IT-PMF: A Novel Community E-Commerce Recommendation Method Based on Implicit Trust

Abstract

It is well-known that data sparsity and cold start are two of the open problems in recommendation system research. Numerous studies have been dedicated to dealing with those two problems. Among these, a method of introducing user context information could effectively solve the problem of data sparsity and improve the accuracy of recommendation algorithms. This study proposed a novel approach called IT-PMF (Implicit Trust-Probabilistic Matrix Factorization) based on implicit trust, which consists of local implicit trust relationships and in-group membership. The study started from generating the user commodity rating matrix based on the cumulative purchases for items according to their historical purchase records to find the similarity of purchase behaviors and the number of successful interactions between users, which represent the local implicit trust relationship between users. The user group attribute value was calculated through a fuzzy c-means clustering algorithm to obtain the user’s in-group membership. The local implicit trust relationship and the user’s in-group membership were adjusted by the adaptive weight to determine the degree of each part’s influence. Then, the author integrated the user’s score of items and the user’s implicit trust relationship into the probabilistic matrix factorization algorithm to form a trusted recommendation model based on implicit trust relationships and in-group membership. The extensive experiments were conducted using a real dataset collected from a community E-commerce platform, and the IT-PMF method had a better performance in both MAE (Mean Absolute Error) and RMSE (Root Mean Square Error) indices compared with well-known existing algorithms, such as PMF (Probabilistic Matrix Factorization) and SVD (Single Value Decomposition). The results of the experiments indicated that the introduction of implicit trust into PMF could improve the quality of recommendations.

1. Introduction

With the vigorous development of E-commerce and the continuous expansion of Internet users, Taobao, Amazon and other online shopping platforms continue to provide a large number of products and services to meet the potential diversified needs, which will bring the problem of “information overload”. How to find appropriate services and effective information has become a difficult problem in front of us. As a way to solve the “information overload” of the Internet, recommendation systems can directly connect users and items, better promote products and reduce the burden of users. Recommendation systems, due to their multi-domain applicability, are among the main topics of scientific interest in recent years [1,2].

As a new business model, community E-commerce focuses on serving relatively stable local consumer groups [3]. It is also faced with endless choices and decisions when shopping online. Community E-commerce is mainly divided into two categories, one refers to the E-commerce that provides the living needs of the regional groups within a certain area, mainly in the way of combining online and offline commerce. The degree of overlap between the activity range and trajectory of the user group is higher than that of traditional E-commerce. The other type is the group of users with the same hobbies, with similar needs forming a community circle, and their hobbies overlap more than ordinary E-commerce. In daily life, consumers are more willing to trust the recommendations of friends or influential people, rather than a lack of unconvincing advertisements. Trust, as the core concept of interpersonal relationships, will directly affect the user’s decision-making process [4]. Compared with traditional E-commerce users, community E-commerce has more communication and mutual trust, which makes it easier to tap the trust relationship between users. Therefore, there is an urgent need to develop a trust-based recommender system for communities E-commerce platforms establishing trust relationships based on users’ purchase history is an important dimension of recommender systems to predict items that users may purchase in the near future [5].

Personalized recommendation is generally divided into content-based [6], collaborative filtering recommendation [7] and the increasingly popular social network-based recommendation [8,9]; however, there are some problems, such as cold start, data sparsity, recommendation accuracy and so on. With the development of social networks, the trust relationship between users is used in recommendation systems. Trust-based recommendation systems are widely studied and have become an extension of traditional recommendations. Many scholars have added social networks or user trust relationships on the basis of traditional algorithms to improve the accuracy of recommendations [10,11,12].

Existing studies have proven that trust between users can improve the accuracy of recommendation, but the existing trust information is very sparse, and there is a lack of research on the implicit trust relationship between users. For the above problems, this paper proposes a novel recommendation approach called Implicit Trust-Probabilistic Matrix Factorization (IT-PMF) for community E-commerce based on implicit trust relationships and in-group membership. The main contributions of this paper are as follows:

• The study generates a user commodity rating matrix based on cumulative purchases for items according to their historical purchase records.
• The study mines users’ local implicit trust information through the users’ similarities and the interactions between users, and the users are soft clustered to calculate the degree of membership to a user category. The local implicit trust relationship and the user’s in-group membership were adjusted by the adaptive weight to determine the degree of each part’s influence.
• The study integrates rating trust and trust information into the probability matrix factorization model, so that the final result is not only affected by its own rating value but also by the recommendations of neighboring users.
• The experiment was carried out on a real community E-commerce data set, and the constructed rating matrix performed well on the traditional PMF algorithm. At the same time, the influence of parameters on the experimental results was evaluated, and the results showed the efficiency of the algorithm.

