formula:(23)1T∑t∈T∑n∈N1xn,trn,t≤π2cγ3TN.
When the eventX¯n,t occurs, the predictions of the RPUC algorithm for all content requests fall within the confidence interval of high probability, so df,n,t−d˜f,n,t≤pf,n,t is always established. From d^f,n,t=d˜f,n,t+pf,n,t, we can obtain:(24)df,n,t−d˜f,n,t≤2pf,n,t.
Combining formulas (20) and (24), it can be obtained that when the event X¯n,t occurs, that is, the loss of storage utility can be defined as:(25)1x¯n,trn,t=∑f∈ℱn,t∗\ℱn,tdf,n,t−∑f∈ℱn,tℱn,t∗df,n,t≤∑f∈ℱn,t∗\ℱn,td^f,n,t−∑f∈ℱn,tℱn,t∗df,n,t≤∑f∈ℱn,t\ℱn,t∗d^f,n,t−df,n,t,(26)≤2∑f∈ℱn,t/ℱn,t∗pf,n,t.
Among them, formula (25) is established because the content in the set ℱn,t/ℱn,t∗ is selected by the RPUC algorithm, so compared with the set ℱn,t∗/ℱn,t, the estimated value of its request volume is higher, that is:(27)∑f∈ℱn,tℱn,t∗d^f,n,t≥∑f∈ℱn,t∗/ℱn,td^f,n,t.
In order to further define the immediate storage utility loss, recalling Lemmas1 and 2, the following formulas hold:(28)∑t∈T∑n∈N1x¯n,trn,t≤2∑t∈T∑n∈N∑f∈ℱn,t/ℱn,t∗pf,n,t,(29)≤2cαT∑t∈T∑n∈Nxf,n,tVf,n−1,(30)≤2cαT∑n∈NT∑t∈Txf,n,tVf,n−12,(31)≤2cαTN2Tlnμ+Tη2/ddμ.
Among them, inequality (28) is established because αt increases with time, and formula (30) is established because the arithmetic average of the sequence is less than its root mean square value. Meanwhile, formula (31) can be obtained directly by applying Lemmas 1 and 2. Finally, the model substitutes formulas (31) and (23) into (21), and combines αT=lnTF1/21/2+ζμ to get:(32)RT≤2cαTN2Tlnμ+Tη2/ddμ+π2cγ3TN=OcNdlnTTlnμ+Tη2/d.
Accordingly, the following theorem holds.Theorem 1.
If the noise of the state model is zero mean, the storage algorithm RPUC asymptotically approaches the optimal storage strategy. Its average storage utility loss functionR (T) is of the order of OcNdlnT/Tlnμ+Tη2/d. That is, when T⟶∞, RT⟶0.
Considering the situation of a specific file at an edge node, in order to simplify the notation, we omit the subscriptsf and n, and rewrite formula (1) as the following state and observation formulas:(33)θt+1=θt,dt=xtTθt+wt.
To predictθ∗ in a dynamic environment, the following prediction loss function is defined:(34)J0=∑t=0Tθ∗−θ∼t2θ0−θ∼0P02+∑t=0Twt2.
Among them,P0 is a symmetric positive definite matrix, which is used to represent the confidence value of the initial prediction θ∼0. When the initial prediction has high uncertainty, a small (eigenvalue) P0 can be used, and vice versa. The goal of the H∞-filtering algorithm is to make a series of predictions for θ∗ that minimize the numerator of the loss function J0. The denominator of J0 can be seen as a combination of all possible initial state predictions as well as arbitrary noisy processes.
The initial stateθ0 and noise sequence combination wtt=1T must be carefully designed. Specifically, the game problem can be described by the following min–max optimization problem:(35)J0∗=minθ⟶tmaxθ0,WtJ0.
For the form of the prediction loss function of formula (34), it is very difficult to directly solve the above min–max optimization problem. In practical scenarios, H∞ filtering starts from the preset parameter ψ>0, and obtains the suboptimal solution of the above problem. Specifically, there are:(36)supJ0<ψ2.
