Using free association networks to extract characteristic patterns of affect dynamics

Abstract

The dynamics of human affect in day-to-day life are an intrinsic part of human behaviour. Yet, it is difficult to observe and objectively measure how affect evolves over time with sufficient resolution. Here, we suggest an approach that combines free association networks with affect mapping, to gain insight into basic patterns of affect dynamics. This approach exploits the established connection in the literature between association networks and behaviour. Using extant rich data, we find consistent patterns of the dynamics of the valence and arousal dimensions of affect. First, we find that the individuals represented by the data tend to feel a constant pull towards an affect-neutral global equilibrium point in the valence–arousal space. The farther the affect is from that point, the stronger the pull. We find that the drift of affect exhibits high inertia, i.e. is slow-changing, but with occasional discontinuous jumps of valence. We further find that, under certain conditions, another metastable equilibrium point emerges on the network, but one which represents a much more negative and agitated state of affect. Finally, we demonstrate how the affect-coded association network can be used to identify useful or harmful trajectories of associative thoughts that otherwise are hard to extract.

1. Introduction

(a). Word association networks as the ‘landscape’ of thought processes

In the extant literature, word association techniques are used extensively as an important tool to gain insight into how people perceive and recall semantic relationships between words and concepts [1,2]. In this approach, human subjects are cued with a certain word and then are asked to consequently report which word comes to mind. The free word associations method is an example of such a technique, which uses words that are cued by other words unaided, i.e. with minimal relevant context [3]. The extant literature demonstrates that the network of word associations [4] is a representation of the ‘landscape’ of the encoded semantic memory and, therefore, is closely related to the individual’s day-to-day decision making and behaviour [5,6]. Consequently, the mapping of associations over a network is, potentially, the mapping of the associative thought processes. For example, there is work that shows that words in the free association network, cluster in groups, i.e. network communities of narrow semantic categories [7,8]. In that case, words which relate to the category of, e.g. animals (sheep, lion), tend to cluster with other words in that category over the network. This property of the structure of the association network is closely related to the way individuals search for information in memory. In [9], it is suggested that this structure enables an efficient cognitive search process that is similar to optimal animal foraging patterns. Other evidence that association network structure is inherently related to thought processes and, therefore, cognitive performance is given by [10], who find that cognitive impairment (e.g. in the case of Alzheimer’s disease) is correlated with a decrease in word-fluency network path lengths and an increase in network clustering. Furthermore, the work in [11] connects the rigidity of thought observed in individuals with Asperger syndrome with the observation that these individuals exhibit a hyper-modular free association network structure, i.e. high network compartmentalization relative to other groups. Another example is given in [12], who find that creativity in individuals correlates significantly with shorter network paths, lower network modularity and, in general, increased small-world properties. The work in [13] further shows that potential search processes over the network differ markedly between subjects that indicate high versus low creativity. In sum, the above examples demonstrate that the structure of the association network may be related, in general, to actual thought processes and behaviour.

One interesting aspect of behaviour, which is attracting increasing attention in the literature, is how affect changes over time, and how this relates to decision making and general behaviour (e.g.[14–24]). Here, we argue that since association networks were shown to be an efficient method to explain aspects of thought processes, they can be a useful tool to investigate affect dynamics, as we describe in what follows.

(b). Words across association networks exhibit varying levels of affect

The dynamics of affect is a topic of increasing interest. There is a developed body of literature which studies affect dynamics using self-reported measures (e.g. [18–24]) and how these relate to behavioural aspects. These measures require subjects to report in real time and are therefore limited in terms of temporal resolution and sample size. Some studies investigate how isolated self-reported affect varies over time [18,20,23], while others use models of a temporal network of coupled emotions [19,22,23] to show how affect dynamics are correlated or even predictive of aspects of well being. The prominent measurement approach in these studies is to use either experience sampling (ESM) or daily diaries, in which subjects report emotional experiences in real time, up to several times a day. Recently, though, in a notable integrative study, [25] have shown that a variety of metrics of these affect dynamics measures add limited prediction of well-being beyond the prediction power of the straightforward affect temporal averages. While this finding raises questions over the usefulness of affect dynamics in the well-being context, it may also be the case that temporal self-reported measures carry limited information for some reason. A potential limitation is the fact that these measures are taken in frequencies that are between hourly and daily, and that sample sizes are limited. Other approaches use physiological methods to approximate affect in real time. These proxies may also be limited in terms of their ability to disentangle between actual affect dynamics [26] or other unrelated physiological phenomena. Here, we suggest that studying association networks is an opportunity to study affect dynamics of the underlying robust landscape of associations in much higher resolution. This follows from the assumption that an association network is a robust expression of how people shift between associations, or between thoughts, in relatively short time scales. Essentially, we expect the association network to be a less noisy measure of thought processes than self-reported real-time sampling. The major down sides of this approach, though, are also noteworthy. First, it is indirect, i.e. it estimates affect indirectly and not by self-report. Second, it also relies on self-report and on the validity of the association network as a credible and stable representation of thought processes and, third, it relies on the extent to which associated words are coupled with actual affect. In that sense, we argue that the associated network approach to affect dynamics is complementary to the extant approaches in studying affect dynamics.

Related to this work is the well-developed text-based sentiment analysis literature. That literature extracts dimensions of sentiment from written texts (e.g.[27] for a review), as opposed to the self-reported association networks we use here. In some cases, advanced affective computing and learning approaches are used to extract emotions [28].

The behavioural literature shows that exposure to words may induce or trigger affect changes in individuals. For example, a common approach of inducing mood or affect is the use of priming, i.e. exposing a subject to an affect-related text [29–31]. We argue that affect levels may change as individuals move between certain associations on the association network. For example, assume a scenario in which an individual is exposed to or primed with the word ‘death.’ In this case, and given the literature, one may assume that either this exposure will induce some level of negative affect, or that the reason this word came to mind is that the person is already in a negative affect state. In both scenarios, activation of negative-affect words in the network is likely correlated with being in a negative affect state. In another scenario, suppose that a researcher observes an individual going through the following chain of word associations: ‘happy’, ‘joy’, ‘party’, ‘good.’ In this case, the researcher may deduce that there is some likelihood that the individual is in a positive-affect state. For example, Nelson et al. [32] show that when primed with certain words, groups of individuals independently agreed that these words triggered a certain affect. This consensus held across a variety of affect types and words. Therefore, we propose to model this probability of a correlation between affect-related words and actual affect states. Knowledge of transition probabilities between words across an association network and the affect levels assigned to words on the network may be used to extract knowledge of how affect tends to change over time.