The rest of the paper is organized as follows. Section 2 summarizes the related work. Section 3 proposes the community E-commerce recommendation algorithm based on trust, including implicit trust relationship and in-group membership. Section 4 presents experimental results and analysis. Section 5 concludes the paper.

2. Literature Review

2.1. Traditional Recommendation Algorithms

The rapid development of information technology and the Internet has facilitated the explosive growth of information, which has exacerbated the problem of information overload. In response to this problem, recommender systems emerge as the times require that systems help users find the content they are interested in. Traditional recommendation algorithms are mainly divided into content-based recommendation algorithms, collaborative filtering recommendation algorithms and hybrid recommendation algorithms. The content-based recommendation algorithm is the earliest recommendation algorithm used. Its idea is relatively simple. It labels users and products and recommends items that are highly similar to historically favorite items to users. The user-based collaborative filtering algorithm was originally proposed by the Groupslens research group [7], followed by a commodity-based collaborative filtering algorithm [13] and a matrix-factorization-based collaborative filtering algorithm [14]. Hybrid recommendation algorithms can overcome the limitations brought by a single recommendation algorithm and combine different algorithms to obtain better recommendation results.

However, with the continuous development of information technology and the advent of the intelligent era, the data of users and commodities are growing rapidly, resulting in typical problems such as sparsity, cold start and long tail. In order to solve the above problems, two commonly used methods are as follows: (1) matrix factorization technology: the rating matrix is decomposed in order to predict the user’s non rated items. The most classic examples are singular-value decomposition technology [15], and the Matrix Factorization method (MF). The MF method is mainly divided into basic Matrix Factorization (basic MF), regularization matrix factorization, Probabilistic Matrix Factorization (PMF), Non-negative Matrix Factorization (NMF), orthogonal nonnegative matrix factorization and so on. (2) Data filling method: other useful information is used to supplement data sparsity and cold start user information, so as to alleviate sparsity. With the gradual rise of social media and social networks, integrating trust into recommendation algorithms can effectively solve common problems such as data sparsity and user cold start.

In order to effectively alleviate the problems of data sparsity and cold starts, the data sparsity is reduced by introducing context information [16,17,18], clustering [19,20,21,22] and other methods, and the user’s own needs are considered to make the algorithm more efficient. Accuracy is greatly improved. The main difference between a social recommendation and a traditional recommendation algorithm is that the former mines users’ social relations, establishes trust relations between users and establishes social relationship network. With the gradual entry of social media into public life, the social network and trust relationship data between users has also become one of the data sources to fill the sparsity of the matrix.

2.2. Recommendation Algorithm Based on Social Network and Trust

With the continuous enrichment of social network information, scholars at home and abroad have opened up new ideas based on trust relationships in social networks and mining trust relationships. For example, the EigenTrust model is a peer-to-peer network reputation management algorithm proposed by Kamvar et al. [8]. The topic model and Markov model integrate user preferences and location information into the model, which greatly improves the prediction accuracy. TidalTrust was proposed by Golbeck et al. [9]. They integrated trust into the social network, and the algorithm refers to the source node when predicting the score. All trusted neighbors rate the items and analyze how the trust level and the length of the trust chain affect the trust agreement between other nodes. Scholars such as Wang et al. [23] proposed a semantic-based social network recommendation system. The idea is to use sensor data from mobile phone users to mine potential friends who are similar to the target user through contextual information, so that the recommendation results more accurately reflect user preferences, as online comments will have an impact on consumers’ purchase behavior. Gong et al. [24] explored the potential of using explicit and implicit information to mine the potential information of the meta-path in recommendation. Ma et al. [25] proposed a recommendation model that comprehensively considers local information and global information. Li et al. [26] proposed a novel RHRM recommendation framework that filters only helpful reviews and reflects them in the personalized recommendation service. Wang et al. [27] explored the credibility of online reviews and verified that deceptive reviews can affect consumers’ purchasing decisions. Zhang et al. [28] proposed the ImDetector method for the imbalance in comment data, which has advantages in detecting fraudulent reviewers.

