Influence in Social Media Marketing A Quantitative Evaluation Framework from a large scale of Empirical Evidence
Junjie Song, Naoum Jamous, Klaus Turowski Magdeburg Research and Competence Cluster for Very Large Business Applications (MRCC) Otto von Guericke University Magdeburg (OVGU) Magdeburg, Germany Junjie.song;naoum.jamous;
[email protected] Abstract—Social media creates a novel marketing mechanism to boost opinion formation and information diffusion. As a crucial idea, social influence sheds light on individuals’ features in the process of communicating brand stories, and changes other consumers’ opinions and behavior. Social media marketing has drawn great interests from scholars in a past decade, but the extant work neglects to establish an effectively quantitative evaluation framework that bridges the gap between the research findings and actual scenes. By scratching a large amount of empirical data, a set of taxonomy methods for extremely imbalanced examples in terms of statistics and relationship analysis have been proposed. The research performance reveals that the inequality social media distribution presents in multiaspects and multiple levels, and our study can precisely classify individuals having diverse social influence into different groups in which individuals possess common characteristics of social influence. Keywords: Taxonomy.
Social
Media;
Social
Influence;
Marketing;
I. INTRODUCTION The rise of social media platforms has radically transformed the conventional means of information dissemination and communication, and, more importantly, forced marketers to formulate innovative strategies responding to challenges in business and marketing. Traditionally, consumers in general passively received marketer-generated sources that they needed, and managers preferred to diffuse brand stories by the mass media in an attempt to embed systemic brand knowledge in consumers’ memories [1, 2]. Two social features that computer-mediated platforms deliver are: the two-way communication and global reach, which create unprecedented chances for individuals to alter the conventional roles in communication through frequent online interactions and increasing user-generated content [3]. Consequently, the influential individuals who act as intermediaries in the traditional communication context can exert more positive or negative influence so that marketers can no longer have control over major consumers in forming opinions and making decisions on social media platforms [4, 5]. Previous contributions have addressed the topics for social influence on how online interactions affect consumers in the interactive marketing context. In theory, the existing literature intertwining multiple disciplines has involved several research
interests, such as brand management [1], eWOM1 [6], customer relationships [7], and Watts and Doodds article “Influentials, networks and public opinion formation” [5]. The other work has endeavored to develop approaches in order to interpret how the social influence can impact information transfer, for example the betweenness centrality [8], clustering coefficient [10], and PageRank algorithm [11]. Although the extant work mentions many aspects of the online business and communication fields, the systemic analysis of how to recognize and descript the influential individuals still lacks sound practicability and veracity. Certainly, the fact is that online social interactions shift the traditional roles of the influential users as intermediaries between marketers and consumers, which require us to survey the characteristics and features of the influential users in social media. Based on a view from theory into practice, we shall explain the issues of who can affect the network formation and information diffusion, and what attributes propel these performances, or how the influential individuals trigger cascade events [12, 13]. This research establishes a quantitative evaluation framework that bridges the gap between the research findings and actual scenes initiated by a large number of social media platforms as various types of social interactions emerge. In the remainder of this paper, a review of the previous literature concerning the intersection of the attributes capable of measuring social influence and the methodologies for our analysis will be presented. Dealing with considerable relationship data of online marketing gathered from Weibo, we fit the probability density functions of the centralities and the clustering coefficient. Based on the gradient of the tangent lines at all points, we identify a pivot cut-off point that can differentiate the influential and non-influential users. Next, we present an enhanced classification standard to segment the influencers with the dense and sparse distributions. Finally, we optimize the quantitative framework for improving measurement precision and summarize main characteristics of social influence for each group. II. RESEARCH BACKGROUND The marketing and communication work suggests that the minority influencers in a given social network play a pivot role in affecting public opinions and behaviors. The influential 1
Electronic Word of Mouth
