1 Introduction

1.1 Background

On trust-oriented e-commerce platforms, like Epinions (epinions.com), after a transaction, a buyer can provide a review to introduce the quality of the purchased product and the experience of the transaction. This review is visible to other buyers, and is much valuable to their decision-making of purchasing. In addition, a buyer can rate the existing reviews given by others as Not Helpful, Somewhat Helpful, Helpful, or Very Helpful based on his/her own experiences [1]. If a buyer usually provides Very Helpful product reviews in a specific domain, like Digital Cameras, his/her recommendation is believed to be trustworthy in that domain. As indicated in the studies of Social Psychology [2] and Computer Science [3–5], a buyer is very likely to make a purchase decision following the recommendations (product reviews) given by trustworthy buyers. Such trustworthy buyers posses strong influences and can impact many buyers’ purchase behaviours in a specific domain. These trustworthy buyers are called the advisors of those participants who trust their product reviews.

1.2 The Problem

In e-commerce environments, a buyer can write product reviews and rate others’ reviews freely, and thus the product review scheme is highly vulnerable to some typical attacks [1]. For example, in order to obtain a strong influence, a dishonest advisor can cheat the product review system via some typical attacks, such as Constant Footnote 1 and Camouflage Footnote 2 [6], by (1) recommending a low quality product, and/or (2) providing an unfair review to a high quality product, each of which severely harms the benefits of both potential buyers and sellers. The problem of unfair rating becomes more and more concerned by not only industrial circles but also academic circles in this filed. Plenty of unfair ratings exist in the reviews of products, which significantly affect the decision-making of buyers [7, 8].

In the literature, the existing influence evaluation methods mainly focus on studying the influence maximization under the popular linear threshold (LT) model and independent cascade (IC) model [9], and evaluating social influence through the process of information diffusion [10]. However, they do not apply any strategies to defend against the afore-mentioned typical attacks, and thus the existing models might recommend a participant as an advisor who has obtained the fake strong social influence by cheating the review systems via the above mentioned typical attacks. Some methods have been proposed to defend against collusive [11] or spamming rating attacks [12], which however cannot be directly applied in defending against the typical Camouflage and Constant attacks in trust-oriented e-commerce environment. The following Example 1 illustrates the process of the typical Camouflage attack in e-commerce platforms.

Fig. 1.
figure 1

The camouflage attack

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Example 1

Fig. 1 depicts a trust-oriented e-commerce environment, which contains two sellers \(S_1\) and \(S_2\) and three buyers \(B_1\) to \(B_3\). Firstly, \(B_1\) and \(B_3\) bought the same product (such as digital camera) from \(S_1\), so there exist the transaction relationships between \(B_1\) and \(S_1\), and between \(B_3\) and \(S_1\), respectively (represented by arrows with dashed lines in Fig. 1). Next, suppose both \(B_1\) and \(B_3\) wrote a review for the camera sold by \(S_1\), and they find that their purchase experiences are similar with each other. Then \(B_1\) and \(B_3\) trust each other, and thus there exist trust relationships between \(B_1\) and \(B_3\) (represented by arrows with solid lines in Fig. 1). Finally, \(B_2\) regards the review of \(B_3\) is Very Helpful, then a trust relationship is established between them. In such a situation, if \(B_2\) wants to buy a new camera, \(B_3\)’s review has a strong influence on \(B_2\)’s decision making. But suppose \(B_3\) wrote an unfair positive review to the camera sold by \(S_2\), whose camera has a low quality. If \(B_2\) wants to buy a new digital camera, naturally \(B_2\) would choose the camera sold by \(S_2\) because \(B_2\) trusts \(B_3\). Then \(B_2\) makes a wrong decision misled by \(B_3\)’s dishonest action. In such a scenario, \(B_3\) is a Camouflage attacker who establishes fake trustworthiness first and then misleads other buyers.

The above discussed typical attacks widely exist in trust-oriented e-commerce, which leads to severe deviation of the reliability of the recommendations [6]. This motivates us to develop a robust influence evaluation method to accurately find the participants who have real strong influence under the typical attacks mounted by dishonest buyers in e-commerce environments.