In the social network environment, the research on recommendation algorithms has also achieved certain breakthrough results, and good progress has been made in the recommendation that integrates trust into the matrix factorization model. For example, Jamali m et al. [11] proposed a social network recommendation algorithm SocialMF based on matrix factorization technology, which connects users’ social relations with recommendation and solves the problem of users’ cold start. Qiu j et al. significantly improved DeepWalk and Line, proposed NetMF and laid a theoretical foundation for the network embedding method based on skip-gram [29]. PMF [30] was first proposed by the University of Toronto, Canada, and was gradually applied in recommendation. It solved the problems of data sparsity and prediction accuracy by using user social network information and user rating records. Chen Ting et al. [4] integrated global trust and local trust to calculate the user’s trust weight value, added the influence of trust weight to the PMF algorithm and proposed the Trust-PMF algorithm. Xu et al. [31] incorporated the social trust relationship of users in social networks into the loss function to improve recommendation accuracy.

In a word, in the recommendation algorithms for the integration of trust, most of the research [4,9,32,33] aims to further dig into the basis of the explicit trust relationship, but there is a lack of research on the implicit trust relationship between users. Often, the unmined implicit trust relationships that users have contain richer information, and the existing trust-based recommendation algorithms cannot be used for datasets without obvious social relationships. Therefore, considering the above problems, this paper proposes an IT-PMF recommendation algorithm on a dataset without explicit social relations. Preferences, purchasing habits and category affiliation affect the strength of trust among users, and trust is incorporated into the probability matrix factorization recommendation algorithm. Experiments show that the algorithm can significantly improve the accuracy of recommendation on community E-commerce data sets without obvious trust relationship.

3. Relevant Work

3.1. Trust Calculation

In order to improve the sparsity of data sets, scholars have made constant efforts to introduce user information in addition to ratings, such as user location, user context and trust relations, aiming at more accurate recommendations. As a complicated social network relation, trust is distinct, fuzzy, transferable, non-symmetrical, combinable and dynamic in nature. The trust relations between users are primarily backed by user social networks. Two forms of social trust relations are commonly found: the trust type and friend type. The main differences between them are described below:

(1)

A trust relation is unidirectional, whereas a friend relation is bidirectional.

(2)

Construction of a trust relation is based on certain similar taste, whereas such similarity may or may not exist in a friend relation.

With the continuous enrichment of social network relationships, trust relationships are also divided into local trust and global trust. Global trust mainly refers to the degree of influence and prestige of users in the entire social network, while local trust is related to the target user. Influencing factors between groups of users have direct interaction. The recommendation algorithms incorporating trust relations enjoy the following advantages over traditional recommendation algorithms. First, the recommendation accuracy is greatly improved. Compared with algorithms based merely on user ratings, the algorithms using trust relations are able to identify user preferences more precisely. Second, the issue of user cold starts can be effectively addressed. Third, the inclusion of user social trust relations leads to more convincing recommendation results. Therefore, with the booming community E-commerce nowadays, trust relations are becoming a more and more influential factor. However, the use of explicit trust relationships is often greatly restricted due to the user’s personal privacy and difficulty in obtaining them, and certain behaviors and preferences of users often contain rich potential trust relationships. Therefore, potential implicit trust relationships begin to appear to fill the gap of explicit trust.

3.2. PMF Algorithm

PMF (probabilistic matrix factorization) is a collaborative filtering recommendation algorithm based on matrix decomposition. It is superior to previously proposed recommendation algorithms when used for traditional rating data. It proves highly effective for Netflix with massive and sparse data. Its underlying concept is that a relation between users and films (i.e., users’ film preferences) can be determined by combining a limited number of factors linearly.

Assume that we have M films, N users, and integer rating values from 1 to $K^1$. Let $R_{ij}$ represents the rating of user $i$ for movie j. U and V are used to denote a user matrix and a film matrix, respectively, and the column vectors $U_i$ and $V_j$ represent user-specific and movie-specific latent feature vectors, respectively. The predictive rating is defined in Equation (1):

$$p\left(R|U,V,{\sigma }^2\right)={\displaystyle \prod }_{i=1}^N{\displaystyle \prod }_{j=1}^M{[N(R_{ij}|U_i^t{V}_j,{\sigma }^2)]}^{I_{ij}}$$

(1)

where $N(R_{ij}|U_i^t{V}_j,{\sigma }^2)$ is a probability density function of the Gaussian distribution with mean $U_i^t{V}_j$ and variance ${\sigma }^2$, and $I_{ij}$ is an index function (if User $i$ has given a rating of Film $j$, $I_{ij}=1$, otherwise it is equal to 0). The potential eigenvectors of users and films are defined in Equation (2):

$$p\left(p|{\sigma }_p^2\right)={\displaystyle \prod }_{u=1}^{n}N(P_u|0,{\sigma }_p^{2}I) p\left(q|{\sigma }_q^2\right)={\displaystyle \prod }_{u=1}^{n}N(q_i|0,{\sigma }_q^{2}I)$$

(2)

