Public Opinion Field Effect Fusion in Representation Learning for Trending Topics Diffusion
Authors: Junliang Li
Yajun Yang
Qinghua Hu
Xin Wang
Hong Gao
Venue: NeurIPS 2023 poster (2023)
Keywords: public opinion field effect
heterogeneous networks
representation learning
trending topic diffusion
TL;DR: For the first time, we consider the public opinion field effect in representation learning for trending topic diffusion.

Abstract: Trending topic diffusion and prediction analysis is an important problem and has been well studied in social networks. Representation learning is an effective way to extract node embeddings, which can help for topic propagation analysis by completing downstream tasks such as link prediction and node classification. In real world, there are often several trending topics or opinion leaders in public opinion space at the same time and they can be regarded as different centers of public opinion. A public opinion field will be formed surrounding every center. These public opinion fields compete for public's attention and it will potentially affect the development of public opinion. However, the existing methods do not consider public opinion field effect for trending topics diffusion. In this paper, we introduce three well-known observations about public opinion field effect in media and communication studies, and propose a novel and effective heterogeneous representation learning framework to incorporate public opinion field effect and social circle influence effect. To the best of our knowledge, our work is the first to consider these effects in representation learning for trending topic diffusion. Extensive experiments on real-world datasets validate the superiority of our model.

Public Opinion Field Effect Fusion in Representation Learning for Trending Topics Diffusion
Junliang Li Yajun Yang 1 Qinghua Hu', Xin Wang', Hong Gao
*College of Intelligence and Computing, Tianjin University, China 2State Key Laboratory of Communication Content Cognition, Beijing, China CCollege of Mathematics and Computer Science, Zhejiang Normal University, China (lijunliang, huqinghua, Bangx)etjju edu, en, jhonggao0z.nu. edu. cn
Abstract
Trending topic diffusion and prediction analysis is an important problem and has been well studied in social networks. Representation learning is an effective way to extract node embeddings, which can help for topic propagation analysis by completing downstream tasks such as link prediction and node classification. In real world, there are often several trending topics or opinion leaders in public opinion space the same time and they can be regarded as different centers of public opinion. A public opinion field will be formed surrounding every center. These public opinion fields compete for public's attention and it will potentially affect the development of public opinion. However, the existing methods do not consider public opinion field effect for trending topics diffusion. In this paper, we introduce three well-known observations about public opinion field effect in media and communication studies, and propose a novel and effective heterogeneous representation learning framework to incorporate public opinion field effect and social circle influence effect. To the best of our knowledge, our work is the first to consider these effects in representation learning for trending topic diffusion. Extensive experiments on real-world datasets validate the superiority of our model.
Introduction
With the rapid development of the Internet, hundreds of millions of people access and share infor- mation on social medias. Social networks have become the most important platform for producing and spreading public opinions. Various trending topics widely spread social networks will bring a series of consequences. For example, fake news quickly spreads on social networks, will cause governments or organizations fall into huge crisis of public opinion (IT). Studying the diffusion and prediction of trending topics can effectively help governments and enterprises to timely discover potential public opinion crisis and deal with avoid their reputation and economic losses [52]
The existing studies on trending topic diffusion are mainly divided into two categories: content- based and baaeo.--based. The content-based methods [54, 21 55 26 aim to predict the dissemination trends, e.g., number of comments and retweets, mainly for a blog based on content features such as tags of text, images, and videos, but not cosider the network features. For network-based methods, various prediction model based on graph embedding techiniques 6 53 34 62 or random walk [33 proposed to calculate the information propagation probability for every node in social networks. Recently, representation learning on heterogeneous graph becomes an effective way to extract now-dimensional node embedding by considering the network structure and node attribute features, which can be applied to downstream tasks of propagation analysis such as link prediction
5T 2 22
and node classification [8 28
30
CCoresponning author
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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Users
Events
Sources
POF
POF)
POD
PDC
Case 11)
Case (2)
g
PoC
0
Mrlendshpp
concern
POF
publication...
citation
(a) Public opinion network.
(h) An example of several pocs and (c) Four cases for nodes in PON. their pofs.
Figure I: Public opinion field effect.
However, the existing representation learning models only consider the information of social network itself but neglect the influence of "public opinion field effect" for trending topic diffusion. In real life, there are often several trending topics or opinion leaders in the public opinion space at the same time. Every topic opinion leader with the people actively following it in social network will form a public opinion field, Research on media and communication has shown that the total amount of public's s attention is always limited [29]. These public opinion field compete for public's attention and such competition will potentially affect the development of public opinion. Obviously, a topic with higher popularity may attract more attention from people who are following other topics. The existence of public opinion field effect makes the existing representation learning model cannot work well the trending topic diffusion. A few works media and communication 66 present some statistics of public opinion field, e.g., the number of people who talk about different topics, but not consider incorporate the public opinion field effect into representation learning for trending topic diffusion. Moreover, in real world, people are always involved in a topic propagation their social cirele is actively talking about the same topic, even though they not interested in this topic at the beginning. This effect is also not considered in existing representation learning model.
53 B4] only
In this paper, we study how to incorporate public opinion field effect in representation learning. To the best of our knowledge, our work is the first one regarding this problem for trending topic diffusion. Our proposed model includes "topic propagation representation" and "social circle influence representation". In topic propagation representation, three kinds of nodes, event nodes, information source nodes and opinion leader nodes, regarded the centers of public opinion for their corresponding topics. We define public opinion field based on center node and propose a kind of paradigm to quantify the "energy" of public opinion field, which reflect the attraction power of public opinion field. We introduce three well-known observations about public opinion effect in media and communication studies, "Attention Competition Effect", "Popularity Dominance Efffect and "Negative Bias Effect", and design the model to obtain the higher quality representation by considering these effects in trending topic diffusion. In social circle influence representation, the social circle influence effect is considered in representation learning. The main contributions are summarized below:
(1) We formalize public opinion field effect and propose a novel and effective heterogeneous repre- sentation learning model by incorporating public opinion field effect for the first time.
(2) We consider the social circle influence, which extensively exists in real world, to enhance the quality of node representation.
(3) We conduct extensive experiments three real-world datasets. The experimental results demon- strate the superiority of our method.
2 Formalization of Public Opinion Field Effect
In order better investigate the diffusion of public opinion events social network, we introduce the "public opinion field effect" in representation learning for the first time. In real applications, the public