That is, theH∞ filtering method attempts to control the supremum of the prediction loss function by preset parameters under the conditions of the game.
To solve the above minimum–maximization problem, we rewrite the prediction loss function as follows:(37)minθtmaxθ0,wtJ≜−12ψ2θ0−θ∼0P02+12∑t=0Tθ∗−θ∼t2−ψ2wt2.
The transformed min–max problem above can be viewed as a zero-sum game problem. For a given value ofψ, our optimization goal is to find a series of estimates θ∼tt=1T such that the prediction loss function J<0. With the help of the Lagrange multiplier method H∞ filtering method, the solution of the above dynamic restricted optimization problem is obtained in an iterative manner. Specifically, there are:(38)θ∼t+1=θ∼t+Rtdt−xtTθ∼t.
Among them, the initial value ofθ∼t is θ0∼=0d, and Rt is the filter gain, which is given by the following formula:(39)Rt=Mtxt1+xtMt2−1.
Furthermore, there are:(40)Mt+1−1=Mt−1+xtxtT−ψ−2Id.
Among them, the initial value ofMt−1 is M0−1=P0−ψ−2Id.
We assume thatψt+1 represents the preset error value in the t + 1th time slot, in order to ensure that Mt+1−1 in formula (40) is not singular, the following formula holds:(41)Mt−1+xtxtT−ψt+1−2Id>0.
We assume thatλmaxA=λ1A≥⋯λkA⋯≥λdA=λminA represents the eigenvalue of the d-order invertible square matrix A, and λkA is the kth largest eigenvalue. According to the minimum–maximum theorem of matrix eigenvalues, ψt+1 needs to satisfy the following formula:(42)λkMt−1+xtxtT>λkψt+1−2Id,∀k∈1,2,…d.
Since∀k∈1,2,…d has λkψt+1−2Id=ψt+1−2 established, then λminMt−1+xtxtT>ψt+1−2. For this reason, the following formula is established.(43)ψt+1−2=ξ−2λminMt−1+xtxtT.
Among them,ξ is a constant close to 1 but greater than 1, which minimizes the amplitude of ψt and is always positive, thus ensuring that the matrix Mt+1−1 is always nonsingular.
Considering the crowdsourcing system model based on the edge network shown in Figure2.Figure 2
Crowdsourcing system model based on edge platform.Definition 1.
(first-order probability dominance). we define the cumulative distribution functionFπ|ε,ζ=∫π1pπ′|ε,ζdπ′ as the probability that the participant’s degree of completion is higher than π when the level of willingness and ability of the participant is ε,ζ. If π∈0,1 holds for any Fπ|ε,ς≥Fπ|ε′,ς, then ε is said to dominate the first-order probability of ε′.
For any functionp⋅ that satisfies the first-order probability dominance, the following lemma holds.Lemma 2.
When users have the same ability level, the participants with a higher willingness to participate have higher task completion.
The proof is as follows: we assume thatε≥ε′, and F′π|ε,ς is the cumulative distribution function of the completion probability function pπ|ε,ς. The definition of first-order probability possession shows that the following formula holds: F′π|ε,ς=1−Fπ|ε,ς≤1−Fπ|ε′,ς≤F′π|ε′,ς. For a participant whose willingness to participate is ε, the expected completion value is Πε=∫01πpπ|ε,ζdπ=πF′π|ε,ζ01−∫01F′π|ε,ζdπ=π−∫01F′π|ε,ζdπ. According to this, Πε−Πε′=∫01F′π|ε′,ς−F′π|ε,ςdπ≥0.. The lemma is proven.
We assume thatv⋅:2w⟶ℝ+ represents the utility metric function of the edge platform. For a selected set of participants S⊂W and A⊆W/S, the set function is defined as follows:(44)ΨvA|S=vA∪S−vS.