The logarithmic posterior distribution function of users and films is shown in Equation (3):

$$\begin{array}{cc}lnp\left(U,V|R,{\sigma }^2,{\sigma }_V^2,{\sigma }_U^2\right)& =-\frac{1}{2{\sigma }^2}{\displaystyle {\displaystyle \sum }_{i=1}^N}{\displaystyle {\displaystyle \sum }_{j=1}^M}{I}_{ij}{\left(R_{ij}-U_i^T{V}_j\right)}^2-\frac{1}{2{\sigma }_U^2}{\displaystyle {\displaystyle \sum }_{i=1}^N}{U}_i^T{U}_i-\frac{1}{2{\sigma }_V^2}{\displaystyle {\displaystyle \sum }_{j=1}^M}{V}_j^T{V}_j\\ & -\frac{1}{2}\left(\left({\displaystyle {\displaystyle \sum }_{i=1}^N}{\displaystyle {\displaystyle \sum }_{j=1}^M}{I}_{ij}\right)ln{\sigma }^2+NDln{\sigma }_U^2+MDln{\sigma }_V^2\right)+C\end{array}$$

(3)

where C is a constant independent of any variable. Maximizing the above formula is equivalent to minimizing Equation (4):

$$E=\frac{1}{2}{\displaystyle \sum }_{i=1}^N{\displaystyle \sum }_{j=1}^M{I}_{ij}{\left(R_{ij}-U_i^T{V}_j\right)}^2+\frac{{\lambda }_U}{2}{\displaystyle \sum }_{i=1}^N\Vert U_i\Vert {}_{Fro}^2+\frac{{\lambda }_V}{2}{\displaystyle \sum }_{i=1}^M\Vert V_j\Vert {}_{Fro}^2$$

(4)

3.3. Trust-PMF Recommendation Algorithm Based on Trust Network

On the basis of the PMF algorithm, Chen Ting [4] brought forward a recommendation algorithm based on trust in social network environments, namely, the Trust-PMF recommendation algorithm. It combines known user trust relations with user similarity data. With both global trust and local trust taken into consideration, the trust weight of users can be derived with trust propagation mechanism. Through the incorporation of the collaborative filtering technique into the matrix factorization process and the use of segmented adaptive weight computing, more accurate recommendation results can be obtained. The basic computational formula is shown in Equation (5):

$$P\left(R|p,q,{\sigma }_R^2\right)={\displaystyle \prod }_{i=1}^n{\displaystyle \prod }_{j=1}^m{\left[N(r_{ij}|\alpha p_i{q}_j+\left(1-\alpha \right)\frac{{{\displaystyle \sum }}_{tϵN_i}{w}_{it}{p}_t{q}_j}{{{\displaystyle \sum }}_{tϵN_i}\left|w_{it}\right|},{\sigma }_R^2)\right]}^{I_{ij}^R}$$

(5)

It is assumed that potential user eigenvectors and potential commodity eigenvectors both follow Gaussian prior distribution with an average of 0, as shown in Equation (6):

$$p\left(p|{\sigma }_p^2\right)={\displaystyle \prod }_{u=1}^{n}N(P_u|0,{\sigma }_p^{2}I) p\left(q|{\sigma }_q^2\right)={\displaystyle \prod }_{u=1}^{n}N(q_i|0,{\sigma }_q^{2}I)$$

(6)

After extending the PMF model, deriving the posterior probability with Bayes’ theorem, and calculating the logarithm, the Equation (7) can be achieved:

$$\begin{array}{cc}lnp\left(p,q|R,w,{\sigma }_R^2,{\sigma }_p^2,{\sigma }_q^2\right)& =-\frac{1}{2{\sigma }^2}{\displaystyle {\displaystyle \sum }_{u=1}^n}{\displaystyle {\displaystyle \sum }_{i=1}^m}{I}_{ij}^R{\left(R_{ij}-g\left(\alpha p_i{q}_j+\left(1-\alpha \right)\frac{{{\displaystyle \sum }}_{tϵN_i}{w}_{it}{p}_t{q}_j}{{{\displaystyle \sum }}_{tϵN_i}\left|w_{it}\right|}\right)\right)}^2-\frac{1}{2{\sigma }_p^2}{\displaystyle {\displaystyle \sum }_{i=1}^N}{p}_i^T{p}_i\\ & -\frac{1}{2{\sigma }_q^2}{\displaystyle \sum }_{j=1}^M{q}_j^T{q}_j-\frac{1}{2}\left({{\displaystyle \sum }}_{i=1}^n{{\displaystyle \sum }}_{j=1}^m{I}_{ij}^R\right)ln{\sigma }_R^2-\frac{1}{2}\left(nlln{\sigma }_p^2+mlln{\sigma }_q^2\right)+Con\end{array}$$