hypothesis that generates from the model of “two-step flow” communication [14], refers to a minority of “opinion leaders” able to impact other individuals’ decision-making by exposure to each other [15]. The opinion leader is not a formally organizational position and obtains the influence by interpersonal communication [16]. The early studies mostly aim at the individual-level attributes that the influencers should have， for instance the degree centrality [9] and betweenness centrality [8], and then extend to the relational structures created by interpersonal interactions. For example, a collection of the six analytical units including micro-, meso- and macro-levels of metrics is laid out [17]. Since the end of the 1990’s, the rise of computational approaches enriched the practicable tools to measure properties of the large-scale online social network, and consequently discovered the novel attributes of interpersonal communication, for example the small world nature [10] and the scale-free feature [18]. Some empirical studies investigate the diffusion capabilities of individuals by the relationship attributes and local topological features [19]. The interactive, dynamic and widely accessible social media radically alters the patterns of how people develop and disseminate social influence. The two-way interactive communication on online platforms makes marketers and influencers minimally dependent on one-way mass media to persuade consumers. Instead, social media presents the potential chances for influencers to participate in the more user-generated content and trending topics [1]. Differentiating passive roles of consumers in the conventional media context, online users can become active spreaders by the universally reciprocal interactions so as to strengthen levels of engagement and transmit opinions to more audiences [7]. As for how many people an influential can affect directly, a majority of investigations do not offer an exact answer, but show some specific boundaries, for instance less than 14 persons [20]. However, an influencer is likely to affect more followers over the limitation above because of the scale-free feature of social media. Concerning the effectiveness of metrics that locate the influencers and distinguish the effects of social influence theoretically, empirical studies imply that all indicators cannot lead to the similar outcomes, even if they gauge the influencers in a network [21]. This inference carries some implications about the complexity of social networks. First, an actual social platform consists of different types of relationships including friends, acquaintances, and strangers, and thereby a variety of events triggered by the same persons disseminate along with the different relationship channels, called “many networks in one network” [13]. Second, the metrics extracted from the undirected networks hardly gauge the influence in the directed networks that the real society universally exists [22]. BorgeHolthoefer, Rivero and Moreno [23] put forward the reverse example that users are still influential, even if they locate at disadvantageous positions. Therefore, a successful solution must choose a combination of proper indicators that can match the algorithm requirements in reality. To construct the feasible framework, we insist on the aggregation of the conceptual distinctions and
complementarities for the metrics. Aiming at the positional and relational analytics, we choose three broadly adopted indicators: the degree centrality [9], the betweenness centrality [8], and the clustering coefficient [10] at individual and clique levels [17]. Centrality is a fundamental measurement to specify the position feature of individuals in social networks, which reflects in part the individual characteristics and in part the attributes of the network [9]. The degree centrality represents the number of the direct connections of a given actor. However, the concept fails to describe the abilities of an actor that transfer and receive information. The betweenness centrality indicates the number of shortest paths passing through a given actor to bridge two different nodes if possible. The higher an actor’s betweenness centrality, the stronger the actor has the influence to transmit information through the network. Compared to the centrality focusing on the individual, the clustering coefficient (local) might evaluate the compactness of a clique in the network through computing the number of the triads. III. RESEARCH SETTING AND DATA ACQUISITION We choose a typical social media platform, Sina Weibo, a Twitter-like social media platform, as the research object. Weibo (WB 2 ) is an extraordinarily popular social media platform in China created by Sina Ltd. As of December 2015, Weibo had 236 million monthly active users3. We consider that the platform can offer sufficient data of interactions on which the frequent marketing events launched by firms can be discovered. We assume that the observed phenomena can explicitly express the intensions of marketing strategies as well as that the observed communication interactivity are informative and descriptive to justify the effective contagion. Therefore, the retweeting network is a suitable research object that can more explicitly show the propagation channels than other platforms. A network crawler used in Python to target 83 marketing campaigns of chosen commercial users on Weibo starting on July 01st and lasting until September 10th, 2015. As a result, we gain 231,109 actors and 265,306 edges disseminated on the platform. To eliminate artificial links and fake nodes, we decrease the density of sampling and scan the retweeting data per minute, so as to screen a large amount of the fake retweeting relations created instantly by spammers or software. The dataset creates a total of 85,402,231 shortest paths and 84431 clustering triangles in the light of the breadth priority searching method of computation, and then deduces the result of the betweenness centrality of each actor. IV. QUANTIFYING THE PARAMETER DISTRIBUTION We initiate a statistic analysis on quantitatively characterizing key properties of the retweeting network in order to explain how to specify the metrics of social influence. Although we delve into a given example, Weibo, availability of concepts, assumptions and approaches are generalized to other social media.