(c). Using affect-coded association networks to uncover characteristic affect dynamics

In order to construct an association network and the affect levels’ mapping of its nodes, we exploit the existence of relatively extensive free association network data composed of 5018 words coded by a group of more than 6000 people [32]. To map the affect levels associated with each word in this network, we use a second dataset of nearly 14 000 English words coded for several dimensions of affect by a total of 1827 people [33]. For simplicity, we focus mainly on the two most commonly researched dimensions of affect: valence and arousal. Valence is defined as the measure of the level of pleasantness, from very unpleasant to very pleasant, in other words, from a very negative feeling to a very positive one. Arousal is the measure of the level of energy of the affect. For example, the word ‘depression’ and the word ‘anger’ both receive low valence ratings, but differ in terms of arousal ratings. The former receives a low arousal score by human coders, while the latter receives a high score. The combination of these datasets provides a word association network, but one in which each word is coded for both valence and arousal—effectively a representative of the type of feelings a group of people experiences when exposed to these words.

The affect-coded association network allows us to investigate how affect levels are distributed across the network of the group of people that produced it. We argue that it is possible to use it to analyse the natural tendency of this group to exhibit specific affect dynamics patterns. For example, it is interesting to see whether the distribution of affect across the network is clustered into negative or positive regions versus just spread out randomly. This has the potential to affect the manner in which an individual transitions between affect states as they move from thinking about one association to the next. In that sense, it is interesting to see how volatile the change is of affect over time, or whether affect changes more slowly, as if changing with inertia. To gain insight into this, we investigated the distribution of affect changes between words via links on the network. Another interesting aspect of the affect-coded association network is the general shape of the affect drift across the network. This drift may be a representation of the average ‘pull’ towards negative or positive associations. Moreover, if a consistent affect drift does exist, is there a specific equilibrium point of affect level that an individual is drawn to, or does affect never converge to a certain level? These types of insights may help reveal fundamental patterns of the dynamics of affect, as captured by the association network.

To further demonstrate the usefulness of the suggested approach, we also show how more local-level analyses of the network structure may further reveal interesting patterns of affect evolution over time. For example, it is interesting to find where the most extreme negative and positive points of affect exist in the network. If one ignores network structure, single words like ‘murder’, ‘torture’, and ‘abuse’ seem to provoke the most negative experiences. However, when the structure of the network environment is taken into consideration, it turns out that the most negative environments revolve around words pertaining to long-term discomfort, e.g.‘headache’ and ‘lost’. We also demonstrate how it is possible to activate, or prime, certain network trajectories so that an individual will spontaneously think of certain target words. Using knowledge of the network structure this way, we show that it may possible to indirectly prime a certain affect. Finally, we also explore a more intricate activation model in which the actual thought process depends on a state of affect. In this case, we find that because individuals will tend to jump to words which better match their current mood, they will be under a higher risk of being ‘stuck’ in a negative state of affect. The suggested approach may be used to identify and perhaps anticipate these network ‘traps’ of affect dynamics.

The rest of the paper is structured in the following manner. In §2, we describe the data. Section 3 reviews the methods and results, and in §4, we list the conclusions, limitations of this work, and suggestions for future directions.

2. Data

The data we used to construct the affect-coded association network is a combination of two publicly available datasets. It is important to note here that the suggested approach is intended for use with any reliable data which includes both the association network and word properties, e.g. in our case—valence and arousal levels. As long as the data faithfully represent people’s tendencies for specific word associations and the affect related to these words, the method should be useful. Here, to provide a meaningful demonstration of the approach, we have chosen relatively extensive and rich datasets which are frequently used in the extant literature, but were not previously combined for this purpose. As detailed below, these data have some limitations, but we argue and demonstrate that given realistic expectations, interesting insights can be extracted from them.

The first dataset is the University of South Florida Free Association, Rhyme, and Word Fragment Norms data base [32]. This highly cited dataset is a collection of 5018 words coded by more than 6000 human coders, including nearly three-quarters of a million responses. Coders were cued by the words included in the database, and the frequencies of their responses were registered. The authors of the database define what they call ‘forward strength’ between cued word i and response word j as the ratio between the number of people who responded with word j, divided by the number of people who were exposed to word i. For example, out of the 148 coders who were exposed to the word ‘depressed’, 78, i.e. about 53%, responded with the word ‘sad.’ This measure, essentially, is a measure of the probability of transition, i.e. the association between word i and word j. A limitation here is that only links between words that are within the 5018 words that were studied are given. Even though this network is one of the most extensive association networks measured, on average, the data cover 82% of the outgoing links per each word. In this respect, our investigation focuses on the sub-network of the major word-to-word transitions. Of course, in the general case, if available, the complete word association network should be used.

The second dataset is a reservoir of 13 915 words coded by individuals for several dimensions of affect [33]. Coders were asked to code words using a numeric scale according to the way that they felt when they were exposed to that word. For the purpose of testing our approach, we focused on the two most investigated dimensions of affect: valence and arousal (see [34,35]). Valence, in this case, is a measure between pleasantness and unpleasantness, between happy and unhappy, or between positive and negative feelings. Arousal is a measure of calmness ranging from highly excited to very calm. Both dimensions were rated on a discrete scale of 1 to 9 and, for each word, a mean and standard deviation of the coder ratings is given in the data. For both datasets, reliability was ascertained in several ways including checks versus other data and internal checks [33]. In terms of overlap between datasets, fortunately, the coverage of words coded for their triggered affect across the association data is rather good. Out of the 5018 words, 4356 (87%) have their corresponding valence and arousal coding. In order to try to conserve the most information contained in the data, we use all 5018 words in the network analysis, but take into account the fact that we do not have the affect coding for 13% of them.

The basic descriptive statistics of both datasets are shown in table 1. The statistics for the affect norms dataset are calculated only for words that exist in both sets. The table shows that the average word valence score (5.33) is a bit above the numeric middle point of the scale (5) and that the average word arousal score (4.16) falls somewhat below the middle point of the scale (5). Below, in §3c, we provide some examples of words with their corresponding affect. The in-degree distribution shows signs of relatively heavy tails, given that the average degree is 12.7, but the standard deviation is high and the maximum degree is 324. The average in- and out-degree are equal because each link is counted in both cases. Other aspects of the network structure are explored in more detail in other works, e.g. [36].