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opinion space includes various public opinion events attracting users' attention in social network. public opinion field can be regarded as a public opinion event with the users paying attention to it high influence user with his/her followers. The interaction of different public opinion fields influences the development of public opinion events. To formalize the public opinion field, we first introduce Public Opinion Network (PON), which is essentially a heterogeneous network consisting of different kinds of entities and links. All of the entities in a PON can be categorized into three types: (i) users in the social network, (ii) public events and (iii) sources that publish the events. All of the links a PON can be categorized into four types: (i) friendship link (user to user), (ii) concern link (user to event), (iii) publication link (source to event) and (iv) citation link (source source). The definition of PON is given below:
Definition 1 (Public Opinion Network): A public opinion network (PON) is heterogeneous directed
graph G = (V. E), where V = U u UUUST is the set of nodes and E S (U x U) U x I) US x ( S) is the set of links among the nodes in V. Note that U, I and S are disjoint sets of the nodes representing the users in social network, public opinion events and sources publishing the
events respectively.
O
Fig. [(a] shows an example of a public opinion network. A public opinion network depicts the public
opinion space in social network. In a public opinion network, every event node, source node and
opinion leader node is also called "public opinion center node", or poc node for simplicity. Note that opinion leader nodes identifying in social networks has been well studied and thus we do not discuss it, but instead consider them as input to our model in this paper. We use Un, and C' to denote the sets of highly influential user nodes and poc nodes respectively, i.c. C == IUSUU, Next we give the definition of Public Opinion Field.
Definition 2 (Public Opinion Field): Given a public opinion network G and public opinion center node oy E C, a public opinion field (or pof for simplicity) P. of oy is defined as an induced subgraph of G on N, U {v:), where N; is the neighbor set of o2 in G.
Fig. [(b) illustrates an example of several poc nodes and their corresponding pofs in a PON. Note that in social network user may be in several distinct pofs at the same time. A poc node can be regarded as the center of "whirlpool"" of a public topic and a pof can be regarded as view in G focusing on poc node with the users pay attention to it. Existing works neglect "public opinion field effect" in representation learning for public event diffusion. However, in practice, the interaction between different pofs always affects the development of public opinion. There are three well-known observations in media and communication studies as follows:
Observation 1 (Attention Competition Effect): The popularity of news decreases with the number of competing items that are simultaneously available. A user's s breadth of attention remains essentially constant and the diversity of memes to which a user can pay attention is bound (29].
Observation 2 (Popularity Dominance Effect): In public opinion space, the topics with the higher popularity are more powerful to attract users' attention 45).
Observation 3 (Negative Bias Effect): The negative events, c.g., fake news or rumors, are casier to spread in social networks 20).
It is noteworthy that we recognize the existence of other effects (e.g.. "Empathy Effect" 50 and "Primacy Effect" [16 56)) in the real world. However these effects are not closely relevant to the influence of coexisting trending topics on information diffusion. In addition, there also are some other effects (e.g., "Snowball Effect" [24 25 and "Herd Effect" [4] in media and communication
studies, but the meaning behind these effects are very similar to three effects introduced in this paper and thus we do not discuss them.
Observation 1 indicates the amount of attention in public opinion space is always constant, the attention on a current public topic may be seized by another rising topic, e.g., "Feng Wang Effect in China. Observations 2 and 3 indicaae that trending topics and negative events probably grab more attention in public opinion space. For fusion of above three effects in representation learning, we define "energy"" of public opinion field to quantify the attraction power of poc node in PON G.
Definition 3 (Public Opinion Field Energy): Given poc node is with its pof P., the energy of P,. denoted as E(P.), defined as E(P.) Er, ENJEN, W where N; is the neighbor set of poc node
Feng Wang is well- known singer in China. Whenever he announces something important, there are always other more trending topics emerging and competing with Feng Wang's event for users' attention.
3