1.3 Contributions

The main contributions of this paper are summarized as follows:

  • We propose a novel Trustworthy Influencer Finding method TrustINF based on the evolutionary trust model [6] and the variations of historical influences of participants, which can measure the attack probability for each buyer, and defend against the typical attacks, Constant and Camouflage.

  • To the best of our knowledge, this is the first work that defends Camouflage and Constant attacks in influence evaluation. The proposed TrustINF approach is based on Skyline [13] and its time complexity achieves \(\mathcal {O}(n^2)\), where n is the number of buyers in e-commerce environments.

  • We have conducted experiments on the four real social e-commerce datasets, i.e., Epinions, Slashdot, Amazon and BeerAdvocate. The average Attacker Identification Ratios of our TrustINF under Constant attack and Camouflage attack achieve 66.33 % and 81.33 % respectively. On average, our Trust-IMM can improve the robustness of IMM by 85.82 %.

2 Related Work

In the literature, according to different influence problems, we categorize them as influence maximization, individual influence evaluation and the unfair rating identification in influence evaluation.

Influence maximization is to find important applications in viral marketing [14], where a product provider selects K influencers in an OSN and provides them with incentives (e.g., free samples) to accept a new product, excepting the social influence of these influencers can work and attract more potential users. [15] propose an algorithm that has a simple tunable parameter, for users to control the balance between the running time and the influence spread. [16] propose an algorithm IRIE that integrates the advantages of influence ranking (IR) and influence estimation (IE) methods. [17] provide a scalable influence approximation algorithm, Independent Path Algorithm (IPA). [18] investigate a novelty decay phenomenon where the influence of a participant decays with the increase of the number of sending the same message to others in OSNs. Then they [19] investigate the effect of the novelty decay in the influence maximization in OSNs. Recently, [20] proposed an algorithm which is based on martingales, a classic statistical tool, to support a larger class of information diffusion model over the existing methods. Moreover, [21] propose a local influence maximization problem. This problem is to find a group of nodes that have the maximal impact on a specified participant. In addition, [22] propose a probabilistic model to discover the latent influence between participants in OSNs.

In individual social influence evaluation, [23] propose an approach, called SoCap, to find influencers in OSNs by using the social capital value. They model the problem of finding influencers in OSNs as a value-allocation problem, where the allocated value denotes the individual social capital. In addition, [24] propose a method to identify influential agents in open multi-agent systems without centralised control and individuals have equal authority. The above existing methods in influence evaluation did not consider any strategies defending against attacks, and thus are vulnerable to the attacks, like Camouflage and Constant, from dishonest participants.

In order to identify the unfair ratings and improve the robustness of influence evaluation models, some approaches [11, 12] have been proposed to defend against the collusive and the spamming rating attacks respectively in trust-oriented e-commerce environments. However, their methods cannot be used directly to defend against the Camouflage and Constant attacks that widely exist in e-commerce environments.

3 Preliminary

3.1 Trust Relationship

In e-commerce environments, a Trust Relationship is a relationship between a buyer and an advisor, which illustrate the probability of a buyer who will make the purchase decision based on the reviews of the advisor. This type of trust relationship widely exist in trust-oriented e-commerce, like Epionions, Amazon, FilmTrust, etc. Let \(T_{i,j}\) to denote the trust relationship between \(B_i\) and \(B_j\).

3.2 Transaction Relationship

In trust-oriented e-commerce environment, a Transaction Relationship is a relationship between a buyer and a seller when they have at least one transaction. Let \(R_{i,j}\) denote the transaction relationship between \(B_i\) and \(S_j\). If \(B_i\) have bought m items from \(S_j\), and the rating values to those m items are \(r_{i,j}=\{r_{i,j}^1,...,r_{i,j}^{m}\}\), \(m>0\), then

$$\begin{aligned} R_{i,j}= \frac{1}{m}\sum _{k=1}^{m}r_{i,j}^k. \end{aligned}$$
(1)

3.3 Evolutionary Trust Model

The Evolutionary Trust Model [6] is usually used to cope with unfair rating attacks from dishonest advisors. By using this model, if a buyer finds the real transactional experience is different with the reviews given by an advisor, the buyer could evolve his/her trust relationships to absorb the advisors whose reviews better match the buyer’s purchase experience and distrust the previous advisor whose review is not recognized by the buyer. The following Example 2 illustrates the evolutionary process.

