# Social Networks through the Prism of Cognition

Authors: Radosław Michalski; Boleslaw K. Szymanski; Przemysław Kazienko; Christian Lebiere; Omar Lizardo; Marcin Kulisiewicz
Journal: Complexity
 (2021)

---

## Abstract

Human relations are driven by social events—people interact, exchange information, share knowledge and emotions, and gather news from mass media. These events leave traces in human memory, the strength of which depends on cognitive factors such as emotions or attention span. Each trace continuously weakens over time unless another related event activity strengthens it. Here, we introduce a novel cognition-driven social network (CogSNet) model that accounts for cognitive aspects of social perception. The model explicitly represents each social interaction as a trace in human memory with its corresponding dynamics. The strength of the trace is the only measure of the influence that the interactions had on a person. For validation, we apply our model to NetSense data on social interactions among university students. The results show that CogSNet significantly improves the quality of modeling of human interactions in social networks.


---

## Body

## 1. Introduction

There is a fundamental difference between the ways social events are currently represented by network analysts and the way they are perceived and cognitively processed by humans. In the former, the discrete nature of events is retained and the weights of social network edges are updated once per each relevant event. In human memory, by contrast, perception of events changes continuously over time. Moreover, the initial strength of a trace depends on cognitive factors defined by states of mind of participants and specific aspects of their interactions. Decisions about whether to initiate, maintain, or discontinue social relations involve cognitive processes operating on all relevant information stored in memory traces over specific time-scales.To date, however, there are no models that accurately represent the dynamics of social relations strictly through their corresponding traces in human memory. To address this gap, we introduce a novel cognition-driven social network (CogSNet) model that captures impact of human memory on perception of accumulated events and on decisions to form, maintain, or dissolve social relations. The model explicitly represents some of the human memory dynamics, such as the gradual decay of memory traces over time. With suitable data, it can be extended to include additional cognitive aspects, such as individual levels of sensitivity to relevant events, emotions, or distractions during perception of events. Hence, the model is capable of capturing the dynamics of social interactions in natural settings from the cognitive perspective of each participant.To evaluate the empirical performance of the proposed model, we compare model’s results obtained with parameters fitted using behavioral communication event data, to the ground truth perceptual data collected from human participants with regard to their most important relations. The comparisons reveal that the perception of the depth of interactions between people is well captured by the CogSNet model. At any given point in time, the model can compute the current strength of memory traces, including the impact of discrete events creating or reinforcing these traces. The computed state of each social relation (e.g., salient versus decayed) can then be compared against the externalization of cognition in the form of self-reports. The CogSNet model with parameters fitted using recorded event data achieves high accuracy in fitting ground truth data for the NetSense network. This success demonstrates the importance of incorporating cognitive processes and memory dynamics for adequate modeling of the dynamics of social relationships.Memory is considered to be one of the most important components of human cognition. This is especially the case given the necessity to efficiently retrieve large amounts of knowledge and to select information from a noisy environment. Hence, one of the fundamental challenges for cognitive science has been to understand the mechanisms involved in managing information in human memory [1]. The exact details of these mechanisms are difficult to firmly establish since the human brain is a highly complex system featuring strong differences across individuals based on experimental tuning [2]. Yet, there have been significant advances in the direction of developing good quality working models of memory and other core cognitive processes. For example, the ACT-R cognitive architecture does a good job of modeling core features of human declarative memory, successfully replicating a large number of well-known effects. For our purposes, the most important among these empirical regularities are the well-established primacy and recency effects for list memory [3].Limited capacity and the gradual decay of traces in memory over time have been confirmed by many studies analyzing the relationship between time and recall [4–6]. The forgetting mechanism is modeled by a parametric function describing how well a given item will be recalled as a function of time. It appears that humans tend to underestimate the number of events they experience, i.e., they actually forget faster than they think they do [5]. Obviously, any reminiscence of a particular event primed by an external situation allows people to remember the information longer. Yet ultimately, the limited capacity paradigm and the forgetting function are chiefly responsible for controlling the lifetime of such reminiscence in memory [7]. There are relatively many papers within the broader domain of link predictions, but they treat human communication as a series of fixed time widows that reflect neither human cognition nor continuity of forgetting. For example, Reader et al. [8] identified over a dozen of predictive factors quantifying phone communication like time of the last call or frequency of calls within a 4-week period that would enable to forecast persistence of social relationships, i.e., communication, also in the following 4-week period. The influences among culture, cognition, and network thinking are mentioned in [9] but in a very qualitative way, without any hint how to quantify such influence into a model, which is essential for our approach. Some other works also study the problem of recalling the names of their peers in a variety of activities [10–12], but they focus on a detailed analysis of personal attributes differentiating subjects in terms of forgetting, while here we concentrate on the models of forgetting.


