Big Data deeply changed both researchers and industries approaches to data management. This impressive amount of data contains a lot of information regarding user suggestions and searches. In this paper, we focus on the e ect of users suggestions on their social environment. Suggestions are provided to user by means of simple rules that are dened on the basis of the data being analyzed. We address the reaction of users in a competitive environment when they were invited to judge each other choices. The above mentioned activity is crucial to perform e cient identi cation of users able to spread their in uence across the network, which is a key activity in several scenarios like tourism promotion, personalized marketing, and entertainment suggestion.
Big Data paradigm is currently driving both research and industrial interests.
Many proposals for innovative data analysis for managing impressive amounts of
data have been developed. These approaches share the common needs to rethink
storage and analysis techniques in order to deal with massive, heterogeneous
data, that are fast varying [
To this end in [
Since the sub-tasks are solved by independent executors, payed for their activities, an important problem regards the quality evaluation of the obtained results. In our context the clients can ask for search directions. Once the result is obtained, we can ask the client to evaluate the obtained suggestion, i.e. give a rank for the executor performing this task. Moreover, some credits to executors suggesting useful search directions to clients are assigned. We analyze what happens with users' evaluations when they are aware of the other ones. In particular, we consider a group of users involved in a research project and we let them know mutual preferences on some topics.
We use Exponential Graph Random Models (EGRM) [
It has been shown in literature, that in many settings the possibility to
observe the other user rankings causes mutual adjustment among raters. In our
framework, higher rankings are associated with positive evaluation (thus higher
rewards), such that being ranked below others is aversive. To properly
measure the above mentioned network dynamics, we compute three values proposed
in [
The data posting framework [
In this section we consider the task requiring generation user suggestions on the basis of information posted in the Web. In the following example we show how this process can be modelled with smart mapping rules.
Example 1. Suppose to have the description of the user ratings (that we call comments) stored in the relation C(U; N; V) with attributes U (user identi er), N (argument of rating) and V (rating value). Suppose also to have a relation T(U1; U2; L) that represents the trust level L of user U2 for the user U1.
In order to suggest to the user some \relevant" arguments we can set the following criterion: \An argument n is suggested to the user u if the following conditions hold: 1) it is su ciently supported, i.e. it is \supported" by at least 20 users whose trust level towards u is greater than 70%; 2) if di erent comments corresponding to the same argument are su ciently supported, only one can be selected, with the greater level of support". In this case, the choice of the comment has to take into account two di erent needs: 1) deciding if the argument has to be suggested to the user; 2) selecting the rating value for this argument.
This scenario can be modeled as follows: { C and T are source relations; { Add(U; N; V) is target relation, specifying the comments to be suggested to U ; { the smart mapping rule is reported below:
C(u2; n; v) ^ T(u1; u2; l) ^ l > 0; 70 u2;20;hv;unique^maxi ! Add(u1; n; v) Intuitively, the body of the rule allows us to restrict the attention to the users whose trust level towards u1 is greater than 70%, the selection criterion has been synthesized on the arrow, indicating 1) the support variable u2, 2) the minimum quantity 20 of support instances to be able to map, and 3) the variable v whose value should be chosen from the set of candidate values following the indication unique ^ max.
More formally, a smart mapping rule has the form 8z[ S (z) y;k;hv;f!i r(x; v) ]; where x; y; z; v are vectors of variables, such that x [ y [ v z and x, y and v do not share the variables; S is the conjunction of source relations and expressions involving comparison operators (>; <; ; ; =; 6=) and variables in z or constants; r is a target relation; y is called a support vector ; k is a natural number (greater than 0) which indicates the support value; the pair hv; f i indicates how the choice for the values of v should be performed: f can be max, unique, the conjunction unique ^ max, or empty.
We assume that each target relation can be de ned by only one smart mapping rule. The smart mapping rule speci es that the tuple hX; Vi is added to r only if it is supported by at least k (di erent) initializations fY1; :::Ykg of y , i.e. for each j 2 [1::k] there exists an initialization Zj of z, that maps x, y e v in X, Yj and V respectively, and that makes true S (Zj). In the case than no further indications of choice are speci ed (the third arrow label is hv; i) all the tuples supported by at least k (di erent) initializations of y are added to r. Otherwise, the set of tuples to be added is further reduced using f content for the selection of values in v.
The hv; uniquei constraints speci es that the r relation must obey the functional dependency x ! v, i.e. for each assignment of values in x the assignment of values in v must be unique. In the case that several tuples are supported by at least k (di erent) initializations of y and they have the same values in x, the choice can be made arbitrarily.
The indication hv; maxi speci es that, for each X only tuples supported by a maximum number of initializations of y must be selected. It is easy to see that this indication does not guarantee the uniqueness of the choice. For example, it is possible that two tuples hX; V1i and hX; V2i have the same degree of support corresponding to the maximum value.
The indication hv; unique ^ maxi speci es that, xed X, only one tuple hX; Vi can be chosen among those supported by a maximum number of (di erent) initializations of y.
The set of smart mapping rule can be translated into the standard data posting constructs by translating every mapping rule as follows. We introduce the unary domain relation D . If f is empty D contains values 1 and 1, otherwise D contains values 1, 0 and 1. We also introduce the target relations A (X; Y; V) and Add (X; V; F lag), where X, Y and V represent vectors of attributes corresponding to the vectors of variables x, y, and v, respectively, while the decision weather to select the pair hx; vi in the target relation r is stored by the attribute F lag: 1 or 0 (not added) and 1 (added). The mapping rules are:
S (z) ! A (x; y; v)
S (z) ^ D (flag) ! Add (x; y; flag) where all the variables are universally quanti ed. Using the domain relation D ensures that only a value among 1, 0 and 1 can be chosen for each initialization of (x; y) in the relation Add .