Example 2

In Fig. 2, suppose there is a low rating given by \(B_2\) to \(S_2\) (i.e., \(R_{2,2}=0.2\)), which is quite different with \(B_3\)’s review with \(R_{3,2}=1.0\). Then \(B_2\) evolves his/her trust relationships to form a new trust relationship \(T_{2,1}=1.0\) with \(B_1\) as \(B_1\)’s review with \(R_{1,1}=0.2\) matches \(B_2\)’s purchase experience. Meanwhile \(B_2\) removes the trust relationship with \(B_3\). Finally, \(B_1\) becomes a new advisor of \(B_2\). This process is called the Trust Evolution.

The below fitness function in Eq. (2) is used for buyers to measure the quality of their trust networks by comparing the two types of derived reputation values of sellers [6].

$$\begin{aligned} f(VT_i)=\frac{1}{m}\sum _{j=1}^{m}|R_{i,j}-\widetilde{R}_{i,j}| \end{aligned}$$
(2)

where m is the number of sellers who have been rated by both \(B_i\) and \(B_i\)’s advisors. \(\widetilde{R}_{i,j}=\frac{1}{|A(B_i)|}\sum _{k=1}^{|A(B_i)|} R_{k,j}\) denotes the average rating value given by \(B_i\)’s advisors to seller \(S_j\). \(f(VT_i)\) means that the little difference of ratings given by a buyer and his/her advisors illustrating the high quality of their trust relationship.

The following Eq. (3) is used to measure the difference of trust relationships between two buyers \(B_i\) and \(B_j\).

$$\begin{aligned} \text {diff}(VT_i,VT_j)=\frac{1}{m'}\sum _{k=1}^{m'}|T_{i,k}-T_{j,k}| \end{aligned}$$
(3)

where \(m'\) is the number of both \(B_i\)’s and \(B_j\)’s advisors; it reflects the difference between the trust relationships of \(B_i\) and \(B_j\). The less the value of \(\text {diff}(VT_i,VT_j)\) the less the difference of the trust value from \(B_i\) and \(B_j\) to their common advisors.

Equation (4) is used to measure the difference of fitness.

$$\begin{aligned} \text {diff}(f(VT_i),f(VT_j))=|f(VT_i)-f(VT_j)| \end{aligned}$$
(4)

In evolutionary process, a function \(\delta (\cdot )\) is used to judge the compatibility of new trust relationship resource and calculated as follows:

$$\begin{aligned} \begin{aligned} \delta (VT_i,VT_j)=&(\text {diff}(VT_i,VT_j)-0.5)\\&\times (\text {diff}(f(VT_i),f(VT_j))-0.5) \end{aligned} \end{aligned}$$
(5)

Here, we set threshold as 0, only when two buyers \(B_i\) and \(B_j\) satisfy \(\delta (VT_i,VT_j)>0\).

Fig. 2.
figure 2

Evolutionary process

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Fig. 3.
figure 3

Four typical cases of FTBA

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4 Impact Factors of Influence

With adopting the Evolutionary Trust Model, we propose two impact factors which have significant impact on real influence evaluation of participants in e-commerce.

figure a

4.1 Fluctuant Trend of Becoming Advisor (FTBA)

Observing the trend of buyers’ trust can largely recognize their reputations [1]. Here, we use the historical data of trust relationships to regress the trend of trust for each buyer, i.e., Fluctuant Trend of Becoming Advisor (FTBA), which illustrates the fluctuant trend of a buyer to become an advisor of a buyer in a certain period. The typical cases of FTBA are depicted in Fig. 3, i.e., “stable”, “ascending”, “descending” and “uncertain”. “stable” means no more other buyers trust the buyer in this period; “ascending” means more and more buyers trust the buyer; “descending” means less and less buyers trust the buyer based on his/her reviews; “uncertain” means the trend of becoming an advisor of the buyer is unclear. We utilize a regression line to model FTBA, whose gradient (denoted as grad) and mean distance (denoted as md) can measure FTBA well [25].