Table 1.

Descriptive statistics for the Free Word Association Data.

	n. obs.	mean	s.d.	max	min
affect-related properties
avg. word valence score	4356	5.33	1.33	8.53	1.40
avg. word arousal score	4356	4.16	0.93	7.74	1.6
network properties
degree (in)	5018	12.7	20.9	324	0
degree (out)	5018	12.7	4.5	33	1
clustering coeff.	5018	0.19	0.08	1	0
closeness cent.	5018	1.15×10−6	1.53×10−9	1.17×10−6	1.14×10−6
betweenness cent. (normalized)	5018	8.12×10−4	14.51×10−4	20.35×10−3	0

3. Analysis and results

(a). Result I: how affect changes across single network links

We now take a closer look at the structure of the network and how affect is distributed across it. The assumption is that a transition between two words on the network is a transition in the valence and arousal values from the origin word to the target word. This stems from findings in the literature that show that a recalled word may have an effect on the affect state of the individual [30,37]. In §3d, we relax this assumption and use a probabilistic model of the affect effect of words. In terms of affect change patterns, the question of whether affect changes exhibit inertia, i.e. change smoothly or discontinuously, is the first question we attempt to answer.

Starting with valence, in figure 1, we plot the mean probability of one-step changes, or jumps in valence, between two words in the network as a function of the valence’s jump magnitude. For example, a jump between words that constitutes a decrease of two valence rating points (−2 on the x-axis) occurs, on average, 6% of the time. On the other hand, a jump of +4 valence rating points occurs about 5% of the time. Red error bars, in the figure around the main curve, mark the standard error around the mean. To visualize the negative-versus-positive horizontal asymmetry in the graph, a grey dashed line is added to demarcate the horizontal reflection of the black solid line. That is, the grey line is the mirror reflection of the black line.

Figure 1.

A plot of the mean probability of valence changes between linked words on the association network, as a function of the magnitude of valence change (black curve). For clarity of visualization, the black curve was smoothed by 0.6 valence points (x-axis). The red bars denote the standard error around the mean. The dashed grey line is the mirror image of the black curve, provided to visualize the horizontal asymmetry. (Online version in colour.)

(i). Valence changes either smoothly or with high jumps

Using figure 1, we can deduce the following observations. First, it seems that both very small and very large jumps in valence are the most probable. Small jumps are the hallmark in stability of affect dynamics. The high correlation between words’ affect on the network may also be related to the inherent categorical similarity between adjacent words. This is consistent with the documented categorical structure of association networks in the literature [8]. On the other hand, very large jumps are also frequent. These large jumps likely allow the jumps between valence categories. For example, the most likely transition from the word ‘sad’ is to the word ‘happy’ (63% likelihood), which is in the same category in terms of word type, but in the opposite category in terms of valence. However, not all of the high valence jumps are between word opposites. For example, the transition from the word ‘cake’ (valence 7.6) to the word ‘fat’ (valence 2.7) is a jump of almost five rating points. Similar big valence jumps between words that are not opposites are, between ‘child’ and ‘brat’ or ‘boyfriend’ and ‘jerk’, among many examples. We conclude, therefore, that affect dynamics alternate between two regimes of change: (1) a smooth change of valence which mostly happens in small increments (≈2 rating points and below), and (2) a discontinuous-like regime in which high jumps between valence states are more likely (≈4 rating points and above).

Another striking feature in figure 1 is the asymmetry between the negative and positive valence jumps, as can be seen by inspecting the differences between the grey dashed line and black line. The grey dashed line in the figure is the horizontal mirror image of the main graph (black curve) around the y-axis. Differences between these two lines accentuate the horizontal asymmetry. If the black curve would have been perfectly symmetrical around the y-axis, the grey dashed line would lie directly on it. In the case of figure 1, the grey dashed line deviates from the black curve, therefore, showing that the black curve is horizontally asymmetrical. Specifically, the figure shows that for medium-level jumps (i.e. jumps of magnitude ≈4 rating points and below), negative jumps are more likely to occur than positive jumps. In essence, this suggests a negative drift of the thought process. As will be explored in the following section, it turns out that while average drift is negative, it does depend on network location and valence levels.

(ii). Arousal changes relatively smoothly

Figure 2 is similar to figure 1, but is calculated for the case of arousal. There is a stark difference between the two graphs. Here, it seems that there is only one type of trend: the smaller the magnitude of the word-to-word jump of arousal, the more likely it is. This is true apart from the relatively small bumps around the ±4 points on the x-axis. The general picture in the case for arousal then is that, during an association process, smaller changes in arousal level are preferred. For example, the probability of remaining within the same level of arousal (up to a resolution of about 0.06 magnitude of change, in the center of the graph in figure 2) is around 1.7 times higher than the probability of moving five rating points on the arousal scale. This pattern suggests that arousal exhibits high inertia, i.e. extreme changes in it are more rare, perhaps because they are more physiologically costly. In terms of asymmetry, it is also noticeable that there is a preference for negative, over positive, arousal change. This suggests that there is a tendency for individuals to move towards calmer, lower arousal states. In the following section, we dig deeper into characteristic drifts and trajectories across the association network and affect states.

Figure 2.

A plot of the mean probability of arousal changes between linked words on the association network, as a function of the magnitude of arousal change (black curve). For clarity of visualization, the black curve was smoothed by 0.6 valence points (x-axis). The red bars denote the standard error around the mean. The dashed grey line is the mirror image of the black curve provided to visualize the horizontal asymmetry. (Online version in colour.)

(b). Result II: characteristic trajectories of affect across the network

The transition probabilities between words in the network shape the characteristic trajectories of the association process. These trajectories dictate how affect potentially changes over time and, therefore, they should be closely related with characteristic affect dynamics patterns. Similar to [13], who studied possible word search processes over association networks, we used probability-weighted random walk models. In our case, we weighted the random walks using the measured empirical transition probabilities between words. Specifically, we wished to focus on how valence and arousal change across network trajectories as a function of an initial starting point word.