The above formula is the marginal value of the participant setδ for a given participant set A. At the same time, we assume that the participants’ feedbacks are different from each other, so there is vw1,w2>maxvw1,vw2. The descending characteristics and monotonicity of the marginal platform utility function are defined as follows:Definition 2.
(below model characteristic). The aggregate functionv⋅:2W⟶ℝ+ is defined. If for A⊆ℬ⊆W and wk∈W/ℬ, Ψvwk|A≥Ψvwk|ℬ is always established, then the set function v⋅ has the lower model property. Correspondingly, for A⊆W and w1,w2∈W/A, Ψvw1|A+Ψvw2|A≥Ψvw1,w2|A holds.Definition 3 (monotonicity).
If for anyA⊆ℬ⊆W, vA≤vℬ holds, then the set function v⋅ is said to be monotonic.
The goal of an edge crowdsourcing platform is to select a set of participantsδi to maximize its utility function, that is,(45)δi=argmaxS⊆W,|S|≤bviδ.
The utility loss functionRn is used to characterize the cumulative utility gap between the speculative learning algorithm design algorithm and the posterior optimal strategy, that is,(46)R˜n=max|S|≤b∑i=1nviδ−E∑i=1nviδi.
To reach the1−1/e-optimal, the utility loss function is changed to the following form:(47)Rn=1−1e⋅max|S|≤bE∑i=1nviδ−E∑i=1nviδi.
It mainly solves the problem of minimizing the cumulative utility loss as follows:(48)minδii=1nRn.
We defineδt=wjj=1t as the set of the first t content crowdsourcing participants selected in turn by the greedy algorithm, and Ψt=EΨvwt|δt−1 as the marginal utility gain function of the tth participant. According to the monotonicity and lower model characteristics of the utility function of the crowdsourcing platform, the following formula is established:(49)EvP≤EvP∪δtEvδt+∑wk∈P\δtΨvwk|δt.
We assume thatv^⋅ is the perturbation utility function based on the perturbation completion degree sequence π^kk=1K, and Ψ^t=EΨv^wt|δt−1 is the marginal utility gain function of the perturbation, then v^wk≤vwk+ϵk is established. Since in the t+1th cycle of the algorithm, wt+1 is selected among the remaining participants; therefore, ∀wk∈P/δt has Ψv^wt|δt≥Ψν^wk|δt. established. Since P/δt≤b, inequality 49 can be written as:(50)EvP≤Evδt+bΨ∩t+1.
Using the lower model properties of the utility functionv⋅, Φ^t+1≤Ψt+1+ϵt+1 is established, and the inequality 50 can be iteratively transformed into(51)EvP≤Ψ1+⋯Ψt+bΨt+1+bϵt+1.
We assumeΨ0=0, and t=0,1,…,b−1 respectively. The formula (52) can be transformed into b different inequalities. We multiply the t th inequality above by the coefficient 1−1/bb−1−t, in turn, and accumulate all the b inequalities. The coefficient of the EvP term on the left side of the obtained inequality is ∑t=0b−11−1/bb−1−t=∑t=0b−11−1/bt=b1−1−1/bb, and the coefficient of the right side term of the inequality Ψt is b1−1/bb−t+∑i=tk−11−1/bb−1−i=b. Hence, there are:(52)b1−1−1/bbEvP≤∑t=1bΨt+∑wk∈Sϵk.
Since the inequalityb1−1−1/bb≤e−1/b is always established, the following theorem is established.Theorem 2.
The upper bound of the utility gap between the expected utility of the linear greedy algorithm and the posterior optimal strategy is∑wk∈Eϵk, that is,(53)EvS≥1−1e⋅EvP−∑wk∈Sϵk.
By setting the perturbation termϵk=0 in Theorem 1, the single-task crowdsourcing utility of greedy algorithm 1 can reach 1−1/e-optimal.