Let \(x_i^j\) denote the number of becoming advisors of \(B_i\) at time \(t_j\), and let \((t_s, x_i^s),(t_2, x_i^2),...,(t_e, x_i^e)\) denote the given data points of \(B_i\) from \(t_s\) to \(t_e\). In this paper, \(t_s\) denotes the start time of the historical transactions and \(t_e\) denotes the end time of transactions. Then FTBA can be computed by Eq. (6):

$$\begin{aligned} y=kt+b \end{aligned}$$
(6)

where k and b are constants to be determined, and k represents the grad value.

Then the shortest distance from point \((t_j, x_i^j)\) to the regression line can be computed by Eq. (7):

$$\begin{aligned} d_i^j=\frac{x_i^j-b-kt_j}{\sqrt{1+k^2}}. \end{aligned}$$
(7)

Based on the theory of least squares [26], the sum of squares of the distance can be calculated:

$$\begin{aligned} S_i^p=\sum _{j=1}^{p}{(d_i^j)^2}=\sum _{j=1}^{p}\frac{(x_i^j-b-kt_j)^2}{1+k^2}. \end{aligned}$$
(8)

Next we minimise the sum of squares of the distance \(S_i^p\) with respect to the parameters k and b, with the method of undetermined coefficients. Since the function \(S_i^p\) is continuous and differentiable, as we know, based on the method of two variables’ function extremum, the minimization point of \(S_i^p\) makes the first derivative of function \(S_i^p\) be zero, and the second derivative positive, which could be easily proved by Taylor formula for function of two variables [26]. For this purpose, we differentiate \(S_i^p\) with respect to k and b, and set the results to zero. Then we can obtain:

$$\begin{aligned} k=grad_i= (-u-\sqrt{u^2+4})/2 \end{aligned}$$
(9)

and

$$\begin{aligned} b=\frac{S_f-kS_t}{n}, \end{aligned}$$
(10)

where \(u=\frac{pS_{f2}-S_f^2+S_t^2-pS_{t2}}{S_fS_t-pS_{ft}}\), \(S_{f2}=\sum _{j=1}^{p}(x_i^j)^2\), \(S_{f}=\sum _{j=1}^{p}x_i^j\), \(S_t=\sum _{j=1}^{p}t_j\), \(S_{t2}=\sum _{j=1}^{p}t_j^2\) and \(S_{ft}=\sum _{j=1}^{p}x_i^j\cdot t_j\).

According to above results, the equation of mean distance can be computed by Eq. (11):

$$\begin{aligned} md_i=\frac{\sum _{j=1}^p|x_i^j-b-kt_j|}{p\sqrt{1+k^2}}. \end{aligned}$$
(11)

4.2 Fluctuant Trend of Total Trustworthiness (FTT)

Here, we propose another impact factor of influence evaluation, Fluctuant Trend of Total Trustworthiness (FTT), together with FTBA to measure the probability of attack for each buyer. FTT illustrates the fluctuant trend of total trustworthiness which is the total value of trust given by buyers to an advisor from \(t_s\) to \(t_e\). We use a regression line to model FTT, which is based on the theory of least squares [26]. The gradient and mean distance of the regression line are denoted as \(grad'\) and \(md'\) respectively. Let \({x'}_i^j\) denote the total trust value at time \(t_j\), and \((t_s,{x'}_i^s), (t_2, {x'}_i^2),(t_3, {x'}_i^3)\),...,\((t_e, {x'}_i^e)\) denote the given data points of \(B_i\) from \(t_s\) to \(t_e\).

$$\begin{aligned} {x'}_i=\sum _{k=1}^m T_{k,i} \end{aligned}$$
(12)

where m is the number of buyers who have trust relationship with \(B_i\).