(7)

where Con is a constant that does not depend on the parameters. Maximizing the logarithmic function in the formula is equivalent to minimizing the loss function. The loss function is shown in Equation (8):

$$L\left(R,w,p,q\right)=\frac{{\lambda }_p}{2}{\Vert p\Vert }_F^2+\frac{{\lambda }_q}{2}{\Vert q\Vert }_F^2+\frac{1}{2}{\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{j=1}^m{I}_{ij}^R{(R_{ij}-g(\alpha p_i{q}_j+(1-\alpha )\frac{{{\displaystyle \sum }}_{tϵN_i}{w}_{it}{p}_t{q}_j}{{{\displaystyle \sum }}_{tϵN_i}\left|w_{it}\right|}))}^2$$

(8)

where ${\lambda }_p=\frac{{\sigma }_R^2}{{\sigma }_p^2}$ and ${\lambda }_q=\frac{{\sigma }_R^2}{{\sigma }_q^2}$.

4. Community E-Commerce Recommendation Algorithm Based on Trust

This study’s proposed IT-PMF method consists of local implicit trust relationships and in-group membership. It should be noted that, in general, data sets contain scoring information, while for data sets without scoring information, we proposed the use of the number of cumulative purchases of goods by users as the users’ ratings of goods. The local implicit trust relationship was calculated based on the similarity of purchase behaviors and the number of successful interactions between users. The user group attribute value was calculated through the fuzzy c-means clustering algorithm to obtain the user’s in-group membership. The local implicit trust relationship and the user’s in-group membership were adjusted by the adaptive weight to determine the degree of each part’s influence. To form recommendation weight based on trust and to use neighbor interaction to make up for the inaccurate prediction score caused by data sparseness, the trust information and rating information are integrated into the probability matrix factorization model, so that the user’s rating of the item not only depends on the interaction of the potential factor vectors between the user and the item but is also affected by the score of the neighbor set. The algorithm flow is shown in Figure 1.

Table 1. Symbols used in formulas and their description.

Index	Symbol	Description
1	$Si{m}_{i,j}$	Purchase preference similarity among users
2	$f$	Number of successful purchase interactions among users
3	$s$	Number of failed purchase interactions among user
4	$r_{u,j}$	Rating of Commodity j given by User u
5	$I_{U,V}$	Collection of ratings given by Users U and V
6	$I_U$	Collection of commodities purchased by User U
7	${\mu }_u$	Average of ratings given by User u
8	${\sigma }_u$	Variance of ratings given by User u
9	$S_{mn}$	Membership degree of User $u_m$ in Type $Sor{t}_n$
10	$Sor{t}_n$	Type n commodity in soft cluster
11	$w_{it}$	Recommendation trust weight between a user and neighboring users
12	$p_i, q_j$	Eigenvectors after factorization of the rating matrix of User i
13	${\Vert p\Vert }_F$	$P$ vector matrix norm

is the main symbols used in the formulas in this paper and detailed description.

4.1. Implicit Trust Modeling

4.1.1. Local Implicit Trust Modeling

Two types of trust should be distinguished from each other: local trust and global trust. Local trust mainly refers to the trust between two individual users, while global trust generally indicates the dependability of a user throughout a social network, which is related to the qualities of the user such as creditability and capabilities.

In this paper, local trust is measured with user purchase similarity, user rating preference and successful interactions between users, as shown in Equation (9):

$$PTrust=Si{m}_{i,j}\times Pr{e}_{i,j}\times \frac{f}{f+s}$$

(9)

where $Si{m}_{i,j}$ is the user purchase similarity expressed as a value of Jaccard Mean squared differences (JMSD) similarity [34], as given in Equation (10):

$$JMS{D}_{u,v}=(1-\frac{{{\displaystyle \sum }}_{I\in I_{u,v}}\frac{r_{u,j}-r_{v,j}}{\begin{array}{c}max-mi\\ n\end{array}}}{\left|I_{U,V}\right|})\times \frac{\left|I_{U,V}\right|}{\left|I_U\right|+\left|I_V\right|-\left|I_{U,V}\right|}$$