The set of target count constraints is constructed as follows. 1. We start by adding support constraints, that ensure that the value 1 is assigned to the variable flag i the degree of support of the combination hx; vi does not reach k. First, we add constraint for values 1 and 1. If f is not empty, we also add constraint for value 0:
Add (x; v; 1) ! #(f Y : A (x; Y; v)g) k Add (x; v; 1) ! #(f Y : A (x; Y; v)g) < k Add (x; v; 0) ! #(f Y : A (x; Y; v)g) k 2. When f = unique the uniqueness choice constraint is added:
0 ! #(f V : Add (x; V; 1)g) = 1 This constraint ensures that exactly one initialization of v for each X is selected. 3. When f = max we add (i) the optimization constraint
Add (x; v2; 1); Add (x; v; 0) ! #(fY : A (x; Y; v2)g) #(fY : A (x; Y; v)g) (ii) the choice constraint, ensuring that at least one initialization of v for each X is selected
0 ! #(f V : Add (x; V; 1)g) 1 4. When f = unique ^ max we add the uniqueness choice constraint and the optimization constraint.
The use of the smart mapping rules o ers a notable simpli cation of the
data posting framework. The user and/or designer can construct the selection
criterion focusing only on the a small set of parameters. The selection criteria
modeled by smart mapping rules are the most widespread in practice. The
standardization of their representation allows us also to optimize the implementation
of the data posting process. Smart mapping rules, initially developed for our
application scenario, can be pro table used in di erent contexts. In particular, we
are investigating their application in P2P Deductive Databases [
In this section we describe the evaluation of the user ranking behaviours. We
report the results obtained on a test set of user searches collected for four months
during a research project. We devised for the experimental evaluation an
approach similar to the one presented in [
We provided each user with two di erent options: 1) they can ask for search suggestion or 2) they can suggest search directions on request. At xed time intervals, users may evaluate obtained results (both as consumer and provider of information) by assigning a rank ranging from 0 to 10 to their experience. As we implemented a rewarding strategy, i.e. users pay for targeted suggestions and are paid when they suggest a proper search, the e ectiveness evaluation is crucial as we do not want user to pay for wrong information.
We model our small network interactions by a random graph that is continuously updated as new links among users appear (i.e. new interactions between a pair of users). In order to better understand the information relevant to our goal we leverage two types of analysis: the rst one, referred as cross-sectional (CS), considers only the variation occurring when data are observed while the second one considers each observation as an independent unit, thus it is referred as dynamic (Dyn). In order to be fair and to evaluate the in uence excerpted by users each other, every participant is aware of the other's scores.
The latter results in the need to analyze factors that are endogenous, i.e., those phenomenon that may arise when users know each the rankings of other thus causing the rankings given by user i to be in uenced by other user rankings except i. To this end we measure the values of GNC, LNC and DA. Evaluation. In order to analyze the evolution of user search e ects, we use the following statistics: overall searches number performed by user; keyword total number; mean assigned keyword rank. For the sake of completeness, we use both CS and Dyn analysis combined with clustering (CL) and Metropolis-Hastings (M-H) sampling. The results are shown in Figure 1. For Dyn analysis we compute fteen graphs (one for each week except the rst one) for the CS analysis we have 16 graphs. It is easy to observe that in tables a and b the values obtained for DA are always high since the beginning. It is worth noting that, as we start rewarding users (at week 4), the DA values further increase. More in detail, both for DYn and CS analysis global nonconformity is not a signi cant factor. The values reported for the other two factors are, on the whole, signi cant, but are uniformly smaller in magnitude for dynamic analysis compared to those of the corresponding weeks in the CS analysis and are less precisely estimated (as represented by uniformly greater standard errors). This is because rather than embodying the structure of the whole network, they embody only the structure of changes in the network over the week, thus the only important value to rely on is the weekly changes of values. This means that \instant" social e ects (e.g., friendship reciprocation) have been absorbed into the Week 0 observation, which is not modeled in the dynamic analysis.
Moreover, above mentioned phenomena can be considered as a kind of social \envy": users tend to decrease the scores of other users in order to get more requests for themselves and thus getting more rewards. We note that also LNC value is high while GNC is not impressive: in a sense, users tend to agree on the general topics but not on the speci c ones. Similar observations can be made for all the analysis reported in Tables c and d. As a nal note, we can observe that the results obtained when sampling data by clustering are slightly better. This behaviour can be explained considering that when leveraging cluster approaches, it is more likely to obtain more homogeneous groups (i.e. group of user sharing common interests and features). 5
The impressive amount of data shared on the WEB contains a lot of information regarding user suggestions and searches. In this paper we focus on the e ect of users suggestions on their social environment. We showed how personalized suggestions can be extracted by using smart mapping rules. This kind of rules, initially developed for our application scenario, can be pro table used in di erent contexts. For instance, they allow us to de ne the fragment of data posting framework, where the data posting problem becomes polynomial. We leveraged many interesting mathematical tools to model several psychological and social mechanisms that proved to be e ective in our scenario. We are aware that, with respect to population-scale networks, the networks considered in our experiments are fairly small. However, this aspect does not decrease the validity of our approach as ranking data of the form analyzed here is typically of interest only in speci c networks, that are by nature fairly small. Thus, highly scalable techniques are less compelling in our setting. Nevertheless, computationally scalable estimation is an interesting challenge for future research in this area and we want to address it in next future.