(i). Valence converges towards a neutral equilibrium point

Figure 3 is an illustration of characteristic trajectories of valence, beginning from various valence levels. The figure represents the results of weighted random walk simulations, limited to 20 steps of the walk from the starting seed word (x-axis). Each random walk is simulated with the option of back-stepping, i.e.with the option for the process to retrace its steps. A random walk process starts initially with a given word in the network. The process is then simulated from that word onward, using the transition probabilities of the association network data.

Figure 3.

A plot of the characteristic trajectories of valence of weighted random walk processes, of 20 steps, over the association network, as a function of their initial valence value. Seed words were divided into nine bins of valence (see legend) and then, per each step (x-axis), the mean valence was plotted. Each coloured line represents each bin, i.e. processes beginning with words within the bin. The black dashed line denotes the steady-state value (i.e. value of all processes reached after 100 steps). The grey line denotes the mean valence value across all words. (Online version in colour.)

In figure 3, the x-axis denotes the number of word-to-word jumps of the simulated process, starting from the initial seed word. In order to study the relationship between the seed word’s valence and the valence trajectory, we partitioned the seed words into nine bins—from very negative to very positive. The nine curves in the figure correspond to the nine seed word bins (see the legend of figure 3). Each curve represents the change in valence as the random walk processes evolve, starting from a certain range of valence values. The y-axis represents the valence value at the n-th step of the process (x-axis), averaged across all processes starting from the corresponding group of seed words. For example, the top yellow curve illustrates the mean valence for each of the 20 steps of random walk processes that begin with seed words of valence in the range of 8.5–9.5. The bottom red curve, on the other hand, represents processes which started with seed words in the valence range of 0.5–1.5. The top yellow curve’s value at Step 1 is 8.5 rating points, but it drops to 7.1 rating points in the second step. For each word, in each of the nine bins, we performed 100 simulated processes for a total of more than 500 000. For the sake of comparison, we calculated the valence value for which the simulated process converges and reaches a steady state. The horizontal dashed black line in the figure marks the steady-state valence value. Essentially, in order to assure we measure full convergence, the steady-state value was taken to be the mean value of valence that the random walk reached after 100 random walk simulated steps. As can be seen in the figure, all curves converge towards that line. Another interesting comparison is the global mean valence across all words in the network, for which the valence is known. This value (valence value of 5.3), denoted by the grey dashed line, is the potential steady-state value in the case where all words were sampled equally.

One major feature in figure 3 is that all curves converge towards a certain steady-state valence value (again, marked by the black dashed horizontal line) after 20 weighted random walk steps. Notably, the steady-state valence level is higher (5.7) than the global overall average (grey dashed line, 5.3) of valence across all words. This suggests that all weighted random walk thought processes converge to a sub-network which, on average, is more positive than the whole network. In essence, this sub-network seems to be the ‘resting state’ or equilibrium sub-network for any thought process starting at any part in the network. In terms of behaviour, the interpretation here is that any associative thought processes in the network constantly drift towards a neutral state of valence. Furthermore, it seems that the convergence is slower, the farther away the starting point is from the equilibrium point. This suggests that the network exhibits local neighbourhoods in which valence is predominantly negative or positive, consistent with the findings in the previous section in which valence was found to change smoothly a considerable part of the time.

The convergence pattern of valence in the figure is reminiscent of an exponential-like decay in which the speed of convergence is proportional to the ‘distance’ from the convergence point, similar, e.g. to a critically-damped oscillator. The farther the system is from the convergence point, the faster it advances towards that point. Conversely, the closer it gets to the convergence point, the slower the convergence becomes. A highly simplified analogy can be made using a differential-equation like relationship in the spirit of dx(t)/dt ∝ −x(t) in which the solution is a decaying exponent with the time scale represented by the proportion constant. In behavioural terms, this suggests that when experiencing an extreme valence, an individual will feel a stronger pull towards the resting state than if the valence only weakly deviates from the resting point.

(ii). Arousal converges towards a relatively calm state

In the case of arousal, figure 4 shows a similar pattern, except that the equilibrium sub-network (black dashed line) is skewed towards lower values of arousal at 4.3 rating points. Here, too, there is a similar decay pattern in which the rate of convergence is proportional to the distance from the equilibrium point. In this case, the equilibrium point for arousal is below the middle of the rating scale, but, as with valence, higher than the overall average of arousal across all words (grey dashed line). This can be seen in the difference between the grey dashed line, which represents the global arousal average, and the common convergence point of the simulated random walk curves. Similar to the case of valence, in terms of behaviour, the higher the deviation from the resting state, the stronger the pull towards equilibrium.

Figure 4.

A plot of the characteristic trajectories of arousal of weighted random walk processes, of 20 steps, over the association network, as a function of their initial arousal value. Seed words were divided into nine bins of arousal (see legend) and then, per each step (x-axis), the mean arousal was plotted. Each coloured line represents each bin, i.e. processes beginning with words within the bin. The black dashed line denotes the steady-state value (i.e. value of all processes reached after 100 steps). The grey line denotes the mean valence value across all words. (Online version in colour.)

The convergence patterns shown for both valence and arousal most likely stem from the specific association network structure and specific relations between words and affect. In electronic supplementary material, S1, we show the convergence patterns for both (1) a randomly permuted network and (2) random permutations of the word–affect relations. In both cases, it seems that the convergence patterns disappear, implying that these patterns stem directly from the specific network structure and the word–affect relations rather than simply the distribution of words and affect.

(iii). Pressure and flow dynamics in the joint valence–arousal space

To illustrate the integrated picture of affect dynamics, we calculated the vector field of flow in the joint two-dimensional space of valence and arousal. The valence–arousal vector field, illustrated in figure 5, represents the expectation of the change of valence and arousal across points in that space. To calculate the vector field, the valence–arousal space was partitioned into square bins, each the size of a quarter of a rating point. The expected change in valence and arousal, per each bin, was estimated using the transition probabilities between words in the network. In terms of behaviour, this vector field is the illustration of the average drift of affect within the valence–arousal space. Another possible interpretation is that the vector field represents the effective force which individuals ‘feel’ as they move between word associations.

Figure 5.