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Public Opinien Natwark
1. Topic Propuration Rupresettation
Secial Circk Inflaence Reproscntaiion
Inteddap
Eabeldap
Clee
Gread
Lovn
Lim-Everere doven
Pallic
DRX MICE
3. Objective
Figure 2: Overall framework of our model.
V/ Why E R is the popularity contribution of vy for poc node v; and Tiy E R is the attention degree of vy for topic represented by poc U/-
Here Wi, reflects how much popularity or attention can be brought if by participates the discussion or propagation of public topic V;- It is obvious that Michael Jordan brings more attention than the ordinary person when discussing basketball topies. Ti.j reflects how much attention that My intends to pay the topic represented by poc node vi.
Note that researchers can calculate w., and Tr.j in any reasonable ways and we utilize attention mechanism function and covariance function to compute them respectively in this paper. We will discuss it in the next section and then prove that attention defined in our representation learning follows Observation] [ i.e., the total amount of attention in the public opinion fields is constant.
If a poc node is related to negative topic, energy amplification factor тι (7 is utilized to amplify the energy of pof P, by y/s E(P,) and thus Observation is satisfied in our representation learning framework.
Notably, reason we use only 1-hop neighbors to construct pof and pof energy is that they are closest to poc. There are also someone know a trending topic indirectly or post their comments on retweeted content. In fact, this phenomenon has been taken account into our social circle influence representation in Section 3.2 Moreover,
model can be easily extended to handle k-hop neighbors by the following equation E(P(*))= Σ Ex., Wi,t where de,5 denotes the distance between nodes v, and Uy. We will experimentally illustrate the soundness of the choice
of 1- 1-hop neighbors in Section 4.5
Representation Learning
We investigate "topic propagation representation" and "social circle influence representation" in our model. In topic propagation representation, public opinion field effect is introduced to reflect that how users actively participate in trending topics diffusion. However, practice, some users are passively involved in a trending topic diffusion because most of his/her friends have participated in the discussion about this topic. For example, someone not interested computer science does not care about the topic about ChatGPT when he/she knows it from news for the first time, but his/her interest will rise if most of his/her friends are talking about ChatGPT and thus he/she will participate in this topic diffusion. We consider such effect in social circle influence representation.
As shown in Fig. our model is divided into three parts: topic propagation representation, social circle influence representation and objective optimization. In topic propagation representation, we first calculate the pof energy, i.e., f5 E(P)) Ev.e,, Wj.aTj.s- Then, pof energy will be combined with the heterogeneous graph convolution module to perform feature aggregation for the four types of nodes in the PON. In social circle influence representation, we combine the representation obtained

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by topic propagation and the PON network to enhance the quality of representation learning. Finally, we optimize our model by supervised entropy loss and unsupervised proximity loss.
3.1 Topic Propagation Representation
In this section, we introduce how to consider public opinion field effect in topic propagation represen- tation. Because the nodes with different types always have different feature spaces, we first utilize h; = Ax; to project the features of all the nodes in G into the same space, where D; is original feature of node i and A is a projection matrix. Note that A is different depending on the type of node, i.e., U, I and S. Next the Wi, and Ti, mentioned in Definition 3 can be calculated as follows:
Wi.j = ^g att(h,,,,, h,) = k a (Wh; + Wh,)), T. ([(ov(WWh Wh, Wh;))
(I)
where aht h2) is graph attention mechanism function, which reflects the importance of ny with respect to poc node vi X is used to measure the influence of " in a social network. Previous studies propose various influence measures such as degree centrality, betweenness centrality and so on, and we use normalized degree centrality in this paper. & is the weight vector for performing graph attention, W is a shared linear transformation weight matrix and @ is concatenate operation.
We select covariance function cov(æ: y) (x: <) g))/(J 1), which indicates the correlation between two vectors æ, y E R/ to measure the amount of attention that vi intends to pay on the topic represented by poc node vs. It is reasonable since most people prefer to talk about the
topics that are more relevant to them.
From Observation we know that the attention amount of every user is limited. If someone intends to pay more attention to new trending topic. his/her interests in other topics will be dropped off at the same time. As per the discussion, Ta essentially reflects the willingness of ey to participate in topic represented by a poc node 1; thus we a normalization operation Tijj for every user vy E U:
Wi.
Tt.5 EmECONN Ws.
Obviously, normalization operation guarantees that the "Attention Competition Effect (Observation D satisfied in our representation learning model. Theorem [ shows that the total amount of attention in public opinion space that is defined in representation model is constant.
Theorem 1: Given a PON G, C and C' are any two distinct poc node sets at different times and t' on G respectively, the amount of attention for the same user set U in G is constant for different times, ie., Em,ec,,EEU Ti.j = Emmeor "EE Ti.j.
PROOF: Because En,co Ti.j = En,eor Tı.j = 1, then EojEC Tijj = Eojerr Ti.j-
In our representation learning model, normalization operation is also necessary on E(P:) to satisfy Observation 3 that is
Ti EEPP))
E(P.) - En :bs E(P.)
(3)
where 7/ > 1 if poc node v; is related to negative topic and otherwise 7): 1.
All the nodes in PON G can be categorized into four cases: (1) poc nodes; (2) user nodes v; whose all
neighbors are normal user nodes, i.c., U1 = {Va |V; U C U - }n (3) user nodes U; whose all neighbors are poc nodes, i.e.. U2= {oy 0
A N, N C): and (4) users nodes is whose neighbors
include both poc nodes and normal user nodes, i.e., U3 = {2, i E U A N, & C A N; & U - U,}. We give an illustration of all cases in Fig. [[c] and investigate node representation in trending topics propagation for these four cases respectively.
Case (1) and (2): We use the self-attention mechanism to update the features of every poc node i E C' and every node 0i E U,. Specifically, the node representation h; of o is given below:
h h I D LuyeN.u(..) Oij Wh;), aij = softmax(att(h,, h2))
as. where alt(-) is similar to Eq. (1) Cii.j is the attention coefficient between and its neighbor uy. By Eq. we know h of a poc node i also can be regarded as a representation of pof P; because aggregates all the features of nodes in P..
5