2 3
Weibo(WB) http://money.cnn.com/2014/04/16/investing/weibo-ipo/ http://ir.weibo.com/phoenix.zhtml?c=253076&p=irol-irhome
A. Distribution Fitting We organize retweeting relationships into a directed network. The outdegree of a specific vertex is termed the number of the edges from the vertex to its direct successors in the directed graph. In addition, we assume that the leaf nodes whose outdegrees are equal to zero no longer affect any other individual, for they are solely information receivers. As a result, the objective dataset consists of 7654 observations after screening the leaf nodes. We express a set of observations in which the vector consists of three attributes ( to represent the values of outdegree, betweenness and clustering triangles. We firstly calculate the statistic distribution of the numbers of actors’ outdegree, betweenness and clustering triangles. Figure 1 shows the three distributions having distinctive heavy tails, where the frequencies of the occurrence of events remain visibly biased. Note that Figure 1 graphically illustrates the many similarities and the few differences between these distribution diagrams; we adopt the function of the power law distribution to fit them.
(a)
(b)
(c)
Fig.1: Distribution scatter diagrams of the number of (a) outdegree, (b) betweenness, (c) clustering triangles in the log-log scales.
The previous work observed the universality of the power law distribution in social systems where both opinion expression and preference formation are generated from interpersonal reciprocities [18]. We suppose that the probability P(x) of the occurrence of the three variables follows such statistical distribution, denoting P(x)∝ , where and are constants. A common solution linearizes the function of the power law distribution to a logarithmic linear model logP(x)= in a log-log scale. For our instances, the least-square approach can generate a credible coefficient of determination, but leads to large systemic errors for some given estimators because the estimators cannot follow a Gaussian distribution. We interpret the constant c and the scaling parameter α by maximum likelihood estimation (MLE), and thereby bring in an approximate expression for the discrete observations [24]: 1+n
,
(1)
where is the lower-bound on the scaling region. Then, the estimator of the constant is:
,
(2)
where the equation (3) is the Hurwitz zeta function. Table Ⅰ reveals descriptive statistics, the lower-bound of the scaling region, estimators of α and c with regard to the outdegree, betweenness and clustering triangles, and shows the three density functions that fit to the power law distributions with the exponents of 2.06, 1.19 and 1.41 respectively.
TABLE I.
MAIN RESULTS FOR THE THREE DENSITY FUNCTIONS
B. Cut-off Point Separating the Head and Tail Regions As the first taxonomic character, we need to gain the precise value to distinguish the head and tail areas on the curve of the distribution function. Phenomena obeying the power law distribution in social systems reveal the “predictable imbalance” tendency proposed by Vilfredo Pareto who observed 20% of the population holding 80% of the wealth, also called “80/20 Rule”. In our study, Figure 2 exposes similar inequality of social influence as well: a minority of influential individuals in the heavy-tailed distribution possesses major diffusion resources while a majority of actors distributing on the head of the curve have few resources. However, major empirical studies fail to offer the mathematical deduction pertaining to the cut-off point of how to distinguish the two parts on the distribution curve, instead consider the point as an a priori argument.
Fig.2: Fitting curves for the distribution functions of the three metrics.
To gauge the exact cut-off point, we turn to a set of differential methods. Because the function of the power law distribution P(x)(x>0) is continuous, the first derivative is (4) If we discover the maximum of the curvature along with the curves shown by Figure 2, the cut-off point will be obtained. A typical method rests on the second derivative of the distribution function . Then, we can express the curvature
K
(5)
However, two conditions constrain the equation (5) to acquire the rational outcomes in the extremely unbalanced dataset. Derivatives at most points are up to leading to
.