A representation of the two-dimensional (valence–arousal) vector field. The valence–arousal space was divided into square bins of 0.25 sides. Each arrow in the figure corresponds to the average change of valence and arousal, in that bin. Per each bin, all the outgoing links of words with valence and arousal values corresponding to that bin, were used to calculate the average. The length of an arrow codes the magnitude of the average change per each bin. To improve the visualization we also code the magnitude using colour—the closer the colour to red, the higher the magnitude of average jump within a bin. (Online version in colour.)

Consistent with figures 3 and 4, in figure 5, it is possible to see the global convergence point in the valence–arousal space. The flow field almost uniformly points towards the equilibrium point, which exhibits a valence value of about 5.7 and arousal of 4.3. Words in this region of the valence–arousal space are relatively affect-neutral words like: ‘big’, ‘component’, ‘characteristic’, ‘flask’, ‘sponge’, etc. Also, as described previously, it seems that the further away they are from the convergence point, the stronger the drift forces are.

It is important to note here that the illustrated valence–arousal vector field is the average field. The actual random walk process is subject to stochastic forces and so moves within an equilibrium sub-network. The average values of valence and arousal within that sub-network, are those which correspond to the convergence point. In §3d, we explore how these patterns change if the random walk process depends on valence, i.e. movement between associated words is affected by the mood state of the individual. Furthermore, to test the scope and applicability of the method, in the electronic supplementary material, we perform the same range of analyses of convergence and affect dynamics but on a text semantic network dataset (Moby Thesaurus II). Interestingly, we find similar results with the semantic data except for some differences. A more detailed discussion is given in electronic supplementary material, S2.

(c). Result III: two examples of the uses of a local-level association network analysis

In what follows, we provide two examples in which association network analysis provides insight into affect dynamics. The first example is used to show that in order to gauge the longer-term affect effect of words on individuals, it is critical to take the local network environment into account. The second example demonstrates how network trajectories’ analysis may be useful when trying to maximize affect influence.

(i). Affect influence of words: the importance of network environment

Within the study of the affect landscape of the association network, it is interesting to study which words in the network harbour the most extreme potential influence on valence and arousal levels. One approach is to study the coded affect of single words. Table 2 lists the five words coded for highest and lowest values of valence and arousal, across the network.

Table 2.

Top and bottom five words of valence and arousal values for single words.

word	mean	word	mean
valence top and bottom five-word list
vacation	8.53	suicide	1.58
happiness	8.48	rape	1.54
happy	8.47	abuse	1.53
Christmas	8.37	murder	1.48
fun	8.37	torture	1.40
arousal top and bottom five-word list
gun	7.74	scene	1.95
sex	7.60	quiet	1.95
lover	7.45	dull	1.67
Tornado	7.45	calm	1.67
nuclear	7.30	grain	1.60

It seems, from the table, that people associate the highest levels of positive affect with joyful experiences. Conversely, people associate the lowest valence with highly violent and, potentially life-threatening events. In terms of arousal, it seems that concepts which are associated with extreme violence, conflict, disaster situations, and sex rank the highest on arousal. Concepts related to more serene contexts are ranked very low. While these are interesting insights in the context of a single-word view, it is also interesting to acknowledge that, over time, thoughts are not expected to be static and to dwell on a single word. Thoughts are assumed to move from association to association. So, it may be more realistic to investigate the affect effect of word environments, rather than the effect of isolated single words. In order to do so, we inspected the average valence of each word’s network environment. Per each focal word, we defined its environment to be all words visited around it, via a random walk process stemming from that focal word to within ten random walk steps. We varied the number of steps we used, effectively varying the random walk radius, and found that it does not change the results qualitatively. The valence, or arousal rank per each focal word’s network environment, is taken to be the average valence of all words visited in the 10-step vicinity of the focal word. The formal expression for the environment valence and arousal of a focal word i is

$$V_{i,e}=\sum _{j=1}^{M_e}{\zeta }_j\cdot v_j$$ 3.1

and

$$A_{i,e}=\sum _{j=1}^{M_e}{\zeta }_j\cdot a_j$$ 3.2

Expression (3.1) is the weighted average of the simulated random walk process. In (3.1), v_j is the valence value of word j. The number of words within the e step environment is denoted by M_e. The degeneracy, or weight, of word j is denoted by ζ_j and is the fraction of the time the random walk process spends on word j starting from word i, given that the process exhibits e random walk steps. We also define the equivalent arousal environment quantity, A_i,e, in (3.2). As noted above, for robustness, we varied the size of the environment (e) for environments in the range other than 10 and found that, qualitatively, the results remained similar.

Table 3 lists the five words for which V_i,e=10 and A_i,e=10 are ranked as highest and lowest.

Table 3.

Top and bottom words of valence and arousal 10-step environment values.

word	mean	word	mean
valence 10-step environment Vi,e=10 top and bottom five-word list
sad	6.92	found	3.49
mom	6.85	ouch	3.60
father	6.82	lost	3.67
wife	6.78	migraine	3.68
husband	6.75	headache	3.82
arousal 10-step environment Ai,e=10 top and bottom five-word list
pistol	5.57	east	3.22
rifle	5.52	west	3.24
weapon	5.45	south	3.26
shoot	5.43	north	3.31
trigger	5.40	table	3.47

Table 3 lists the five words for which V_i,e=10 and A_i,e=10 are ranked as highest and lowest. Also, to gain a better understanding of the actual 10-step environment of each word in table 3, we list, per each word, the ten most frequent words within its 10-step network environment. For the V_i,e=10 words of table 3, we show the environment words in table 4, and for A_i,e=10, in table 5. These tables will help us gain insight into the composition of network environments.

Table 4.