(10)

where $I_{U,V}$ represents the common rating collection of Users u and v, and max and min indicate maximum rating and minimum rating, respectively. However, since JMSD does not reflect the interaction between user rating preferences and users, Equation (11) calculations are adopted for further dependability derivation:

$$Pr{e}_{u,v}=\left\{\begin{array}{c}{e}^{\left(-\left(\left|{\mu }_u-{\mu }_v\right|+1\right)·\left(\left|{\sigma }_u-{\sigma }_v\right|\right)\right)}\\ e^{\left(-\left(\left|{\mu }_u-{\mu }_v\right|\right)·\left(\left|{\sigma }_u-{\sigma }_v\right|+1\right)\right)}\\ e^{\left(-\left(\left|{\mu }_u-{\mu }_v\right|\right)·\left(\left|{\sigma }_u-{\sigma }_v\right|\right)\right)}\end{array}\right.\begin{array}{c},{\mu }_u={\mu }_v且{\sigma }_u\ne {\sigma }_v\\ ,{\mu }_u\ne {\mu }_v且{\sigma }_u={\sigma }_v\\ ,\mathrm{Other} \mathrm{cases}\end{array}$$

(11)

where $Pr{e}_{u,v}$ denotes the rating similarity between User $u$ and User $v$. ${\mu }_u$ and ${\sigma }_u$ represent the average and variance of the ratings of User u, respectively. It can be seen from the above formulas that a significant difference between Users u and v in terms of rating average or variance will lead to low rating similarity between them.

In real life, a user tends to put more trust in users with successful interaction with him/her, and less in those failing to interact with him/her. In order to introduce this tendency into our calculations, we first divide user ratings into two categories: positive and negative. Positive ratings are higher than average, while negative ones are lower than average. If the ratings of the same commodity given by two users fall into the same category, their interaction is deemed successful; otherwise, their interaction is deemed failed. This relation is expressed with Equation (12):

$$Inte{r}_{u,v}=\left\{\begin{array}{c}1 \\ 0 \end{array}\begin{array}{c}\mathrm{Successful} \mathrm{interaction}\\ \mathrm{Failed} \mathrm{interaction}\end{array}\right.$$

(12)

The posterior trust value between two users is expressed as the ratio of successful interactions to total interactions.

4.1.2. In-Group Membership

Social groups can be divided into in-groups and out-groups based on the users’ sense of belonging. In-groups refer to groups in which a user often participates and can be viewed by the user as “our groups”. Groups other than in-groups are regarded as out-groups, or “their groups”. The concept of the in-group was brought forward by American sociologist W. G. Sumner in 1906. With this concept, he intended to describe users’ group belonging, group awareness and influence of groups on individuals. For the degree of in-group membership, the fuzzy clustering c-Means technique is used in this paper for the purpose of clustering. Some scholars have studied cluster analysis for mixed data [35]. The fuzzy clustering c-Means algorithm was first proposed by Dunn and then further promoted by Bezdek [36]. Users are not classified directly into established types. The membership degree of users is calculated instead. The main calculation steps include the following: (1) Clustering users based on fuzzy c-means clustering algorithm, where the degrees of user membership in different types of groups are calculated; (2) the user in-group membership is calculated based on Cosine similarity.

(1)

Clustering users based on fuzzy c-means clustering algorithm

Fuzzy c-means clustering algorithm is used to calculate the membership of users for each commodity category. A membership matrix between users and category can therefore be obtained, as shown in

Table 2. User—membership matrix.

	${\mathit{u}}_1$	${\mathit{u}}_2$	${\mathit{u}}_3$	……	${\mathit{u}}_{\mathit{m}}$
$Sor{t}_1$	$S_{11}$	$S_{21}$	$S_{31}$	……	$S_{m1}$
$Sor{t}_2$	$S_{12}$	$S_{22}$	$S_{32}$	……	$S_{m2}$
$Sor{t}_3$	$S_{13}$	$S_{23}$	$S_{33}$	……	$S_{m3}$
……	……	……	……	……	……
$Sor{t}_n$	$S_{1n}$	$S_{2n}$	$S_{3n}$	……	$S_{mn}$

.

The columns in the matrix refer to user types, while the rows refer to users. $S_{mn}$ represents the membership degree of User $u_m$ in Type $Sor{t}_n$.

(2)

Calculate In-group membership

Cosine similarity is used to calculate in-group membership degree between users, as shown in Equation (13):

$$Group=si{m}_{u,v}=\frac{{{\displaystyle \sum }}_{i=1}^n{U}_i\times V_i}{\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(U_i\right)}^2}\times \sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(V_i\right)}^2}}$$

(13)

where $U_i$ and $V_i$ denote membership degree of Users $U$ and $V$ in Type $i$.