Therefore,
the
curvature
K
. Moreover, a majority of observations
show because is decreasing rapidly. The curvature K in the equation (5) is close to zero in most cases. In order to look into the appropriate process, we shall return to the first derivative (4) to analyze the rate of change of the slope of the tangent lines from the unit arc According to the definition of the curvature, we set K , where ∆s is the length of the arc and ∆θ represents the included angle of the two tangent lines from the point M to shown by Figure 3. The value of ∆θ is equal to the distinction of the two included angles between the horizontal ordinate and the tangent lines at M and (θ and θ+∆θ). Since the curve of the power law distribution is smooth and , the gradients of the tangent lines at all points increase with adding x. The change of the slopes is positively related to ∆θ. As known conditions, the attenuation of the power law distribution in the heavy-tailed region is prominently slower than that of the exponent function. Thus, we define M as the cut-off point where . Table Ⅱ presents the threshold beginning at the tail part and the percentage of the number of individuals in the tail area for three metrics.
V. ENHANCED CLASSIFICATION METHOD FOR THE HEAVYTAILED REGION
Utilizing the cut-off point above to classify the original instances produces a rough category. For descriptive statistics, the sets of influential actors shown by Table Ⅱ are still unbalanced and have greatly different rates of individuals, as the whole set of actors are divided by the three indicators, respectively. We shall turn to our discussion with regard to a further classification standard in the heavy-tailed area. A. Relationship Type and Structure In Table Ⅱ, in relation to the description of the tail part, the number of individuals with the higher betweenness centrality is apparently more than the population of the other two variables’ distributions. Our findings imply that the location of an individual in the directed social network takes the distinct effects for the value of the variables shown in Figure 4. Figure 4 exposes two examples to discuss the between centrality of points at different layers and changes that the new actor causes. The left plot of Figure 4 offers a typical situation in a directed network. First, the points A and B have the same numbers of the betweenness centrality, but stand at different layers. In general, we consider that the more a point triggers the information cascades, the stronger the point has the influence. Second, the right graphic of Figure 4 shows that the betweenness centralities of the points A, B and C soar when the point D joins in this network, but the other two metrics of the points do not show any change. We will explore an improved approach to measure social influence of an actor by connecting the positional with relational analytics in the directed social network. D C A
C B
A
B
Fig 4: Plots of two examples
Fig.3: Graphic of ∆θ as the included angle of the two tangent lines from M to M'
TABLE Ⅱ: RESULTS OF THE CUT-OFF POINTS AND THE RATES OF ACTORS LOCATING AT THE TAIL PART
Exploring types of relationships has so far been a fundamental tool to capture the formation and feature of the relational structure in the analysis of a directed social platform. In Figure 5, the red ball is assigned as the objective point. We derive directed and reciprocal online relationships from the interpersonal interactions (see Figure 5.a). What’s more, the existing work has surveyed the roles of two types of cliques: wedges and triangles that are comprised of triads with different relationship structures in sociology [25]. Some studies conclude 6 types of wedges that two actors, without any contact to each other, interact with, where a common objective point in Figure 5.b, and 7 in the forms of triangles that consist of connections between each pair of vertices in Figure 5.c [22]. Now suppose that a direct network is defined as a twoelement set of G=(V,E)that includes vertices and edges
connecting pairs of vertices, the three pairs of relationships in Figure 5.a are described respectively as (6) (7) (8) where is the objective point and connects with via an edge in the set . Considering the combination of relationships of the wedges from ⅰ to ⅵ, we can express every pair of relationships from left to right in Figure 5.b as . (9) Correspondingly, seven types of interactions in Figure 5.c can be written as
,
(10)
where describes the combination of relationships in terms of the sequence (left, right, the left point of the opposite edge of the objective point). In essence, the salient distinctions of the fundamental directed structures embody a positive correlation to shape the centrality and clustering efficient.