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Case (3): For each user node i E U2. its different poc neighbor nodes will compete for user v; 's attention (Attention Competition Effeet). The poc neigbor node with the larger pof energy will gain more attention from (Popularity Dominance Effect),, We consider both self attention mechanism and public opinion field effect in node representation hi for vs E U2:
h Σ eJENN and h2). h Wh, + +0 htj
(5)
Da.jj softmax(att(he,, h θ)), att hj. θ) 0j att att(h,, h2)
(6)
Note that h1 is node representation of poc node oy calculated in case (1), 02 is the normalized pof energy of Uj. i.e., 03- = E(P)), and thus O - (0),... ......... .0ic)) is the vector of all the normalized pof energy. Specifically, we need to second normalize the pof energy of all poc neighbors v E U2: 8, + 0,,/ EN,EN, 0g. In Eq. (5), the term B, hj is utilized to reflect the influence of pof P3 for representation of v; because hi the representation of P. as explained in case (1).
Case (4): For every node v, E U3. it has two kinds of neighbors, poc neighbors V/ E C and normal user neighbors Vj Un. To consider heterogeneity, RGCN 44 designs different feature projection matrices for different types of links. Inspired by this, we use two different weight matrices 1 and 22 to calculate different attention coefficient ah, and az that is
J = softmax(att) 4 h4, )2,),, att Kk. h4 h2) = ( (Wh, @ Why))
(7)
where k = 1 if i; E S1 = -N C' and l = 2 if by E E = N (U - Un). Therefore, the node representation h1 of u; E Ug is given below:
h4 - Σ esss
die h + Enyes: ai, Why), h Wh, + +0 h¹j
(8)
Like case (3), h2 is node representation for poc node "y E St calculated in case (1).
3.2 Social Circle Influence Representation
As per the discussion, users are always involved in the diffusion of trending topics that their social cir- cle are talking about. To investigate such influence, we propose social circle influence representation after topic propagation process. In social circle influence representation, user node will be imposed influence from their neighbors who have paid attention to the some trending topic. In PON G, every user node in U will receive different amounts of topic information from its user neighbors. We use the graph attention mechanism, Pt.j voftmax(att(h; h2)),. ), to measure the influence weight for node iú from its neighbor Vy. where h; and h are the topic propagation representation of node is and vj in Section 3.1 Therefore, the total influence user E U' from its social circle (i.c., N,) can be computed as follows:
Pool(h E EN. = Eu,EN Pi. hi
Note that even though i, can be influenced by its neighbors, its own representations learned from topic propagation representation are fundamental and important. Thus the final representation z; of a user node v. U is as follows:
2; = (W (h, ① Pool(h,Ius E N.))
(10)
3.3 Optimization
Note that after topic propagation representation and social circle influence representation, the features of all the nodes in are updated to Z E V
Unsupervised Proximity Loss. In real world, proximity exists extensively in a public opinion field. The users within the same pof always have similar features such as background, career, interest and so on. For example, users who actively discuss ChatGPT usually have the same background or interest in computer science. Moreover, the features of the nodes within a pof should be correlated with feature of poc node in this pof, which is the reason that they prefer to pay attention to this poc node, In this paper, we utilize such proximity property, by enhancing the correlation of embeddings between poc node and all the nodes within the same pof, to obtain higher-quality embeddings from

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our representation learning model. Specifically, we first use the readout function to aggregate the features of all the nodes within pof P. generate their common embedding e; E RR:
e Readout(H., H
(11)
where H, E RUN denotes the embedding of all the nodes in the pof P. Readout(:) denotes a simple commutatiioninvariaan function (e.g., sum and mean). Let E RiIIs and E RRC) denote the readout embedding of all pofs and the embedding of all poc nodes, respectively. In order to maximize the correlation between the poc node and all the nodes within the same pof, the mutual information (MI) between E, and Ze is maximized. Specifically, given two random variables X and Y, we adopt MINE method proposed in 3 to maximize the lower bound of MI(X, Y) as follows:
max MI Y) 2 Y) [D(X, - log ((())(())
e DiX,))
(12)
where D(X, Y) is a binary discriminator. Therefore, to maximize MI Ec, Ze), the unsupervised proximity loss Ln is defined below:
Lp(Ec: Ze) = -BP(a...) [D(e,, 2,)] log ((e))(())
(13)
where e, and z; denote the readout representation and the original representation of the poc node 44- The discriminator () is defined as a simple neural network, D(e,, = aee, W 2,). In the experiment, for each batch, estimate the first term in Eq. (3) by selecting set of {(e,, 2; ( ) from the joint distribution P(e;, 2,), and then we shuffle the 2; in the batch and generate "negative pairs" in order to estimate the second term.
Supervised Loss. For downstream tasks, we can minimize the cross-entropy loss function between ground truth and prediction:
L. 1.=-Ets I'I(CC
(14)
where Ć is the parameter of the classifier, L is the set of labeled nodes/edges, Y and Z' are the label vector and embeddings of the labeled nodes/edges respectively. Finally, We define the total loss by linearly combining these two component losses: L L. + μLL + &pLreg where p is the hyperparameter that controls the proportion of unsupervised proximity loss and yp Treg is the regularization term to alleviate overfitting.
4 Experiments
4.1 Experimental Setup
Datasets. Detailed statistical information of the datasets is shown in [ (1) BuzzFeed and PolitiFact. The two datasets are from a compre- hensive fake news detection benchmark dataset,
Table I: Statistics of datasets.
Averaee Avenge Clusering Connectivity Degree
Relation
4B
FakeNewsNet 47 48). They are collected from two platforms with fact-checking: BuzzFeed and PolitiFact, both containing news content with labels and social context information. (2) Twitter. This dataset [31 47 contains multiple articles, with each article corresponding to one event. For each event, the dataset includes its source, list of participating users, and their tweets. This dataset also includes Twitter profile description and the list of Twitter profiles each user follows. More information on the three datasets can be found in Appendix A. and Appendix A.2
Coetficiont
UsIt user
15257
15257
634750
BuzzFeed
15257
88.01
0.087
True
samcc--veet
28
182
174
23865
23865
574744
PolliFaact
23865
240
32791
53.13
0.066
17
240
236
54461
3172794
Twitte
Uses-event
54461
442
1054
1054
75509
1054
118.25
010044
442
442
3707
Baselines. For simplicity, our model is denoted as POFD (Public Opinion Field Effect Fusion
Representation Learning for Trending Topics Diffusion). We compare our model against three
categories of graph representation learning methods: (1) Homogeneous-noddeeeee [3]. GCN 66)
and GAT [57] (2) Heterogeneous-mp2ree [8) HAN (88) HetGNN 63, HGT 17 and HALO
(3) Misinformation detection- FANG [35] and MetaHG 44].
7