We assume thatπ˜i,k represents the experience completion value of the participant wk when the crowdsourcing task ti arrives, and π¯i,k represents the upper bound of the experience value. Since πk∈0,1, we have:(54)π¯i,k=minπ˜i,k+ci−1,fi−1k,1.
Among them, the perturbation is as follows:(55)ci,fik=μlogifik.Lemma 3 (Chernoff–Hoeffding inequality).
IfX1,X2,…,Xn∈0,1 is a sequence of random variables and EXt|X1,X2,…,Xt−1=ξ is established. We assume Sn=X1+X2+⋯+Xn, then for ∀a≥0, the following inequality holds:(56)ℙSn≥nξ+a≤e−2a2/n,ℙSn≤nξ−a≤e−2a2/n.
By applying the Chernoff–Hoeffding inequality, the actual completion degreeπi,k of the crowdsourcing task of the participants can be obtained as follows:(57)ℙπ˜i,k−πk≥ci,fik≤2e−2μ2logi=2i−2μ2.
That is, the disturbance term form of the formula (54) effectively guarantees: when μ≥1, the actual completion degree πk of the crowdsourcing task of the participants falls within the interval π˜i,k−ci−1,fi−1k,π˜i,k+ci−1,fi−1k with a high probability.
We assume thatS∗=argmax|S|≤bE∑i=1nviS represents the posterior optimal participant selection scheme for all n crowdsourcing tasks, and the set P is the suboptimal solution obtained in polynomial time based on the greedy algorithm. From Theorem $4.1$, we can obtain:(58)E∑i=1nviP≥1−1e⋅E∑i=1nviS∗.
We assume thatδi represents the set of participants selected by the UCBG algorithm for the crowdsourcing task ti and define the loss of the crowdsourcing utility of the platform after the set of participants completes the task as Ri=EviP−EviSi. According to the formula (47), the cumulative utility loss of the crowdsourcing platform satisfies the following formula:(59)Rn≤E∑i=1nviP−E∑i=1nviδi=∑i=1nRi.
Sinceπk∈0,1 and |P|=Si=b, then Ri≤b holds for ∀ti∈T.
We assume that eventxi=∃wk∈W:π˜i−1,k−πk≥ci,fik means that when assigning participants to a crowdsourcing task ti, there is at least one participant whose actual completion degree πk falls outside the high confidence interval of the estimated value π∼i−1,k. We assume that X¯i represents a complementary event to xi, that is, the actual completion of πk for all participants falls within the high confidence interval of the estimated value π∼i−1,k. Accordingly, we decompose the cumulative utility loss shown in formula (49) into the following three categories and analyze them separately:(60)Rn≤∑i=1i0Ri+∑i=i0+1n1xiRi+∑i=i0+1n1x¯iRi.
Here,1xi is an indicator function; when the event xi occurs, its value is 1, otherwise, its value is 0.
Since all participants are selected at most once in the initialization phase of the algorithm, the utility loss in this phase satisfies the following formula:(61)∑i=1i0Ri≤i0b≤K.
In the online selection stage, the cumulative frequency of eventxi can be obtained from the Chernoff–Hoeffding inequality to satisfy the following formula:(62)∑i=i0+1n1xi≤∑wk∈W∑i=1n∑f=1iℙπ˜i,k−πk≥ci,fik≤2∑wk∈W∑i=1n∑f=1ii−2μ2≤2K∑i=1∞i−2μ2+1.
Whenμ2≥3/2, ∑i=1∞i−2μ2+1≤∑i=1∞i−2=π2/6 holds. Since Ri≤b holds for ∀ti∈T, the second term on the right-hand side of Inequality (59) satisfies the following formula:(63)∑i=i0+1n1xiRi≤π2Kb3.
When the eventX¯i occurs in the online selection stage, the actual completion degree πk of all participants falls within the high confidence interval of the estimated value π∼i−1,k, that is, for ∀wk∈W, πk−ci−1,fi−1k≤π˜i−1,k≤πk+ci−1,fi−1k holds. From πk∈0,1 and π¯i,k=minπ˜i,k+ci−1,fi−1k,1, the following inequality holds:(64)πk≤π˜i,k≤πk+2ci−1,fi−1k.