B. Hierarchy Decomposition Every individual embedded in the retweeting network can be marked in the light of relationship forms and triad structures. We carry out an algorithm routine to hierarchically decompose the entire network in order to label the individuals. (1) Removing all objective points that have relationships outdegrees are equal to zero.
and
(2) Detecting the triangles that contain the loop structure . If there are two points without any successor in one triangle, the triad is merged into one point. (3) Investigating the reciprocal edges . If one point in a pair of such edges no longer has any successor, two points are merged into one line. We iteratively operate three steps above until all points are removed. As a result, each vertex is classified into a unique layer beneath the largest value 23. All points are in Figure 6 as long as the value of the metric is over its cut-off point. Figure 6 adopts the linear-log scale. For convenience, the vertical ordinate is attenuated to one tenth of the actual value. The five kinds of colors respond to the density of points in a given area from the sparsest to the densest. densest dense
normal
Objective point
sparse sparsest
(ⅰ)
(ⅱ)
(ⅲ)
(a) (ⅰ)
(ⅱ)
(ⅳ)
(ⅴ)
(a)
(ⅵ)
(b)
(ⅰ)
(ⅳ)
(ⅱ)
(ⅴ)
(ⅲ)
(ⅵ)
(b)
(c)
Fig 6: Heat maps of the distribution density of (a) outdegree, (2) betweenness and (3) the number of clustering triangles at different layers in the heavy-tailed region.
(ⅲ)
ⅶ
(c)
Fig 5: Graphics of interactions expressed by directed edges between nodes and structures formed by directed pairs (a), wedges(b) and triangles(c).
Both reciprocal relationships and transitivity of directed triangles ad hoc play a key role in network formation and information dissemination [19]. Empirical studies reveal that four types of triangles including the loop impetus the intense transitivity of information, even if the triangles do not have any interactional edge in the real social network [26]. The effects of triad structures for social influence are summarized in [22]. They point out edges are more likely to form a given type of triangle in , and the objective point generally holds a dominant position in the wedge. The clique or , including the loop , accounts for the low proportion of triangles, which holds for the power of interactions.
C. Classification Result We look on three maps in Figure 6 in an attempt to set an initial rule in order to split the dense and sparse areas. The initial rule focuses on a “rectangle” scope limited in the size of . So far we can construct a classifier by integrating the taxonomy rules in Table Ⅱ and Figure 6. Table Ⅲ offers the performance of a decision-making tree algorithm by the If-then method after filtering out all null groups. Moreover, we can gain some insight into optimizing the decision system by examining the confusion matrix on the basis of ensemble learning. Due to the extremely imbalanced instances, we have to focus on the sampling classification algorithm- RUSBoost - to evaluate the grouping results. TABLE III: TABLE OF THE GROUPS GENERATED BY THE DECISIONMAKING TREE ALGORITHM..
We compute the findings in Figure 7 with regard to True Positive Rates (TPR) and False Negative Rates (FNR), and consequently gain the accuracy of the classification equal to 72.5%. As a rough heuristic, we must pay attention to the overfitting problem of the small dataset and the tradeoff between the model complexity and evaluation accuracy. From Table Ⅲ, the groups 2,3,4 and 6 keep the tiny sizes, and Figure 7 shows that they have similar error distributions to adjacent groups. Thus, we merge the groups 2, 3 and 4 into the group 1, and the group 6 into the group 5. Furthermore, we continue to iteratively adjust the dimension of the limit rectangle to X10.
Fig 7: Graphic of the primary evaluation of the confusion matrix.
We see the optimized grouping results and the evaluation of the confusion matrix shown in Figure 8. Adopting an enhanced decision-tree algorithm, the classifier splits the dataset of observations into six groups and makes its accuracy up to 99.8%. To verify the effectiveness of the taxonomy, we introduce the neural networks as a “black-box” tool to examine the correlation of grouping results and the input variables: the outdegree centrality, betweenness centrality and clustering triangles. We sample 75% of the instances into the training set and 25% of them into the test set. By employing the hyperbolic tangent in the hidden layer and the Softmax regression to output multiple categories, the neural networks verify 97.7% accuracy in the training set and 99.6% precision in the test set.