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Table 2: Experimental results (%) for the public opinion concern prediction task.
Dasavet
Metrics
node2vee
GCN
GAT
mp2vec
HAN
HeGGNN
HGT
HALO
FANG
MetaliG
POFD
BarsFood
AUC
AP
71. 11.46-0..27 92 44+11.49 92 06661199
76. 12.0.377 91.77...58 91 79.50.53 86 1310.33 93.43...11 93.77 0.68
KS 8592400.34
91.95=0.57
92.39-0.55
95.88
92.49-0622
$4.32.00 10.45 AS 90.9210.1 91.07.0.33 96.36.1..3
21984036
N0.124041
91 1L66660229
96,09100.56
PolidFact
1944.77 02400.2
7240,32
89,3440.43
9521-0027
92,45-031
92,05-022
92.7540
4144)
95.770033
Twitter AP
AUC
79, 191141041 s2. 1240.41 su 05
78 78.6740.24 92, 50-H0.34 92, 74+0.42 87 84-04445 92.82-00511
88 20.00
93 03.00:0.22
92.41=043
92.01 -0.38 18
92:50-0
93.12-0020
24
91 66-6660.55
91.0300.29 2y su
92. 02.50--0.55 94.99:00225
12440.44
96.820044
Parameter Settings. We set the embedding dimension to 256, return parameter to in-out parameter to 1. path length to 40, and window size to 10 in node2vec and mp2vec. All GNN models are two-layer structures with hidden layer dimension of 256 and an output dimension of 128 and are implemented through the PyTorrch Geometric (PyG) package [0]. The models that require setting the number of attentional heads are to 4. In POFD, we select the top 500 user nodes in degree ranking as Uh- The energy amplification factor of the fake news event is set to 3. For all neural network models, the learning rate 0.001, the number of training epochs is 200. For all methods, we run 10 times with the same partition and report the average results. The dataset and code with running instructions are available at lttpt:t://// // trittuu..com cww/ ki1j///OFF
4.2 Public Opinion Concern Prediction
Setting. In this paper, define public opinion concern prediction two types of link prediction: user-user and user-event. Specifically, we randomly sample 10% of the two types of links from the dataset to generate test edges. In the test edges, the positive and negative edges are each 50%. Then, we mask the positive test edges from the dataset to prevent information leakage. We report the AUC and average precision (AP) of all models in Table
Analysis. It clear that POFD consistently performs better than all baselines on three datasets. Compared to the best performance of baselines, POFD achieves high improvement in both AUC and AP, which indicates the effectiveness of considering public opinion field effect and social circle influence in representation learning. We also observe that GNNs generally achieve better performance than random walk-based methods, due to the fact that random walk-based methods can only simply exploit structural information in the PON without considering feature information that is crucial in topic diffusion.
4.3 Event Classification
Setting. We also conduct the event classification task to evaluate the embeddings learned from POFD. Specifically, since the properties of the event (positive or negative) are unknown, we first set the energy amplification factor of all poc nodes 1. Then for each dataset, we randomly split event nodes into 70%, 10%, and 20% for training, validation and testing. We report the accuracy and F1 scores of all models in Table 3
Analysis. Based on the results reported in Table 3 we observe that POFD achieves the best perfor- mance on all metries for all three datasets. By capturing the interactions between pofs of different events, POFD can learn more meaningful event node embeddings and thus achieves the best perfor- mance on the event classification task.
4.4 Universality Analysis
In addition pof in PON, there are various fields in real life, such academic in DBLP [2 Specifically, DBLP is a well-known heterogeneous academic network containing four types of nodes (author, paper, term and conference) and three types of links (author-paper, paper-term and paper-conference). More information about DBLP can be found in Appendix A..1] Like events attract users in PON, conference nodes in DBLP attract the attention of authors and their papers (and terms). Specifically, authors may be attracted to multiple conferences (this attraction is linked through author-paper and paper-conference).
Setting. In this experiment, we the conference nodes be poc nodes and then conduct the research domain classification task for the author nodes. We use the DBLP dataset provided in PyG [10), which
8