Then FTT can be computed by using the theory of least squares [26] (i.e., replace \((t_j,x_i^j)\) with \((t_j, {x'}_i^j)\) in Eqs. (9–11)).

Intuitively, these trends are conducive to indicate the changing process of trust of a buyer and detect the behaviors of the typical attacks. FTT reflects the changing trend of the quality of trust, but FTBA reflects the changing trend of the amount of trust.

Thus, in order to indicate the trust of a buyer more completely, both FTBA and FTT are needed to be combined to in the measurement of trust for a buyer in trust-oriented e-commerce environments.

5 Trust-Aware Influencer Finding Algorithm

In this section, we propose a Trust-Aware Influencer Finding method, TrustINF, that considers four parameters, i.e., FTBA’s gradient, FTBA’s mean distance, FTT’s gradient and FTT’s mean distance which have significant impact on trust-oriented influence evaluation. Finding influencers with multi-attributes is a typical multi-criteria optimal decision making problem [27]. Let P denote the parameter sets of all buyers, and let \(X_i=\{X_i^k|k=1,...,4\}\) denote FTBA’s gradient, FTBA’s mean distance, FTT’s gradient and FTT’s mean distance respectively. Intuitively, a buyer with lower gradients and higher mean distances will have a higher probability to be an attacker. Without loss of generality, we equally treat four parameters by setting \(X_2\) as the negative value of FTBA’s mean distance and \(X_4\) as the negative value of FTT’s mean distance in our algorithm.

A skyline query retrieves all points that are not dominated by any other point, which is an import method to solve the multi-criteria optimal decision making problem [13]. In order to accurately identify attackers, we adopt a Skyline method to evaluate the probability of an advisor to be an attacker, and propose the concept of Influencer Domination based on the definitions in [28] as follows.

Definition 1

Influencer Domination: A buyer \(B_i\) dominates another buyer \(B_j\) on an trust-oriented e-commerce platform if and only if for all \(k \in \{1,...,4\},~X_i^k \ge X_j^k\) and \(\exists ~t \in \{1,...,4\},~X_i^t > X_j^t\).

Based on Definition 1, we use \(N=\{N_i\}\) and \(N'=\{N'_i\}\) to denote the dominating number of buyer \(B_i\) and the number dominated by other buyers respectively. If \(N'_i\) has a large value and \(N_i\) has a small value, the trust trend of \(B_i\) is downward, causing by the drastic change of ratings to sellers, which is a representative feature of Camouflage attack [6]. Thus, we define a function to measure the probability of \(B_i\) to be an attacker as Eq. (13).

$$\begin{aligned} P_i=(N'_i-N_i)/(n-1), \end{aligned}$$
(13)

where n is the number of buyers and \(P_i \in [-1,1]\).

The pseudo-code of the TrustINF algorithm is given in Algorithm 1. As the impact factors have been pre-calculated and pre-stored, Algorithm 1 only needs to calculate \(N=\{N_i\}\) and \(N'=\{N'_i\}\) by iteratively scanning the set of impact factors n times. Thus, the time complexity of TrustINF is \(\mathcal {O}(n^2)\), where n is the number of buyers.

Summary: In our TrustINF, firstly, we improves evolutionary trust model and adopt it to evolve trust network after every transaction to obtain the trustworthy historical ratings. Secondly, we calculate every buyer’s FTBA and FTT based on these historical ratings to indicate the trust trend of each buyer. Finally, as the social influence evaluation with defending against attacks is a typical multi-criteria optimal decision making problem, and the Skyline method is an important method to solve such a problem, we adopt the skyline method in our TrustINF.