Top 10 words occurring in the 10-step environment of top/bottom valence seed words of table 3^**.

dad	mom	father	wife	husband	found	ouch	lost	migraine	headache
mom (25%)	dad (25.3%)	mother (14.4%)	husband (26.5%)	wife (33.1%)	lost (61.1%)	hurt (11%)	found (57.9%)	hurt (11.8%)	pain (10%)
father (15%)	mother (12.6%)	son (13.6%)	woman (8.5%)	man (6.6%)	lose (4.6%)	pain (8.5%)	find (4.4%)	pain (7.3%)	hurt (7%)
hate (4.3%)	love (6.3%)	girl (5.9%)	wife (5.2%)	girl (5.9%)	found (3.6%)	sad (3.2%)	cat (3.4%)	sad (2.6%)	sick (2.7%)
love (3.3%)	man (2.6%)	man (5.2%)	boy (4.9%)	husband (3.7%)	dog (3.5%)	happy (2.8%)	lost (2.8%)	back (2.1%)	sad (2%)
woman (3.3%)	girl (2.5%)	mom (4.6%)	mother (4.2%)	love (3.6%)	happy (2.6%)	back (1.5%)	sad (2.5%)	cry (1.9%)	cut (1.9%)
daughter (2.7%)	hate (2.0%)	love (3.6%)	love (3.2%)	father (3.1%)	mouse (1.1%)	cold (1.3%)	gone (2.1%)	happy (1.7%)	happy (1.9%)
boy (2.4%)	mom (1.8%)	hate (3.1%)	girl (2.8%)	hate (2.0%)	sad (0.9%)	sick (1.3%)	missing (1.3%)	cold (1.5%)	cry (1.6%)
dad (2.4%)	like (1.7%)	father (2.7%)	hate (2.4%)	woman (1.6%)	look (0.7%)	front (1.2%)	right (1.1%)	Ill (1.5%)	cold (1.5%)
happy (1.4%)	friend (1.6%)	son (2.6%)	spouse (2.1%)	boy (1.5%)	gone (0.6%)	cry (1.1%)	see (0.8%)	sick (1.5%)	ouch (1.3%)
mother (1.4%)	sad (1.6%)	boy (1.6%)	man (2.0%)	female (1.5%)	keep (0.6%)	good (1.1%)	smile (0.6%)	cut (1.4%)	bad (1.1%)

^**The number in parenthesis is the frequency of appearance of each word within the 10-step environment random walk simulations.

Table 5.

Top 10 words occurring in the 10-step environment of top/bottom arousal seed words of table 3^**.

pistol	rifle	weapon	shoot	trigger	east	west	south	north	table
death (3%)	kill (2.8%)	good (2.7%)	sad (2.6%)	happy (2.7%)	west (35.9%)	east (32.5%)	north (19.5%)	south (20.8%)	down (6.3%)
gun (2.8%)	good (2.4%)	death (2.3%)	death (2.5%)	gun (2.2%)	south (7.5%)	north (7.1%)	west (13%)	east (12.2%)	chair (5.7%)
kill (2.5%)	gun (2.4%)	happy (2.3%)	kill (2.5%)	death (2.1%)	east (1.9%)	California (1.9%)	down (4.4%)	up (3.7%)	stand (2.8%)
life (2.2%)	sad (2.3%)	sad (2.3%)	good (2.2%)	pain (2.1%)	slow (1.8%)	cowboy (1.9%)	Florida (2.6%)	cold (3.5%)	table (2.1%)
pain (2.2%)	death (2%)	kill (2.2%)	bad (2%)	kill (1.9%)	cold (1.3%)	wild (1.6%)	hot (2.3%)	hot (1.6%)	sleep (2%)
sad (2%)	murder (1.9%)	pain (2%)	gun (2%)	die (1.8%)	crazy (1.3%)	down (1.4%)	house (1.4%)	pole (1.5%)	up (1.8%)
good (1.8%)	cold (1.7%)	cold (1.7%)	happy (2%)	sad (1.8%)	sun (1.3%)	west (1.3%)	high (1.2%)	low (1.1%)	sit (1.6%)
hurt (1.6%)	dead (1.6%)	bad (1.4%)	life (1.7%)	murder (1.7%)	up (1.3%)	cat (1.2%)	border (1.1%)	state (1.1%)	high (1.1%)
live (1.5%)	hurt (1.4%)	hate (1.4%)	cold (1.6%)	good (1.6%)	coast (1.3%)	direction (1%)	city (1.1%)	sun (1.1%)	soft (1.1%)
happy (1.4%)	destroy (1.3%)	dead (1.3%)	pain (1.5%)	cold (1.5%)	dog (0.9%)	south (0.9%)	night (1.0%)	light (1%)	drink (1%)

^**The number in parenthesis is the frequency of appearance of each word within the 10-step environment random walk simulations.

It is interesting to contrast the results in table 3 with those for single words in table 2. In table 3, it seems that, in contrast to the single-word case, the top positive valence words are mainly family-related concepts. Consequently, this approach suggests that while positive experiences rank very high in terms of valence (table 2), when taking a word’s environment into account, family-oriented concepts may be related to a longer-lasting and more robust expression of positive affect. In terms of structure, this means that family-oriented words are connected within a cluster of positive words in the network. The five leftmost columns in table 4 show that family-related words are connected very strongly among themselves, but also predominantly to other positive concepts such as ‘love’ and ‘happy’. Since all these words rank high in valence, their effective network environment is also highly positive.

At the negative end of the spectrum, while extremely violent events trigger very low valence (table 2), longer-lasting low valence (table 2) is mainly associated with pain, headaches, and words related to the feeling of loss or sickness (see the five rightmost columns in table 4).

In the case of high arousal environments (table 2), it seems that concepts related to violence and conflict (e.g. pistol and shoot) lead to longer-lasting high arousal mainly associated with weapons, pain, death and polarized emotions (e.g. happiness and sadness), as the five leftmost columns in table 5 show. In this case, sex-related and disaster-related concepts only seem to be associated with a more short-term increase of arousal (table 2).

The picture for lowest-ranked arousal environments shows that these are dominated by words for cardinal directions (east, west, south and north) and the word ‘table’. The five rightmost columns in table 5 seem to suggest that the cardinal direction words are highly clustered within themselves. Therefore, these four words construct a well-knit and relatively closed cluster. Given that their arousal values are low and range between 2.5 (east) and 3.5 (south), it is understandable why their network environments exhibit very low arousal. On the other hand, the word ‘table’, as the rightmost column in table 5 shows, is associated mostly with low-key, passive activities like ‘down’, ‘chair’, ‘sleep’, ‘sit’ and others. Consistent with this is the fact that the next words on the list of lowest network environment words (sixth to tenth place) in terms of A_i,e=10 (not shown here) are: ‘chair’, ‘seat’, ‘circle’, ‘arm’ and ‘recliner’.

In sum, the association network, coupled with the mapping of affect over it, seems to allow differentiation between short-term and deeper, longer-term affective experiences. For the purpose of broadening the scope, we provide in the electronic supplementary material, a similar analysis of a word network environment, but for a text semantic dataset. Interestingly, the results exhibit similar patterns (see electronic supplementary material, S2.5 for a more detailed discussion).