Fig 8: Graphic of the evaluation of the confusion matrix tested by the optimized decision-tree algorithm.
VI. INFLUENCE ANALYSIS Some significant evidence listed in Table Ⅳ reveals distinctive properties of social influence in each segment. The subordinate individuals account for approximately 70% of consumers in group 1, but only possess the lowest values for all of the three metrics. In the real society, they are generally considered as consumers that marketers induce and audiences that influencers affect. According to the performance in TableI, the betweenness centrality can effectively measure the effects of social influence of actors in the first group no matter how much of the outdegree centrality and clustering coefficient they can keep. Note that the groups 2 and 3 contain more members similar to the points B and C in Figure 4, and their actors have to large extent capabilities to spread information. Compared to the group 2, the third group of members has better transitivity. However, we cannot explain why the individuals with fewer followers largely function in triggering information cascades because the question exceeds the mission of this study. We are able to enumerate several potential reasons including successors’ motivation, social content and actors’ communication preferences. Opposing the two segments above, the forth group is a minority of people who nearly have the influential characteristics similar to the point A in Figure 4. They occupy on the lower layer and rely on the direct influence to transmit messages. In another word, their influence power is limited in part by their neighbors keeping fewer interactive relationships and in part by their position neat at the bottom of the communication chain. TABLE IV: TABLE OF A TOTAL OF SIX GROUPS CLASSIFIED BY THE OPTIMIZED ALGORITHM.
In this research, “diffusion resources” is defined as a total of the number of the outdegree, betweenness and clustering triangles each actor owns. The size of the scattering points is the logarithm of the actual values in order to conveniently display. Figure 9 plots the amount of members and diffusion resources in every group. As it can be seen, the most influential individuals, also called “hyperinfluentials” [5], in group 5 and 6 account for approximately 2% of the total actors. The quantitative evidence updates the priori hypothesis for the percentage of the influencers in social networks even if studies are based on different assumptions concerning the nature of interpersonal influence. The top 2% as the most influential individuals possess a large amount of successors and tremendous abilities of information transfer and transitivity, in which the highest level of 0.62% of actors in group 6 with a high variance occupy the top of the diffusion channels. Figure 9 denotes that the inequity social media distribute presents in multi-aspects and multiple levels. Our study defines “diffusion resources” as a total of the number of the outdegree, betweenness and clustering triangles each actor owns. The size of the scattering points is the logarithm of the actual values in
order to conveniently display. Thus, it demonstrates that about the top 30% of the individuals excluding in the first group are termed the influential individuals in social media marketing as long as they have one or several features to impact others in opinion formation and information diffusion. What’s more, a tiny amount of the most powerful influencers can leverage more superior resources than a majority of subordinate individuals.
[2] [3]
[4] [5] [6]
[7]
[8] [9] [10] Group
Fig 9: Plot of the amount of members and diffusion resources in every group.
VII. CONCLUSION This paper acquires a myriad of typical relationships that transmit marketing stories on a typical social media platform while marketing events based on social media diffusion are defined as a series of complex applications on computermediated platforms. Our work endeavors to build on a quantitative measurement in terms of the mathematical deduction in order to bridge the gap between the research findings and actual scenes. We propose a set of taxonomy methods for extremely imbalanced examples in terms of statistics and relationship analysis, as well as verify accuracy of taxonomy methods on the basis of the combination of metrics. The research performance reveals that the inequity social media distribute presents in multi-aspects and multiple levels. Therefore, the significance of our study not only precisely splits individuals having diverse social influence, but also exposes the complexity of consequences of social interactions. Our research shows that the most influential individuals account for approximately 2% of the total actors as opposed to about 70% as subordinate individuals in the entire marketing network. Our empirical study also demonstrates that almost the top 30% of the individuals can be named as the group of influential individuals in social media marketing as long as they have one or several features to impact others in opinion formation and information diffusion. The top 2% represents the most influential individuals that possess a large amount of successors and tremendous abilities of information transfer and transitivity and thereby a tiny amount of the most powerful influencers can leverage more superior resources than a majority of subordinate individuals. REFERENCES [1]
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