Sequence-based trust with time factor

In this section, we illustrate the trust computation model considering the time factor. Each user has a document sequence and corresponding rating sequence, where the ratings of documents are ordered by a time index. The documents / ratings of users are aligned according to their relative time index in corresponding sequences.

The conventional trust model calculates the ratio of accurate predictions made according to past ratings without considering the time factor. Our proposed trust model derives the trust value of a given user not only based on the ratio of accurate predictions but also on the time that the accurate

predictions were made.

Fig. 2 Concept of trust involved with time

For example, in Fig. 2, both Target user and Recommend user have a set of documents aligned according to accessing time and each document is specified by a distinct ID. Rec user is a recommender preparing a suggested document for the target user. Suppose Rec user gives an accurate prediction to Target user on documents which were accessed by both Rec user and Target user. With Hwang and Chen’s trust model [13], each document prediction provides equal weight when counting how much the Target user may trust Rec user. Those predictions which are closer to now should, however, instill more confidence in the target user, because people normally pay more attention to recent events. Thus, in order to show time effect on trust relationship, we present a sequence-based trust model.

Similarly to the conventional trust computation models [13, 28], we also use a simple version of Resnick’s prediction formula [34] to calculate a target user c’s predicted rating of a document dk, pˆ_c^p_,d, which is derived from a recommender p’s rating of dk, as defined in Eq. 13.

) that both the target user c and the recommender p have a similar perspective on document dk. The more similar the perspective, the more trust they have, as illustrated in Eq. 14.

M

T is the pure trust value between target user c and recommender p pertaining to document dk that is derived from the rating data without considering the time factor; and M is the range of the rating score, which equals the difference of the maximum and minimum rating scores.

Generally, the latest documents accessed by a given user more precisely reflect his/her current information needs. Similarly, an accurate prediction made in the recent past contributes more trustworthiness than the one made some time ago.

A document sequence of a user c is a time-ordered sequence arranged by the access times of the documents. Let _S^D_pand _S^R_p be the document sequence and rating sequence of a recommender p respectively. The document sequence is defined as _k1,c¹ _{kj,c ,}

,...,^tc , ^tcj , , ^tcf

D

c kf c

S = <d d " d > and t_c1<t_c2<"<t_cf, where d_k^tcj_,cdenotes the document dk that the user c accessed at time tcj; tc1 is the starting time index of the first document accessed in his/her sequence; and tcf is the index of the time the user accessed the most recent document in his/her sequence. The rating sequence of user c, S_c^R, can be similarly defined.

Assume that a document dk is accessed by user c at time tcj and accessed by recommender p at time tpi.

is defined in Eq. 15, which considers the time weights of user c’s rating ^,

cj

The two time weights are calculated from the time index tcj of user c’s sequence and the time index tpi of user p’s sequence respectively. Higher time weights are given to ratings with more recent time indices. The time weight of a rating made at time tpi by user p is defined as

1 tcj by user cis defined similarly. The time factor uses the harmonic mean of the two time weights; thus the time factor of a prediction will be high if both the time weights of the ratings are high, i.e., both the ratings are made in more recent time. Here is a scenario.

Fig. 3 Illustration of time factor calculation

For example, if user Uc has ten documents ordered by accessed sequence, so does Up. As the result of Doc5 in Uc’s flow is in the ninth position while in Up’s flow it is in eighth position, the time

factor TF_{c tcj,}^{p t,pi}, is calculate by

Equation 14 derives the pure trust value of a prediction without considering the time factor. We further use the time factor of a prediction to denote the importance (weight) of the prediction contributing to the trustworthiness. The trust value of user c with respect to recommender p is then derived by taking the weighted average of the pure trust values of predictions made on co-rated documents between them. Consequently, _Tc^TF_,p, the sequence-based trust metric considering time factor is defined as in Eq. 16.

Pc d is the target user c’s predicted rating on a document dk, which is derived from a recommender p’s rating on dk at time tpi, as defined in Eq. 13; S_c^Dand S are document sequences of _p^D the target user c and recommender p respectively; and M is the range of the rating score, which equals the difference of the maximum and minimum rating scores.

In addition, any one document may appear in the user’s document sequence several times.

Because each user has different information demand over time, it is possible that he gives different ratings to the same document accessed at different time. Therefore, each document in the user’s document sequence should be counted respectively.

Here is a simple example.

Fig. 4 Illustration of sequence-based trust with time factor

Up is a recommender and Uc is a target user. Both of them have average rating with a score of three. Note that Up is trustworthy if s/he has a similar view to Uc on identical documents at recent time index of their document sequences. Referring to the Fig. 4, Doc1, Doc4 and Doc5 exist in both knowledge flows. We use Up’s opinion to predict Uc’s score.

According to Eq. 13, Uc may give Doc1 a rating score of four in Up’s opinion. Considering the time factor in Doc1 in Uc’sand Up’s document sequence, Uc may trust Up as below. compute the weighted average on all co-rated items, and then we obtain the trust degree with time factor 0.8217.