Table 1. The details of datasets
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6 Experiments

6.1 Experimental Setting

Dataset. In our experiments, we collect four real trust oriented e-commerce datasets, i.e., Epinions, Slashdot, Amazon and BeerAdvocate from snap.stanford.edu/data/, to investigate the performance of our TrustINF algorithm. These datasets have been widely used in the literature for the studies trust-oriented e-commerce [6]. The details of these datasets are listed Table 1.

The Setting of Attacks. In our experiments, we consider two typical attacks, i.e., Constant and Camouflage. We randomly choose \(\alpha \) buyers from each of the dataset as attackers, \(\alpha \in [5\,\%,10\,\%,15\,\%,20\,\%,25\,\%]\). Then, we investigate the attacker identification ratio of our TrustINF, and investigate the performance of our Trust-IMM and IMM [20]. Based on the definitions of the two types of attacks [6], we define the typical attackers in our experiments as below:

Constant Attacker: Dishonest buyers constantly provide unfairly positive/negative ratings to sellers [6].

For an attacker \(B_i\), we set the ratings of \(B_i\) to give all products which \(B_i\) will buy from different sellers as extremely positive ([0.9,1]) or extremely negative ([0,0.1]) values. In our experiments, we randomly select \(\alpha /2\) negative attackers and \(\alpha /2\) positive attackers. The rating of product \(p_k\) can be calculated as below:

$$\begin{aligned} r_{i,k}= \left\{ \begin{array}{lr} \text {rand}(0.1) &{} \text {if}~B_i~\text {is negative}, \\ \\ 1-\text {rand}(0.1) &{} \text {otherwise}. \end{array} \right. \end{aligned}$$
(14)

Camouflage Attacker: Dishonest buyers camouflage themselves as honest buyers by providing fair ratings to build up their trustworthiness first and then gives unfair ratings [6].

For an attacker \(B_i\), if \(B_i\) rated product \(p_k\), then

$$\begin{aligned} r_{i,k}=(r_{i,k}+0.5)~mod~1. \end{aligned}$$
(15)

After updating all ratings of \(B_i\) based on Eq. (19), \(B_i\) becomes a Camouflage attacker in our experiments. In

We define the Identified Attacker and Attacker Identification Ratio to measure the performance of our method:

Definition 2

Identified Attacker: Attacker \(B_i\) is an Identified Attacker if and only if \(B_i\) is an attacker and the probability of attack \(P_i\) for \(B_i\) is ranked in Top- \(\alpha \), where \(\alpha \) is the ratio of attackers included in trust-oriented e-commerce environments. This means that these attackers can be identified by influencer finding approaches.

Fig. 4.
figure 4

The Attacker Identification on the four datasets. The color of each block reflects the proportion of the attackers in different ranges of ranking. (Color figure online)

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Definition 3

Attacker Identification Ratio: Attacker Identification Ratio is the ratio of identified attackers to the all attackers, which is to measure the scale of identifying attackers delivered by influencer finding approaches.

Fig. 5.
figure 5

The attacker identification ratio on the four datasets.

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Parameters in IMM and Diffusion Models. In this paper, we adopt two typical diffusion models, i.e., Linear Threshold (LT) model [29] and Independent Cascade (IC) model [9] to investigate the performance of Trust-IMM.

  • IMM: IMM [20] is an influence maximization algorithm which adopts sampling method to return an approximate solution under the triggering model. In this experiments, we consider two kinds of triggering models, i.e., LT and IC. For IMM, we set \(\varepsilon =0.5\), \(\ell =1\), and \(K\in [10,20,30,40,50]\).

  • Linear Threshold (LT) Model: LT model is the first model to imitate the diffusion process of information. The approach is based on the node-specific thresholds [29]. In the model, at time step t, all buyers that were influenced in step \(t-1\) remain being influenced. A buyer \(B_i\) is influenced based on a monotonic function of its influenced neighbors \(f(In(i,t)) \in [0,1]\) (see Eq. (16)) and a threshold \(\theta _i \in [0,1]\), i.e., \(B_i\) is influenced at time t if \(f(In(i,t)) \ge \theta _i\).

    $$\begin{aligned} f(In(i,t))=\sum _{B_j \in In(i,t)}b_{i,j} \end{aligned}$$
    (16)

    where In(i, t) is the influenced neighbors of \(B_i\) at time step t. Here, we set \(b_{i,j}=T_{i,j}/\sum _{B_k \in Ad_i}T_{i,k}\); \(Ad_i\) is the advisor of \(B_i\) and \(\sum _{B_j \in Ad_i}b_{i,j} \le 1\). In our experiments, in order to investigate the effectiveness of our method based on different thresholds, for each \(B_i\), we set \(\theta _i = rand()\).