4.2. Model of IT-PMF

The local trust and the membership degree of the in-group membership obtained above are linearly added through Formula (14) to obtain the user’s trust matrix:

$$w_{it}=Trus{t}_{u,v}=\beta PTrust+\left(1-\beta \right)Group$$

(14)

After the user trust matrix is derived, the TOP–N neighboring users are extracted based on user trust weight. User ratings and trust information are then incorporated into the PMF model. In this way, the predictive ratings of specific commodities given by users are not only dependent on previous user rating records but are also affected by neighboring users. In addition, adaptive weight $\beta$ is adopted to dynamically determine the impact of in-group membership degree and user local trust, thereby obtaining more practical calculation results. After the introduction of user trust relations, the user predictive rating can be defined in Equation (15):

$$R_{i,j}=\alpha p_i{q}_j+\left(1-\alpha \right)\frac{{{\displaystyle \sum }}_{tϵN_i}{w}_{it}{p}_t{q}_j}{{{\displaystyle \sum }}_{tϵN_i}\left|w_{it}\right|}$$

(15)

where $w_{it}$ is the user trust weight derived from trust calculation. The conditional probability distribution of users’ rating $R$ in relation to eigenvectors $p \mathrm{and} q$ is given below in Equation (16):

$$P\left(R|p,q,{\sigma }_R^2\right)={\displaystyle \prod }_{i=1}^n{\displaystyle \prod }_{j=1}^m{\left[N(r_{ij}|\alpha p_i{q}_j+\left(1-\alpha \right)\frac{{{\displaystyle \sum }}_{tϵN_i}{w}_{it}{p}_t{q}_j}{{{\displaystyle \sum }}_{tϵN_i}\left|w_{it}\right|},{\sigma }_R^2)\right]}^{I_{ij}^R}$$

(16)

5. Experimental Results and Analysis

The experiments were conducted on a computer with 1.70 GHZ Intel Core i5, 8 GB memory and the Windows 10 operation system. The proposed algorithm and other comparative algorithms were all realized in a python 3.8 programming environment. Two indices widely employed in academia were used to evaluate performance of the recommendation algorithms—Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The experiments were completed with real-life community E-commerce user purchase data.

The data set used contained 89,525 user purchase records from August 2019 to 21 September 2020 in T-APP software (hereinafter abbreviated as T-APP). The original data were subject to a cleaning process to eliminate data generated during APP test stage and data corresponding to abnormal purchase orders. By merging repeated commodity IDs, we concluded that the data set involved 3321 users, 3245 commodities and 77,258 normal purchase records. The data-cleaning process is shown in the Figure 2 below.

The description of some commodities is given in

Table 3. Description of some commodities in T-APP.

User ID	Commodity ID	Commodity Name	Purchase Amount
1023	2	Commodity 1	3
566	38	Commodity 2	5
378	61	Commodity 3	3
22	68	Commodity 4	2
1155	69	Commodity 5	10
2048	73	Commodity 6	1

. Every data entry has basic attributes such as user ID, commodity ID, purchase time, purchase amount and payment method. Four attributes are mainly used in this paper: User ID, commodity ID, commodity name and purchase amount.

Since the data set consists of user purchase records, it is first necessary to generate user-commodity rating data. A rating indicates how much a user likes a commodity, while a purchase frequency can be said to reflect a user purchase preference (preferred commodities are purchased more frequently than less preferred ones). Hence, we take a user’s purchase frequency of a commodity as his/her rating of the commodity, thus building a “pseudo rating” matrix, i.e., a predictive rating data set. In order to normalize the rating range, the ratings in the data set were converted into the interval [0, 1] with the ratio $\frac{r}{r_{max}}$. The number of neighboring users is set at three.

5.1. Impact of Parameters

In this section, the dependence ($\alpha$) of the number of iterations and predictive ratings on user preferences is analyzed, together with the impact of the proportion ($\beta$) of local trust in total trust on the recommendation results of the proposed algorithm. Ten dimensions are assumed for the eigenvectors.

It can be seen from Figure 3 that both MAE and RMSE vary with the number of iterations. The recommendation error first decreases with the increasing number of iterations and then gradually converges.

Figure 4a,b depict the impact of $\alpha$ on MAE and RMSE, respectively, and $\alpha$ indicates the dependence of a predictive rating on a user preference. $\alpha$ should be in the interval [0, 1]. In the experiments, the values in the sequence 0.1, 0.3, … are taken in turn for $\alpha$. When $\alpha =0.9$, both indices reach an optimal value. At this point, the dependence of the final predictive rating on preference of friends is 10%, while its dependence on the preference of the user is 90%.