(ii). Using the network to maximize indirect influence

Priming is the action of exposing a subject to a certain concept or stimulus [38]. In the affect behavioural context, priming may be used to affect a subject’s awareness of that stimulus, e.g. to improve the subject’s mood, to induce positive thoughts, or in general, to affect valence and arousal (e.g. [39–42]). But, in some cases, a direct approach to priming a subject may prove to be less efficient than an indirect priming approach. For example, priming outside of the subject’s acknowledged awareness may work better than direct and conscious exposure [43]. It was also shown, for example, that children were more motivated to perform goal-congruent tasks by indirect priming (e.g. story-telling) than when given explicit instructions [44].

Here, we demonstrate how the association network may be a useful tool to find indirect association trajectories in order to prime a certain concept in an individual’s mind. For example, assume one wishes to prime a certain person to the word ‘stop’, e.g. to reduce arousal levels. Also, suppose that the person may not respond to that word, if shown explicitly, or even to words which are semantically close to it (e.g. the word ‘halt’ which is one step away [32]). An alternative approach, in this case, may be to try to expose the individual to a certain word in the association network, and to do so in expectance that the person will reach the target word (stop) by indirect association. Given knowledge of the association network, it is possible to answer the following question: Which primed words increase the probability that the person will naturally reach, by association, the word ‘stop’ within a pre-determined number of network steps?

For the sake of demonstration, we calculated the words that are optimal if the purpose is to reach the word ‘stop’ by association in five steps or less. The list of the top ten optimal words to achieve this is given in table 6. For example, if a person is primed by the word ‘come’, they are likely to, 29.1% of the time, think of the word ‘stop’ within five network steps or less. Primed with the word ‘ready’, individuals will think of the word ‘stop’ 26.5% of the time, within five association steps or less. Notably, if each word on the list in table 6 may only be used a limited number of times, e.g. because of saturation effects, it may be possible to use a portfolio of several words in the table to try and maximize the probability of indirectly priming the word ‘stop.’

Table 6.

Percentage of five-steps visits to the word ‘Stop’.

word	percentage of visits
come	29.1%
ready	26.5%
let	17.0%
beginning	13.4%
begin	13.2%
finish	12.1%
leave	12.0%
stay	11.9%
start	10.7%
attend	10.6%

(d). Result IV: mood-dependent random walk

Basic random walk models have commonly been used to investigate processes occurring over word association networks. In these models, the thought process is modelled to be a random walk across an association network. Transitions between nodes occur in this model according to the association transition probabilities, calibrated by using human subjects. In the context of affect, it may be interesting to test a more realistic model in which the random walk depends not only on the empirical transition probabilities, but also on the evolving affective state of the individual. For example, a more realistic model would be one in which a person in a negative mood would tend to recall associations that are more negative.

In the basic random walk model, the probability of transition is not assumed to depend on the current affect state of an individual. Essentially, one can imagine that the human coders who were used to measure the transition probabilities of the association network could have been in any affect state at the time the association data were collected. Therefore, it may be reasonable to assume that the recorded association network represents an effective measure, most likely, independent of affect. As much as previous works have shown that basic random walk models can add important insights, this assumption of independence between association network transitions and the state of affect may be questionable. The literature shows that the association process depends on the mood of the individual [45,46]. Therefore, we are interested in testing, in the context of our data, a model in which word-to-word transitions may depend on the current affect of the individual. Furthermore, it is useful to test to what extent some of the above findings, based on the basic random walk model, depend on the affect independence assumption.

(i). The mood-dependent random walk model

In order to model mood-dependence, we modified the basic random walk model in the following way. For simplicity, we focused on dependence of the random walk on valence and not arousal. An extension into a model which also includes arousal is straightforward, but out of scope here. To introduce valence-dependence into the model, we added three components to the basic random walk model we used thus far: (1) we added a valence state variable, (2) we modelled how this valence state variable changes over time steps and (3) we modelled how this state variable affects, i.e. biases, the walk over the network.

The first modification to the model is the addition of a state variable that encapsulates the state of valence of an individual at each step of the random walk process. This valence state variable is denoted by S_v(t), in which t denotes the step number elapsing since the beginning of the random walk process. The units of S_v(t) are rating points, and they range between 1 and 9, corresponding to the range in which coders were asked to provide rating in the data used here.

The next step was to model the manner in which the state variable S_v(t) of an individual changes when that individual is exposed to a word on the association network. For simplicity, initially, the state variable attains the exact value of the starting point word. For example, if the process begins with the word ‘fantastic’, S_v(t = 1) will attain the valence value of that word, 8.4. Next, when the random walk process resumes, the state variable changes according to the following time-evolution equation:

$$S_v(t)=\delta \cdot S_v(t-1)+\eta \cdot (S_v(t-1)-v_k).$$ 3.3

Here, for the purpose of simplicity, we chose a linear progression form of temporal modelling. The state variable changes in linear proportion to the difference between the current valence state, and the valence value of word k that the individual ‘lands on’ in the network (v_k). The parameter δ represents the level of inertia, and the parameter η models the level of susceptibility of the individual to the words reached in the network. The higher η is, the more susceptible the individual’s affect state to the recalled words’ influence. For example, if an individual in a state of valence of, e.g. 6 recalls (reaches) the word ‘suicide’ with the low valence of 1.58, the valence state decreases according to the value of η times this difference (=η · 4.42). A very low value of η represents a scenario in which an individual is not very susceptible to recalled words, and a high value of η represents a situation in which an individual is highly susceptible.

The third and last modification of the basic random walk model is that its process transition probabilities from node to node now depend on S_v(t) at each step in the following way:

$$T_{i,j}^{\text{valence}}=T_{i,j}\cdot {\text{e}}^{-\lambda \cdot {(S_v(t)-v_j)}^2}.$$ 3.4

Here, $T_{i,j}^{\text{valence}}$ is the valence-dependent probability of a transition between word i and word j. T_i,j is the empirical, i.e. affect-independent transition probability that is given in the data and was used in the previous sections to model the basic random walk process. The exponential factor in equation (3.4) decreases as the difference between the current state of valence of the individual (S_v(t)) and target word valence (v_j) increases. Practically speaking, this exponential factor reduces the probability of jumps in valence that are too high. The parameter λ represents the measure of how likely a given person is to be sensitive to this difference between their current affect state and the recalled word. An individual with a higher λ will be more reluctant to associate words that are incongruent with their affective state.