## 2. Materials and Methods

The human brain records events as they arrive, but only a small fraction of the incoming information is stored in long-term memory due to its limited capacity. The forgetting mechanism dictates that the chance to recall a given event decreases gradually as we move forward from the time of first exposure [6]. In some sense, it is similar to graph-streaming [13] and feed-based social media network cascades [14] scenarios where incoming events are ordered by their arrival time, but only some of them are kept.Accordingly, the CogSNet model uses aforgetting functionf to account for the decreasing probability of keeping aging of memory traces over time. Forgetting is thus a monotonically nonincreasing function of time with f0=1 and ft≥0 for all t>0. It is defined by three parameters: reinforcement peak0<μ≤1, the forgetting intensityλ (both used in the ACT-R model), and additional third parameter, forgetting threshold0<θ<μ.For clarity, we present here the basic CogSNet model; a more general version is defined in Appendix and Appendix equations (A.1) and (A.2). This model processes an event happening at time t as follows. If the event involves a pair of unconnected nodes i and j, an edge ij linking these nodes is created. This edge is assigned weight wijt equal to the reinforcement peak value μ. Otherwise, if the nodes involved are already connected, the forgetting function f is used to set the weight of the edge connecting these nodes:(1)wijt=μ,ifwijtijft−tij<θ,μ+wijtijft−tij1−μ,otherwise,where tij is the time of the preceding event for this edge. Processing of each event ends with advancing tij to t. Initially, tij and wij0 are set to 0. Equation (1) and limit on value of μ ensure that a weight of any edge is at most 1.The weightwijt of an edge ij between two nodes at any user selected time t is computed as follows. Once all the relevant events up to time t are processed, we simply set wijt=wijtij∗ft−tij. If the result is less than the forgetting threshold θ, wijt is reduced to zero and the edge is removed. A threshold is needed with forgetting functions, such as power and exponential forgetting, that are positive for nonnegative arguments. Otherwise, an edge would get positive weight at creation and would always stay positive; i.e., all created memory traces would never cease to exist. The reinforcement peak μ defines the impact of an event on the weight of the edge relevant to this event. This peak is a global model parameter here. In principle, the peak can be adjusted according to the event or node type to allow for individualized event perception.In Figure1, we compare the CogSNet model with the previous proposals for representing temporal network dynamics. The most common approach for representing social network dynamics is to use interaction sequences [15]. Under this method, each event is time-stamped and the weights are added to the edges connecting nodes involved in this event cf. Figure 1 ((I) and (IIa)). Moreover, a given edge is active (exists) only at a given time t. This is the most granular approach as it is capable of tracking all the events occurring between nodes while preserving the temporal order of events.Figure 1
Various approaches to modeling dynamic networks and edge weighting (relation strengths) for the 4-node network at a given timet: (I) and (IIa) interaction sequence; (IIb) static (time-aggregated) network; (IIc) sliding windows; (IId) incremental network, all events from the beginning time t0 to the current time t are considered, and the frequency of interaction in the period constitutes the frequency-based (FQ) reference; (IIe) network based on n=3 recent events, used for recency-based reference RC; (IIf) cognition-based social network model (CogSNet), introduced here.In contrast, a static binary network representation, as shown in Figure1 (IIb), aggregates all events by making all edges time-independent. Consequently, an edge existing between a pair of nodes corresponds to an event between these nodes occurred at least once in the whole observed period [16]. Such an edge representation throws away information on the temporal ordering of events, making it impossible to study dynamic processes in static networks.The incremental network solution accumulates events only up to the current timet of analysis. The classical approach, used early in [17–19], views a dynamic network as a series of time-ordered sequences of static graphs (see Figure 1 (IIc)). More recently, this method was applied to modeling network and community evolution [20, 21]. The drawback of this approach is that it does not preserve the ordering of interactions within time slices. Applying a simple frequency-based aggregation creates a frequency-based (FQ) metric cf. Figure 1 (IId). Taking into account only a given number of the most recent events leads to the recency-based (RC) model cf. Figure 1 (IIe). Both of these models are used here as baseline models.Figure1 (IIf) shows an example of dynamic social network generated using the CogSNet model. All other social network models presented in Figure 1 ((IIa)–(IIe)) can also be represented by CogSNet by setting appropriate parameter combinations to achieve, as needed, no decay, instant decay, and so forth. In this way, CogSNet can be thought of as a universal generative dynamic model for temporal social networks, encompassing previous approaches as special cases.In general, the forgetting functionfΔt over time interval Δt can be of any type (linear, power, and logarithmic), but here, informed by work in the cognitive psychology of memory [5], we evaluate only two such functions: the exponential function fexp and the power function fpow defined as follows:(2)fexpΔt=e−λΔt,(3)fpowΔt=max1,Δt−λ,where λ denotes the forgetting intensity; typically, λ∈0,1. The use of max in the power function ensures that perception of events that happened less than a time unit ago is not changed by forgetting. The time unit in which the forgetting function is expressed scales the values of the parameters. Our experiments use one hour as the time unit.To simplify optimal parameters search, we aggregate all three parameters into thetrace lifetime L defining the time after which an unreinforced memory trace is forgotten, i.e., is too weak to be recalled. In the model, L is the time over which the forgetting function reduces the edge weight from μ to θ causing the edge to be removed cf. Figure 2. For the exponential forgetting function (equation (2)), trace lifetime Lexp is(4)Lexp=1λlnμθ,while for the power function, the formula is(5)Lpow=μθ1/λ.Figure 2
Dynamics of relations in CogSNet network with exponential and power functions and with parameters set toμ=0.4, θ=0.1, and L=10 days.Please note that according to the CogSNet model the relationship weights belong to rangeθ;1∪0. Edge’s weight value tends to 1 when the node encounters large number of tightly successive contacts. The larger the number of events is and the closer to each other they are, the closer to 1 the weight is.