  • Independent Cascade (IC) Model: IC model is a dynamic cascade model for the diffusion process. The model is based on the interacting particle system from probability theory [9]. At each time step t, each buyer is either influenced or susceptible. A buyer \(B_j\) that was influenced at time step \(t - 1\) has a single chance to influence each of its incoming neighbors \(B_i\). The influence succeeds with probability \(P_{i,j}\) (see Eq. (17)). Therefore, for buyer \(B_i\), if at least one of its influenced advisors succeeds, \(B_i\) gets influenced. The probability of buyer \(B_i\) getting influence at time step t is:

    $$\begin{aligned} f(i,t)= 1 - \prod _{B_j \in In(i,t-1)}(1 - P_{i,j}) \end{aligned}$$
    (17)

    where \(In(i,t-1)\) is the influenced neighbors of \(B_i\) at time step \(t-1\). Here, we set \(P_{i,j}=T_{i,j}\), i.e., the trust value from \(B_i\) to \(B_j\).

Experimental Environment. All experiments were run on a machine powered by two Intel Core i5-3470 CPU 3.20 GHz processors with 8 GB RAM, using Windows 7 operating system. The code was implemented using Java 8 and the experimental data was managed by MySQL Server 5.6.

6.2 Experimental Results and Analysis

Figure 4 plots the probabilities of the identified attackers who are ranked in Top-\(\alpha \) delivered by TrustINF model on four datasets. From the Fig. 4, we can see that our TrustINF method can identify the attackers who have been ranked in the top of the e-commerce (the dark color of blocks). Namely, our TrustINF method can help identify those influencers who have fake strong influence. In addition, with the increase of \(\alpha \), \(\alpha \in [5\,\%,10\,\%,15\,\%,20\,\%,25\,\%]\), our TrustINF can always identify the attackers with the corresponding Top-\(\alpha \) ranking (the triangle area of the dark blocks). This is because our TrustINF has considered the historical data of trust and regress the trend of trust to measure the probability of a buyer to be an attacker. Figure 5 plots the Attacker Identification Ratio of our TrustINF on the four datasets, where we can see that the range of Attacker Identification Ratio delivered by TrustINF is \([36.02\,\%,86.64\,\%]\) under the Constant attack, and is \([53.67\,\%,92.41\,\%]\) under the Camouflage attack. Based on the statistics, on average, the Attacker Identification Ratio of Constant attack is 66.33 %; and 81.33 % for Camouflage attack. This is because when an advisor providing unfair ratings to sellers, the buyers will no longer trust them based on the trust evolutionary model, and FTBA and FTT of the advisor will descend.

Summary: From the above experimental results, we can see that our TrustINF method can effectively identify the attackers who involve in the Camouflage attack and the Constant attack. In addition, TrustINF can effectively identify the attackers who have fake strong influence, which can greatly help buyers and sellers in the transactions in trust-oriented e-commerce environments.

7 Conclusion and Future Work

In this paper, we have proposed a novel Trust-Aware Influencer Finding (TrustINF) method which can defend against the Camouflage and the Constant attacks in trust-oriented e-commerce environments. The experiments conducted on four real e-commerce datasets have demonstrated our proposed TrustINF method can greatly help identify the attackers in the influencer finding, and can greatly improve the robustness of the influence maximization in trust-oriented e-commerce environments.

In future work, we plan to incorporate our TrustINF method into some influence evaluation methods in real e-commerce systems to further investigate the effectiveness of our model in defending against attacks.