Figure 5a,b depict the impact of $\beta$ on MAE and RMSE, respectively. Different values of $\beta$ correspond to different proportions of local trust and global trust in the calculation of overall trust. In this paper, the algorithm leads to the minimum prediction error if $\beta =0.1$. This suggest that, in the research context of this paper, most users have limited trusted friends, and consequently, it is difficult for target users to gain subjective knowledge and understanding of other users. As a result, the overall trust can only be largely determined with the impact of trusted friends.

5.2. Experiment Results and Analysis

Comparison with traditional PMF algorithm without trust information: The PMF algorithm only makes use of user ratings without considering user trust weight information. The algorithm proposed in this paper makes recommendations on the basis of user ratings and implicit user trust relations generated. It can be seen from Figure 6 that this algorithm is significantly superior to the traditional PMF algorithm, meaning that the addition of trust relations leads to more accurate prediction of user needs.

Table 4. Comparison between the proposed algorithm and other baselines.

Algorithm	MAE	RMSE
PMF	0.1090	0.1346
TTPMF	0.1258	0.1508
SVD	0.0938	0.1284
SVD++	0.0991	0.1310
NMF	0.1375	0.1570
This paper	0.0757	0.1147

shows the comparison between the proposed IT-PMP approach with the baseline matrix factorization algorithms (e.g., SVD (Single Value Decomposition), SVD++ and NMF), the regular PMF algorithm and the PMF algorithm based on 0–1 trust matrix, and we named it the Traditional Trust Probabilistic Matrix Factorization (TTPMF). It can be seen that the algorithm proposed in this paper is superior than the above algorithms in the MAE and RMSE indices. The reason for the poor performance of the comparison algorithms may be that PMF, SVD, SVD++ and NMF only use rating information without introducing trust information, and TTPMF only stays on the surface information of trust without fully mining the deep trust relationship between users. It shows that the introduction of implicit trust information can make up for the problem of low recommendation accuracy caused by data sparseness in collaborative filtering.

In the process of trust matrix generation using the algorithm proposed in this paper, the values in the interval [0, 1] are derived by means of weighted calculation. Most traditional trust matrices, on the other hand, take the form of a 0–1 matrix. It is obvious that, compared with TTPMF and PMF, the MAE and RMSE obtained by the algorithm proposed in this paper are lower, and the prediction error is smaller and closer to the actual value.

The experiment results show that the “pseudo-rating” matrix and user trust similarity matrix constructed in this paper are suitable for recommendations for community E-commerce users without rating and trust information. In addition, the implicit trust information for user mining proposed by us can reduce existing recommendation errors and can be used for trust-based recommendation methods. It leads to smaller recommendation errors compared with other PMF algorithms and consequently results in more accurate recommendations.

6. Conclusions

This study proposed a new recommendation method named IT-PMF based on implicit trust relationships consisting of local implicit trust relationships and in-group membership. The local implicit trust relationship was calculated based on the similarity of purchase behaviors and the number of successful interactions between users. The new algorithm established a user’s preference model to generate the target user’s neighbors. Combined with the user’s purchasing preference and the influence from his or her neighbors, the algorithm could predict the target user’s scoring on certain commodities, which provides a new perspective for trust-based recommendation research.

The IT-PMF was verified by extensive experiments, in which the dataset was collected from a real community E-commerce platform. The proposed method was trained in the training set and evaluated in the test set. Two indicators, namely, MAE and RMSE, were adopted to assess the algorithm’s performance. The result showed that the IT-PMF method had a better performance in both MAE and RMSE indices compared with baseline algorithms, such as PMF and SVD.

This study founded that, in T-app dataset, the final prediction score was mostly affected by the user’s purchasing preference (90%) and partly affected by his or her friends’ preferences (10%). This conclusion was deduced through the experiment of the IT-PMF’s parameters’ sensitivity, namely, α and β. In the experiment, when the value of β was assigned as 0.1, the error of the algorithm was the smallest. The value range of α was set to [0, 1], and the experimental results showed that when the value of α was 0.9, the evaluation indicators were all optimal.

The algorithm proposed in this paper can provide decision-making support for enterprises to implement precision recommendation strategies to improve the efficiency of marketing on community E-commerce platform. Although the proposed IT-PMF method performed well in this study, there are still some gaps to be explored in the future.

First, the amount of data that T-app could provide at this time is limited. In this research, the author only analyzed the data of 12 months, starting from August 2019. In the future, with the accumulation of consumption data, the author will work on a dynamic model of trust relationship, which takes the time factor into account.

Second, the dataset analyzed in this paper was limited to users’ purchase data. This means that the results of the experiment might be limited, too. Future research could integrate the user’s social, location and other contextual information into the establishment of trust relationship, which will further improve the accuracy of the recommendation.