TidalTrust This formula is at the heart of Golbeck et al.’s recommendation algorithm [15]. The novelty of this algorithm mainly lies in the way the trust estimates ta,u are inferred; a trust metric that they have called TidalTrust. In [18], the authors give an overview of the observations that have lead to the development of Tidal- Trust. In each experiment, they ignored an existing trust relation from a user a to a user c, and focused on all paths that connect a to c. In short, by comparing the propagated trust results from these paths with the original, hidden, trust value, they 660 Patricia Victor, Martine De Cock, and Chris Cornelis noticed that (1) shorter propagation paths yield more accurate trust estimates, and that (2) paths containing higher trust values yield better results too.
Hence, taking into account the first observation, only allowing shorter paths should yield the best results. However, in some cases only a few users will be reachable if a limit is set on the path length. This trade-off is incorporated through a variable path length limit: the shortest path length that is needed to connect the target user with a user u that has rated the item (i.e., a rater) becomes the path depth of the algorithm. Like this, the depth of the breadth-first search varies from one computation to another.
One way of addressing the second observation (higher trust values on the path yield better trust estimates) is to limit the information such that it only comes from the most trusted users. However, every user has its own behaviour for issuing trust values (one user may give the maximum value quite often while another one never does), and in addition, it will often be the case that only a few paths contain the same high trust value. This is why Golbeck et al. opted to incorporate a value that represents the path strength (i.e., the minimum trust rating on a path), and to compute the maximum path strength over all paths leading to the raters. This maximum (max) is then chosen as the minimum trust threshold for participation in the process.
The TidalTrust formula is given by Equation (20.2), in which WOT+(a) represents the set of users for whom a’s trust statement exceeds the given threshold max. This means that each user in the process computes its trust in another user as a weighted mean, and only takes into account information from users that he has rated at least as high as max.
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TidalTrust is a recursive algorithm; the trust value ta,u is recursively computed as the weighted mean of trust values tv,u for all TTPs v that are the first link on the shortest path from a to u. The users assure that the maximum path depth is not exceeded by keeping track of the current path length. Note that this algorithm belongs to the class of gradual trust approaches and is an example of a local trust metric.
Golbeck et al. have shown that using trust-based weighted mean in combination with TidalTrust does not necessarily offer a general benefit over computing the average or applying collaborative filtering, but that it does yield significantly more accurate recommendations for users who disagree with the average rating for a specific item (see e.g. [15, 18]).
Trust-based collaborative filtering Whereas Golbeck’s approach is an example of a weighted average implementation, another class of trust-enhanced systems is tied more closely to the collaborative filtering algorithm. In collaborative filtering, a rating of target item i for target user a can be predicted using a combination of the ratings of the neighbours of a (similar users) that are already familiar with item i [53]. The classical formula is given by Equation (20.3).
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The unknown rating pa,i for item i and target user a is predicted based on the mean ra of ratings by a for other items, as well as on the ratings ru,i by other users u for i. The formula also takes into account the similarity wa,u between users a and u, usually calculated as Pearson’s Correlation Coefficient (PCC) [22]. In practice, most often only users with a positive correlation wa,u who have rated i are considered.We denote this set by R+. However, instead of a PCC-based computation of the weights, once can also infer the weights through the relations of the target user in the trust network (again through propagation and aggregation); see Formula (20.4) which adapts Formula (20.3) by replacing the PCC weights wa,u by the trust values ta,u. This strategy is also supported by the fact that trust and similarity are correlated, as shown in [69].
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We call this alternative trust-based collaborative filtering. Note that, because the weights are not equal to the PCC, this procedure can produce out of bounds results. When this is the case, pa,i is rounded to the nearest possible rating. MoleTrust Formula (20.4) is at the basis of Massa et al.’s recommendation algorithm which incorporates a new trust metric, called MoleTrust [38]. This metric consists of two phases. In the first stage, cycles in the trust network are removed, while the second stage includes the actual trust computation. Since it is often the case that a large number of trust propagations must be executed in trust experiments (think e.g. of the large test sets from Epinions.com), it is much more efficient to remove trust cycles beforehand, so that every user only needs to be visited once for obtaining a trust prediction.
The removing of the cycles transforms the original trust network into a directed acyclic graph, and hence the trust prediction for ta,u can be obtained by performing a simple graph walk: first the trust of the users at distance 1 is computed (i.e., direct trust information), then the trust of the users at distance 2, etc. Note that because of the acyclic nature of the graph, the trust value of a user at distance x only depends on the already computed trust values of the users at distance x?1.
The trust of the users at distance 2 or more is calculated in a way similar to Golbeck et al.’s algorithm, i.e. formula (20.2). However, the details of the breadth-first implementation differ significantly. In TidalTrust, a user u is added to WOT+(a) only if he is on a shortest path from target user a to target item i. On the other hand, 662 Patricia Victor, Martine De Cock, and Chris Cornelis Table 20.2: Characteristic features of two state-of-the-art recommendation approaches that mine a trust network to predict a rating for target user a and target item i, based on ratings of other users u for i