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Table 3: Experimental results (%) for the event classification task.
Dasavet
Metrics
mode2vee
GCN
GAT
mplvve
HAN
HeIGNN
HGT
HALO
FANG
MetafiG
POFD
BarsFood
ACC
F1
09 09.23401.51
30.78.0.33 s6 111.55 58.59 50.39..222
76461.34
RS (17122222
72 42,000:446
50.66.0.77 86.11 85.33 0.45
82.76=0.31
78.57=0
26
82.54=044
0.51
83.55
$6.1111.25 SS 89.89..34
A8 83.35+044
SS $8.890.411
54.6240.35
94.4400.34
92.31
PolidFact
7083100.1
484400
84 18
72:35+0.44
72.920047
86.06m0:44
37.50-0
89.55-0
90.48-H0
67,18-4035
98.24+0.32
Twitter
ACC
F1
61. 14.1490.9 68 24200.34 68 72200.27
61. 32+0..44 50 +0.88+0.33 62 06-00.054 64 20-0.41 74.15-0.117 66.67-0.27
06.2220.35
72.35-0045
72.22-0042
71,43-055 0.
77,78-0
82.9220.1
74.35+0031 72.45+0445
78.6740.33
74.3010.33 80.57:10.34
45.31:0.45
Table 4: Experiment results (%) on the DBLP for the node classification task.
Metrics
mode2ves
GCN
GAT
mp2vec
HAN
HeIGNN
HGT
HALO
FANG
MetaßGG
POFD
Macro-FI 83.67+0.34 91 31.80 90 5040-42 07.42-0.24
45400.38 92 0.40
92.01 $0.37 92.81 02.81-0.25 90.06-60 91. 13:0.22..3 95.03-0.24
Micro-FI 85.27:00.11 92.62:0.24 91 048007337 87.92=0.34
85:00.34
92.09-0.37 02.00:0:224 93.34-0.24 90.75.00.25
91.74:00.25 95.33:-0.22
0.98
PORO
PORD
0.98
0.94
ROFD
PORT
0.94
PCRD
POFD
0.94
0.94
0.90
0.90
0.92
0.92
0.85
0.88
0.58
0.88
0.84
0.84
0.86
0.86
0.82
0.82
AUC
AP
ACC
(a) Public opinion concern prediction.
(b) Event classification.
Figure 3: Ablation study on BuzzFeed dataset.
contains a predefined training, validation, and testing set. We report the Macro-F1 and Micro-F1 of all models in T
Analysis. As shown Table POFD achieves the best performance on DBLP. The experimental results indicate that the academic field formed by conference nodes effectively capture the potential influence of conference (poc) nodes on authors and their published papers, which in turn can indirectly guide the classification task of author nodes through conference information (authors always tend to publish in conferences related to their research fields).
Multi-hop Public Opinion Field
In this section, we experimentally demonstrate the reasonableness of our choice of 1-hop neighbors Definitions 2 and We give experimental results for 1-hop to 4-hop neighbors in Appendix A.3 The experimental results show that the use of multi-hop neighbors does not improve the model performance, probably because multi-hop neighbors introduce more redundancy. This indicates that pof energy is mainly determined by the 1-hop neighbors of poc nodes.
4.6 Centrality
In Eq. (1) we define Wij = >y att(h;; h,), where X, is used measure the influence of node dy in the PON. In this paper, we let '5 be the degree centrality of ey. It is well known that there various other centrality metrics such as Eigenvector Centrality. However, as we stated earlier, there have been many studies on how measure the influence of nodes in a network. X; is only used an input for study in this paper, and how to choose X, not part the study in this paper. this section, we investigate the impact of different centrality metrics the model performance. The experimental results and analysis can be found in Appendix A.4
4.7 Ablation Experiment
Setting. In this section, we investigate how the three components of POFD affect its performance.
Specifically, we create the following ablations: (1) POFD,,; keep topic propagation but remove social circle influence. (2) POFD seii keep social circle influence but remove topic propagation (we
use GAT [57] to replace topic propagation). (3) POFD remove unsupervised proximity loss. We conduct ablation experiments BuzzFeed, and the experiment results are shown in Fig.

---

Analysis. Fig. rreports the results of the ablation experiments. We observe that POFD outperforms the three variants mentioned above, which indicates that all three modules of POFD can individually improve the model performance.
5 Related Work
The content-based methods focus on the difussion of information from blogs or news content. Mahdikhani et al. [32 collected over 1.25 million tweets containing timestamps to predict the popularity of tweets (based on the number of retweets) by extracting the features of the tweets. Tsagkias et al. (54) used two-stage binary classification to predict the number of comments online news reports. Kaltenbrunner et al. [21 proposed growth model for predicting the popularity of slashdot stories. Lee et al. [26] investigated the probability that web content will continue to be followed by online readers after a period of time. In general, this type of approach often requires the processing of content to produce manual features, often with significant workload.
Content-Based.
Homogeneous Network-Basse With the rise of graph mining techniques [37 [3] 60 13 57]. a large number of people have started to study how model information diffusion using graph structures. Bourigault et al. [5] embedded nodes in a continuous latent space and calculate the contamination scores of nodes activated by source nodes through diffusion kernel function in the latent space. Inf2vec [9] studied the problem of influence embedding of nodes in social networks. RNe2 [46] estimated the information diffusion probability based on the random wandering method. Based the state of the nodes' network and local neighborhoods, DeepInf 41 aimed to predict the activation probability of the nodes. CaNSeqGCN [59] combined network structure and time series to predict the information cascade. None of these models can model complex social contexts such as user-event relationships, and thus cannot extract high-quality embedding representations.
Heterogeneous Network-Bate -aase.. The heterogencous netork-bbasee methods learn high-quality embedding representations through diverse neighborhood relationships. Although carlier studies such as 19 38 39 49] also considered heterogeneous scenarios, they all optimized specific objective (e.g., fake news detection) rather than extracting abundant node representations, and thus were not very generalizable. FANG [35) improved the quality of node representation learning by capturing the rich social interactions between users, news and media to improve the accuracy of fake news detection. Such approaches mainly improve the embedding representation by considering heterogeneous information in the network, but they do not make use of some deeper semantics such as public opinion field effects.
6 Conclusion
In this paper, we propose for the first time to fuse the public opinion field effect into the representation learning of trending topics diffusion. Then, we propose representation learning framework POFD) that includes both topic propagation and social circle influence. Experimental results including public opinion concern prediction and event classification demonstrate the effectiveness of POFD. We also show that POFD also effective for other types of fields (e.g., academic fields DBLP).
Ethics Statement. An important application of our study is fake news controlling. For example, wiping out $130 billion in stock value after false tweet claimed that Barack Obama was injured in an explosion 42 Our intention behind this work is that studying trending topic diffusion can help timely discover potential crises caused by fake news and clarify the truth with evidence as soon as possible to avoid unnecessary losses.
Linitations and Future Work. We note that POFD does not consider the dynamics of PON, such as the disappearance of old events and the emergence of new events. Therefore, in the future we will investigate representation learning for dynamic PONs.
Acknowledgement
This work was supported by the State Key Laboratory of Communication Content Cognition Funded Project No. A32003, National Natural Science Foundation of China No. U22A2025 and No. 61972275.
10