(ii). Valence–arousal vector field becomes fragmented with mood-dependence walk

Figure 6 represents the valence–arousal vector field, calculated in the same way as figure 5, but using the valence-dependent model. For the sake of demonstration, this figure represents a scenario in which δ = 1, η = 0.1, and λ = 3. In the electronic supplementary material, to gain more insight, we performed runs of the model with a wider range of parameter values (see electronic supplementary material, S3).

Figure 6.

A representation of the two-dimensional (valence–arousal) vector field for the valence-dependent random walk model. The valence–arousal space was divided into square bins of 0.25 sides. Each arrow in the figure corresponds to the average change of valence and arousal in that bin. Per each bin, all the outgoing links of words with valence and arousal values corresponding to that bin we considered for the average. The length of an arrow codes the magnitude of the average change per each bin. To improve the visualization we also code the magnitude using colour—the closer the colour to red, the higher the magnitude of average jump within a bin. (Online version in colour.)

Interestingly, in comparison to the vector field of the basic weighted random walk (figure 5), which exhibited a homogeneous flow towards a single global equilibrium point, the valence-dependent model exhibits a more fragmented vector field. Furthermore, as can be seen by the pattern of flow, there is a second meta-stable equilibrium point for this model, for these chosen parameters. This second semi-equilibrium point is situated in the low valence region (around 2.8) and the higher arousal region (around 5.2).

Translated into behaviour, when one takes mood-dependence into account, the data show richer scenarios of affect dynamics. In this example, it seems that individuals may be ‘trapped’ for longer times within a state of higher negativity and increased agitation, before converging towards the neutral global equilibrium point shown in §3b. Words with valence and arousal values in the vicinity of the values of this more-negative meta-stable equilibrium point are words such as: ‘cruel’ ‘punishment’, ‘destroy’ and ‘pest’, suggesting that this region in the valence–arousal space is not normally a desirable region to inhabit.

This type of analysis demonstrates how the suggested approach can be used to map and identify possible negative ‘trapping’ states in the valence–arousal space. Knowledge of the affect landscape may help provide better insight into potentially harmful affect patterns. Perhaps, the ability to map and identify harmful dynamics may translate into the ability to control or reduce their negative effects on well being.

4. Conclusion, limitations and future directions

Overall, we suggest an approach that exploits the properties of free word association networks in order to map and estimate dynamics of affect that are otherwise hard to observe. In order to do this, we used an extensive mapping of affect dimensions over the association network and extracted some fundamental insights into patterns of affect evolution.

We found that valence changes smoothly, on the one hand, but also occasionally exhibits large discontinuous jumps. Arousal, on the other hand, changes mostly slowly and smoothly, over time. These findings suggest a different dynamic mechanism for each dimension. We also found that both valence and arousal of individuals naturally tends to return to a neutral and relatively calm resting state. We observed a certain pattern in how affect decays to the resting state, over time, which may hint towards certain types of affect regulation mechanisms. For example, it seems that the stronger the deviation from the resting state, the stronger the pull towards that state.

Furthermore, through a more targeted analysis, we showed that the network environment of a word may be critical to understanding its influence on the basic affective experience of individuals. For example, while violence-related words induce the highest levels of short-term unpleasantness, it seems that pain-related words induce the highest levels of unpleasantness when the network environment is taken into account. In a second example of network targeted analysis, we demonstrated how one can use our approach to identify network routes for more efficient indirect affect priming. Finally, we studied how mood-dependent weighted random walk processes may help reveal more diverse aspects of affect dynamics. For example, we observed how introducing mood-dependence leads to the emergence of a negative high-arousal ‘trapping’ state in the valence–arousal space.

The purpose of this work was to try to lay out the foundations for an approach that may be used to study human affect dynamics on the group level, or even on the level of the individual. Potentially, if an individual’s association network is known, it is possible to try to use it, e.g. with an approach similar to the one presented here to identify and map critical affect patterns. Mapping and quantifying these patterns may help an individual or care-giver to develop ways to moderate behaviour for increased well being.

The usefulness of the suggested approach depends on several factors. First, it depends on the quality in which a given association network captures actual thought processes. This hangs on both the quality of the empirical data and the fit of the thought process modelling approach. In our case, for example, the data, while being relatively extensive, are not entirely complete in either the network aspect or the affect coding aspect.

In terms of the modelling approach, although the basic weighted random walk model is used in the literature, it is not clear how well this model fits the actual association process. This calls for experimental validation of the approach suggested here. One approach for validation is to test and see if individual-level association networks help predict that individual’s affect-oriented tendencies or behaviour. Another shortcoming of the current approach is that it does not take word context into account. For example, the word ‘hit’ can be interpreted as representing a violent act or as describing a successful event (as in ‘this song is a hit!’). We suggest that future work account for potential multiple meanings of words during its data collection and modelling stages. One way to achieve this is to collect data which include information on the varying contexts of each word. Other approaches in the literature also suggest that association occurs in the form of multi-branched activation, rather than in the basic random walk approach. Thus, these types of models may also be useful. An important avenue may be to use experiments to test which models better fit actual association processes in the context of affect dynamics. Such experiments can also be used to gauge the actual manner in which affect and association interact. For example, they could test the conditions under which words have no effect on the affect state of the individual, or, in other cases, that have a strong influence. Even though the mood-dependent approach more realistically models this interaction, further data are needed in order to estimate, e.g.the empirical values of mood dependence and susceptibility parameters (e.g. in this case: δ, η, and λ) in real-life scenarios.

In conclusion, while we acknowledge that this subject may still be in its early stages, given that high-resolution cognitive data are becoming easier to collect, as time and technology progress, we believe that approaches similar to the one described here may help researchers model and reach a better understanding of the dynamics of behaviour and perception.

Data accessibility

This paper uses public data. References for the datasets used in the paper are given in the text.

Authors' contributions

Both authors contributed equally to the draft and gave final approval for publication and agree to be held accountable for the work performed therein.

Competing interests

We declare we have no competing interest.

Funding

This research was funded partially by the Israel Science Foundationgrant no. 1124/16.