## 3. Results and Discussion

In this section, we assess the empirical validity of the propose model by estimating the accuracy with which the CogSNet model reproduces the dynamics of social relations in a dynamic social network. Our computational experiments use the NetSense dataset introduced in [22].The data contain 7,096,844 human mobile phone communication events, including both calls and text messages. These are augmented by 578 surveys containing self-reports on top contacts. It is worth underlining that this dataset provides a unique opportunity to evaluate how the communication frequencies are recalled by the study participants because students reported their perception of the frequency—detailed information on how this information has been reported and how data were processed is provided in Appendix.We use this dataset to study the evolution of two coupled social networks of university students. The first is a behavioral network representing interactions between individuals in the form of the records of their mobile calls and text messages. The second one has perceptual edges defined by the personal nominations. These nominations are based on students’ perception of the corresponding relations as one of the top twenty most interacting peers in the surveys administered to participants. These surveys cover the first four semesters of the student’s college experience (beginning of freshman year to the end of the sophomore year). We compare the list of nominations predicted from the CogSNet network model purely from the communication event data with the list of nominations collected in a given survey. Figure3 shows an example of dynamic social network generated from a subset of NetSense data using the CogSNet model.Figure 3
Four-node CogSNet network for the sample of real NetSense data:μ=0.4, θ=0.1, and L=10 days; nodes A, B, C, and D correspond, respectively, to participants with ids 40997, 11360, 10841, and 1232. (a) Relation strengths according to the CogSNet model over 4-month period (one term); (b) network snapshots at four timestamps t1–t4 and at the survey time ts.
(a)(b)For comparison, we also implement three baseline models using the mobile phone communication data. The first is afrequency-based (FQ) model which orders the peers by the number of interactions, regardless of their time order. Under this model, the highest ranking peers whose number equals the number of the nominations listed in the corresponding survey are selected on the basis of their communication frequency. The recency-based (RC) model selects the top interacting peers who for each individual given a number of recent events. Finally, the random sampling (RND) model creates the list by randomly selecting peers from those who are recorded in the history of interactions of a given node. While random baseline can be considered as a simplistic lower bound, the two aforementioned are actually regarded to be state of the art since they express two cognitive phenomena. The recency effect was uncovered by the experiments of Hermann Ebbinghaus on recall. The forgetting curve he proposed is based on studies in [23] and recently confirmed in [24]. In these papers, the authors demonstrate that the learning curve rises the chances for recalling at the beginning and at the end of the contact period, while the chances to recall events are lower in the middle of it. However, as the question in surveys mainly refers to the present, we focused on the recency instead of primacy. The second baseline, frequency-based, is an implementation of scientific results taken from the domain of lexical memory [25]. The authors of this study show that the frequently repeated words are being recalled faster. Unfortunately, to the best of our knowledge, there are no other approaches suitable to be used in similar tasks.To compare the performance of all the models, we use aJaccard metric, equation (C.1), in Appendix, which measures the ratio of the number of nominations produced by the model that are also ground truth nominations listed in the corresponding survey divided by the number of unique nominations on both lists. Due to the nature of the question formulation in the survey, it was impossible to use any approach based on ordering such as Kendall’s or Pearson’s ranks since we had to consider the list as unordered.Figure4 shows the results of this comparison over the range of parameters corresponding to reported values for forgetting of one to 14 weeks. As reported in [26], the ability to recall information about social interactions starts to degrade after about one week. The experiments using NetSense dataset reveal that the performance is the highest when the forgetting of unreinforced memory traces happens after two weeks. The results remain satisfactory for forgetting thresholds as low as one week. With the two-week threshold, the CogSNet model is with either power or exponential forgetting statistically significantly better than any baseline model. In the literature, the power forgetting was found to perform significantly better than the exponential forgetting when a range of parameters was limited [3]. We do not observe such superior performance of power forgetting here. Both functions have similar peak of Jaccard metric, albeit for the different lifetime values.Figure 4
The plot of the Jaccard metric as a function of lifetimeL. The metric measures the overlap between the two sets of peers, one identified by CogSNet and the other listed by students in the survey. These plots are compared to the results achieved by the three baseline models: recency-based with the best results obtained with the number of recent events set to 400, frequency-based, and random. The results are plotted for the CogSNet running with various parameters for (a) exponential and (b) power forgetting functions.
(a)(b)When comparing the results of surveys with the states of the CogSNet network at the times of the surveys, the Jaccard metric is as high as 29.98% for exponential function forL = 3 days. The distant second is recency-based RC model which delivers much lower Jaccard metric of 17.8%. Nevertheless, when looking at relative simplicity of the RC metric, one can also say that it performs quite good—this is due to the fact that primacy and recency effects come into play when listing peers [27].