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13

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A Appendix
A.1 Datasets Processing Details
In this section, we describe how the dataset is processed obtain the inputs for the model.
process the textual content of the news and generate an embedding of dimension 768 for each news node. For user nodes and source nodes, we use metapath2vee [ to generate embeddings of dimension 128 for both types of nodes since there is not enough information input.
BuzzFeed and PolitiFact. For the news nodes, we use the BERT
Twitter. We follow the settings in FANG BS] in this paper. For the news nodes, construct a TE.DD 43 vector from the text body of the article. We enrich the representation of news by weighting the pre-trained embeddings from Glove [36] of each word with its TRIDF value forming a semantic vector. Finally, we concatenate the TEIDF and semantic vector to form the news article feature vector. We calculate the user vector the concatenation of a pair consisting of a TF.DD vector and a semantic vector derived from the user profile's text description. Similarly to article representations, for each source node, construct the source feature vector as the concatenation of its TFIDF vector and its semantic vector derived from the words in the homepage and the "About Us" section, as some fake news websites openly declare their content to be satirical or sarcastic.
DBLP. In the universality analysis experiment, directly the DBLP dataset provided in PyG [1O]. The dataset contains 4057 authors, 14328 papers, 7723 terms, and 20 publication venues. The authors divided into four research areas (Database, Data Mining, Artificial Intelligence, and Information Retrieval). Each author node is described by a bag-of-words representation of their paper keywords. For semi-supervised learning models, the author nodes are divided into training, validation, and testing sets of 400 (9.86%), 400 (9.86%), and 3257 (80.28% nodes, respectively. Since there no initial features for the publication venue nodes in this dataset, we use the torch.randn function to generate initial features of dimension 128 for each publication venue node.
A.2 Dataset Attributes
We describe some basic properties of the three datasets in Table I such the number of nodes and the number of edges. In addition, we also give the Average Degree, Connectivity and Average Clustering Coefficient of the three networks. Furthermore, give the degree distribution of the three networks in Fig.
k2
%
(a) BuzzFeed.
(b) PolitiFact.
(c) Twitter.
Figure 4: The degree distribution of the datasets.
A.3 Multi-hop Public Opinion Field
In this section, we investigate the impact on model performance when constructing pof and pof energy using multi-hop neighbors of poc node. We give experimental results for 1-hop 4-hop neighbors in Table 5, Experimental results show that using multi-hop neighbors only degrades the performance of the model. We speculate that using multi-hop neighbors may bring additional redundant information.
14

---

A.4 Degree Centrality and Eigenvector Centrality
We describe the effect of degree centrality and eigenvector centrality on model performance in Table 6 where p and POFD, denote the POFD using degree centrality and eigenvector centrality, respectively. Based on the experimental results, we find that the performance of the models implemented with the two centrality metrics is approximately equivalent. We hope that there will be follow-up work in the future to investigate how assess the importance of nodes in the public opinion space.
Table 5: Multi-hop neighborhood experiment.
Table 6: Centrality experiment.
Dataset
Metrics
I-hop
2-hop
3-hop
4-hop
Dataset
Metrics
POFD,
POFD,
BuzzFeed
AUC
AP
9..36=0.33
9.30
93 18=0.73
23.
3.06
82. 82.72=0..2 03
90.3240.36
79.22-0043
BuzzFoed
AUC
96 06.36-0.33 33
96.09+0.36 36
9.39--0.3
96.75+0.28
PolitiFact
95.44-0.377
53
79.83-0.62
PolitiFact
05.44-0.37 37
95.72-40.41
AP
95.57
0.33
9443--.22 0122
90.55++0.4
78.89-0.34
AP
95.57+0.33
95.51+0.225
Twitter
AUC
96.18-0.44
0.44
91.22-0.26
87.344-0.51
79.28--0.28
Twitter
AUC
96.18-
95.86++-055
AP
94.99
0.25
91.33
88.21.10.25
80.40.10.33
AP
94.99.0.25
0.25
94.13.10.25
15