For the sake of brevity, the intersectionJi=δi∩P is defined, and the complements δid=δi/P,Pid=P/δi are defined. The utility loss for completing the crowdsourcing task ti is rewritten as:(65)Ri=EviJi+ΨviPid|Ji−EviJi+ΨviSid|Ji=EΨviPid|Ji−EΨviδid|Ji.
At the same time,v¯⋅ represents the upper bound function of crowdsourcing utility calculated based on participant completion degree UCB. Since the participant set δi is selected by the algorithm, the upper bound of its crowdsourcing utility is higher than the upper bound of the crowdsourcing utility obtained by the posterior optimal participant set P, that is, v¯isi≥v¯iP. Furthermore, the following inequality holds:(66)Ψv¯iδid|Ji≥Ψv¯iPid|Ji.
According to the lower model properties of the utility function and inequality (63), the independent utility upper bound for a single player satisfies the following formula:(67)Eviwk≤v¯iwk≤Eviwk+2ci−1,fi−1k.
Accordingly, for the participant setSid, the upper bound of its marginal utility gain relative to the set Ji satisfies the following inequality:(68)Ψv¯iδid|Ji≤EΨviδid|Ji+2∑wk∈Sidci−1,fi−1k.
Meanwhile, the inequality holds as follows:(69)Ψv¯iPid|Ji≥EΨviPid|Ji.
The inequalities (65), (66), (68), and (69) can be combined to obtain that when the event X¯i occurs, that is, when the utility loss satisfies the following formula:(70)Ri≤2∑wk∈Sidci−1,fi−1k.
The set of participants with fewer selections in setδid is as follows:(71)Qi≜wk∈Sid:fi−1k≤αlogn.
Accordingly, the following two events are defined:(72)yi1=Qi≥γ,yi2=Qi<γ,∃wk∈Sid:fi−1k≤βlogn.
Among them,α and β are positive constants. Rmin=miniRi, the following lemma can directly get the cumulative utility loss when the event X¯i occurs.Lemma 4.
When eventx¯i occurs, 0<γ≤b,α=16μ2b2/Rmin2,β=16μ2γ2/Rmin2, then one of event yi1 and event yi2 must happen. The cumulative frequency of event yi1 and event yi2 satisfies ∑i1yi1≤K/γαlogn and ∑i1yi2≤Kβlogn/γ, respectively.
The above lemma can be briefly proved in two steps as follows. First, the event is defined as follows:(73)y¯i=Qi<γ,∀wk∈δid:fi−1k>βlogn.
The above definition shows that eventsyi1,yi2, and y¯i are mutually exclusive events, and the sum of their probability of occurrence is 1. Therefore, if event y¯i does not occur, then one event yi1 and event yi2 must occur. It is now proved that event y¯i cannot happen because of the following paradox:(74)Ri≤2∑wk∈Sidcn,fi−1k=2∑wk∈Sid/Qicn,fi−1k+2∑wk∈Qicn,fi−1k,(75)<2μblognαlogn+2μγlognβlogn=Rmin.
We assumeRmax=maxiRi; according to Lemma 3, the third term of formula (60) satisfies the following formula:(76)∑i=i0+1n1x¯iRi≤Rmax∑i=i0+1n1yi1+1yi2≤16μ2Kb2γ+γ2RmaxRmin2logn.
We assumeγ=b2/3, and substitute formulas (61), (63), and (75) into formula (60) to obtain the mean cumulative crowdsourcing utility that satisfies the following formula:(77)Rn=32μ2Kb4/3RmaxRmin2logn+π23Kb+K.
It can be seen from the above formula: whenn⟶∞, Rn/n⟶0. Therefore, the above theorem holds.