## 4. Conclusions

The results demonstrate that accounting for event perception and memory dynamics is essential for faithfully modeling the interaction dynamics in social networks. The CogSNet performed statistically significantly better than any of the base temporal models (see Table1 in Appendix). With suitable data, the model can be extended to represent individual sensitivity to events and the impact of emotions and distractions on event perception to further improve modeling quality.Table 1
Numerical and symbolicp values adjusted by Simes–Hochberg step-up method of nonparametric pairwise post hoc Nemenyi test comparing values of Jaccard metric for results obtained by each method with parameters fitted using recorded event data with the ground truth based on surveys taken over semesters 1–4.
PowerExponentialRecencyFrequencyRandomPower—∗∗∗∗∗∗∗∗∗∗∗∗Exponential0.0000—∗∗∗∗∗∗∗∗∗Recency0.00000.0000—∗∗∗∗∗∗Frequency0.00000.00000.0000—∗∗∗Random0.00000.00000.00000.0000—These results show how each method in the leftmost column performs versus the method in the first row. The part of table under the diagonal shows numerical values of the test, while the part above the diagonal presentsp values coded as follows: ∗∗∗p<0.00005 represents high confidence in the performance differences between the methods since typically values of p>0.05 are considered indicative of nonsignificance.The dataset on which we operate contains data limited to a relatively small fraction of human social activities. Hence, it cannot be stated that there were no other events happening that could have affected participant memory about others. Examples of such events are face to face interactions, indirect references to someone else, and personal reminiscences about others. In addition, emotions can also play a significant role in these processes, and they can be potentially identified with some confidence from available data [28].As a result, the reinforcement peak value can be adjusted for a given person and for an individual event cf. also equation (A.1) in Appendix. What is observed here is a partial manifestation from human memory. However, even taking into account that the model was built based on a single data source, over 6 million telephone calls and messages among the NetSense study participants, the model fitted with the recorded event data yields results well matching the salience of social contacts over all 578 surveys completed by 184 participants. It is observed that even when using the same values of model parameters for all participants, the results are satisfactory. Nevertheless, this accuracy most likely could have been increased if the parameters had been individually adjusted for each participant. Apart from that, one should remember that the recall task is highly contextual, so the individuals will provide different sets of peers depending on the situation [11, 12].The findings of this work can be also considered as an important building block on how to maintain healthy relationships or how to discover anomalies. For instance, based on the results, it is anticipated that, in order to keep a living relationship with a peer, the contacts should not be sparser than lifetimeL, preferably even more frequent. On the contrary, these findings also demonstrate on how long a grieving period after breaking the relationship could potentially last and how to handle the recovery process afterwards in order to make it effective. Lastly, small modifications making the model closer to ACT-R would enable its use for instance in the case of Alzheimer disease where one could monitor whether the peers recalled by patients are in line with what a CogSNet model generates based on the contacts or visits. If there will be any discrepancy found between the model and observations based on interview, this could be an early sign or disease emerging or becoming more active. Another interesting case would be to see whether the strengths of new links are decaying slower than the old ones.In future work, we plan to extend the model in the directions outlined in Appendix including accounting for distractions during interactions, individualized strength, asymmetric of interactions of significance to participants (e.g., hierarchical relationships), and the impact of forms of interactions and of associated emotions. Hence, the CogSNet model represents an important first step towards modeling social network dynamics through the prism of human cognition. In literature, there are three approaches that are used widely to understand human cognition: cognitive bandwidth (CB), dual-process morality (DPM), and implicit association tests (IAT). In [29], those methods are compared and their common drawback is pointed out—the lack of perspective that takes a cultural background into account. Our approach makes such considerations possible, and we see this challenge as one of the future work directions. Lastly, we would love to see more datasets that are so extensive as the NetSense dataset that could allow us to evaluate our model.



---

*Source: 4963903-2021-01-08.xml*