## 4. An Improved Online Folk Sports Culture Exchange Model Based on Multimedia Data Analysis and Edge Computing

Through the edge computing mentioned above, the data processing of cultural and communication platforms is carried out to improve the efficiency of data sharing. Figure3 shows the structure of the folk culture resource optimization system based on the multimedia data platform. The system is divided into the application layer, business logic layer, and data layer. The application layer mainly serves users, and users can log into the system on the front-end interface of the system, and the external interface is the communication carrier between the application layer and the business logic layer. The business logic layer can schedule diverse folk sports and cultural resources according to user requests. The data layer provides distributed storage services for folk sports and cultural resources. Hadoop is a distributed file storage system composed of a variety of databases, and the database uses the open source tool Sqoop to realize the transmission of folk sports and cultural resources. This distributed file storage system has good stability, and the storage of folk sports and cultural resources has extremely high security. Therefore, users can make full use of the advantages of cloud platform clusters for fast resource scheduling and storage without knowing the underlying details of the distribution.Figure 3
The structure diagram of the optimization system of folk sports cultural resources based on cloud platform. The structure of the Hadoop distributed file storage subsystem is shown in Figure4.Figure 4
Structure diagram of distributed file storage subsystem.The multilateral platform for public digital cultural services takes co-construction, co-governance, and sharing as the strategic goal, and its service principles are inclusive, open, and equal. According to the development status of public digital cultural services and the multilateral platform model introduced above, this research constructs a conceptual framework of multilateral platforms for public digital cultural services that conforms to the characteristics of public digital cultural services (Figure5).Figure 5
Conceptual framework of the multilateral platform for public digital cultural services.From the perspective of resource integration, this study proposes a bottom-up overall construction idea from the three levels of data, platform, and service, and builds a path model for the integration of public digital cultural resources, as shown in Figure6.Figure 6
Model of the integration path of public digital cultural resource.In order to achieve nationwide resource sharing, a unified interoperability model for national resources is defined, as shown in Figure7. Provincial nodes and national central nodes save their own resource data, including material and finished product resources and metadata of resources, as well as the local resource directory of the node.Figure 7
Resource sharing mode.Figure8 shows an example of folk sports culture. In the cultural exchange model constructed in this study, the feature extraction of the above folk culture can be realized, which is convenient to achieve effective folk culture sharing. On this basis, the effect of the folk culture communication model in this study is verified, and the results shown in Table 1 are obtained.Figure 8
Example of folk sports culture. (a) Example 1 of folk sports culture. (b) Example 2 of folk sports culture. (c) Example 3 of folklore sports culture.
(a)(b)(c)Table 1
Improved online folk sports culture exchange model based on multimedia data analysis and edge computing.
NumberCultural exchange191.07293.06389.73489.95592.44691.67789.34893.39993.741093.071192.061288.681391.021487.091592.841688.381792.591891.911990.192088.692191.822288.112387.262490.312590.912687.332789.132888.912993.523089.913191.623293.783391.913488.723590.303692.283788.273892.703993.354087.25It can be seen from the above research that the improved online folk sports culture exchange model based on multimedia data analysis and edge computing can realize the effective exchange of folk culture.


## 5. Conclusion

Changes in cultural beliefs can most directly reflect changes in folk sports activities. With the improvement of people’s material living standards and cultural level, the folk sports activities that were originally intended to entertain gods and pray for good fortune, physical fitness or force to protect one’s family, and entertainment have now evolved into cultural and entertainment activities that focus on entertainment and performance, which have completely lost the seriousness and sublime of cultural beliefs. On the other hand, these changes are not without merit. On the contrary, it reflects the adaptation and adjustment of folk culture to modern culture. This study proposes an improved online folk sports culture communication model based on multimedia data analysis and edge computing. The experimental study shows that the improved online folk sports culture communication model based on multimedia data analysis and edge computing can realize the effective communication of folk culture.



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*Source: 1642988-2022-09-05.xml*