Reviews:
[{"review_id": "1g6g0C0Tm4", "reviewer": "Reviewer_NVSH", "summary": "This paper proposes a Representation Learning method that considers field information in topic diffusion, i.e., situations with multiple topics and opinion leaders. It defines new concepts (public opinion network/field and public opinion field energy) and proposes a method for incorporating some observations into Representation Learning. It has been shown to perform better than conventional methods with multiple tasks and multiple data sets.", "questions": "It would be helpful if the authors could answer the points I mentioned in \"Weakness\".", "limitations": "- The authors appropriately mention Limitations.\n- As the authors say, they could be used by governments and businesses to anticipate and take action in advance to prevent the spread of information that is inconvenient to them, but they need to be sure that preventing the spread is the ethically correct thing to do.", "rating": 5, "confidence": 2, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "-  The paper is well-structured and easy to follow.\n- The definitions in section 2 are clear, and Figure 1 is helpful in understanding them.\n- The validation is performed using multiple real data sets; Although the sources are not specified for the DBLP data sets, they are probably all open data, and the proposed method's source code is publicly available. Hence, they are likely to be reproducible.\n- The proposed method outperforms relatively new existing methods in the Public Opinion Concern Prediction task, the Event Classification task, and the research domain classification task.", "weaknesses": "- I could not clearly understand how the roles of w={i,j} and tau={i,j} are different. I understand that each is expressed in equation (1), but it isn't easy to understand intuitively. What would tau={i,j} represent in Michael Jordan's example?\n- I felt that Observations 1-3 were shown abruptly. Why should these three effects be prioritized and only these be addressed? Are there any other candidate effects that should be treated?\n- In the section on experiments, the parameters of the proposed and baseline methods are clearly described, but there is no mention of how these values were determined. I wonder if this is a fair comparison. How were the best parameters determined? Did you search for the best parameters for each method?\n- Why are Node2vec and mp2vec less accurate? Other than Node2vec and mp2vec, some methods score close to the proposed method (POFD), but is it possible that the parameter settings and randomness may reverse the superiority of the methods? Statistical tests would be helpful.\n\nOthers\n- Typo: \"Becasue\" at P4", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the positive comments on the strength of experiments and good presentation. We also appreciate the  suggestion about more discussion on public opinion field effect and the fairness of the experiment. We respond carefully to the reviewer’s questions and hope our answers could address your concerns.\n\n**[W1&Q1]: $w_{i,j}$ and $\\tau_{i,j}$**\n\nIntuitively, in our model, $\\tau_{i,j}$ indicates the preference degree of a user $v_j$ to participate in a topic $v_i$. For example, the users who are interested in basketball are more willing to participate in discussion about the basketball-related topics than those who are not interest in basketball. $w_{i, j}$ reflects how much attention from other people will be brought if a user $v_j$ participate in a topic $v_i$. For example, Michael Jordan is a world-famous basketball superstar. When Jordan talks about some topic on social media, it will bring more public attention (e.g., from his fans ) to this topic than ordinary people. We will explain this point more clearly in revised paper. \n\n**[W2&Q2]: Why prioritise the three effects in the paper? Are there still candidate effects?**\n\nWe are very grateful to the reviewers for their questions. We acknowledge that we do not have a corresponding explanation for why we chose the three effects and promise that we will add a reasonable explanation in the final version. A detailed explanation of the reasons for choosing the three effects and whether there are more candidate effects is given in **[Common Q1]** of the global response.\n\n**[W3&Q3]: Fairness of Experiments**\n\nThanks a lot for your question. We give details of the parameter settings in **[Common Q2]** of the global response. Further, we give the results of the significance tests in **[Common Q3]**. These explanations ensure that our comparisons are fair.\n\n**[W4&Q4]: Node2vec, Mp2vec and Statistical Tests**\n\nIn contrast to graph neural network models that utilize both node feature information and network topology, **node2vec and mp2vec can only perform node embedding based on the topology information of the network**, ignoring the important initial node feature information, and thus exhibit poor performance. In order to prove the superiority of our model, we give the significance test in **[Common Q3]** of the global response and the experimental results prove that our model is significantly better than the comparison model.\n\n**[L1]: Ethical Concerns**\n\nThanks for your suggestion. We do understand the reviewer's concern. We have provided a detailed response to this issue in **[Common Q4]** of the global response.\n"}, {"review_id": "6YxRPpzrY1", "reviewer": "Reviewer_7Tx8", "summary": "In the manuscript, the authors consider two interesting novel factors for trending topics diffusion, which are public opinion field effect and social circle influence effect. They propose a representation learning framework to incorporate the two effects and conduct extensive experiments to validate the effectiveness of the proposed model.\n\n", "questions": " The authors introduce three specific kinds of public opinion effect, “Attention Competition Effect”, “Popularity Dominance Effect” and “Negative Bias Effect”, and design the model to obtain the higher quality representation by considering these effects in trending topic diffusion obvia fusing these effects in trending topic diffusion. As there could be many other effects in reality, is the proposed model fixed or can it be extended to other effects? \n", "limitations": "The authors introduce three specific kinds of public opinion effect, “Attention Competition Effect”, “Popularity Dominance Effect” and “Negative Bias Effect”, and design the model to obtain the higher quality representation by considering these effects in trending topic diffusion obvia fusing these effects in trending topic diffusion. As there could be many other effects in reality, is the proposed model fixed or can it be extended to other effects? If fixed, the potential of proposed model seems to be limited.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "\n\nThe motivation is clear and the manuscript is easy to follow. The consideration of the two effects in representation learning for trending topics diffusion is novel. The technique part seems to be reasonable. ", "weaknesses": "The authors introduce three specific kinds of public opinion effect, “Attention Competition Effect”, “Popularity Dominance Effect” and “Negative Bias Effect”, and design the model to obtain the higher quality representation by considering these effects in trending topic diffusion obvia fusing these effects in trending topic diffusion. As there could be many other effects in reality, is the proposed model fixed or can it be extended to other effects? If fixed, the potential of proposed model seems to be limited.\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for positive comments on novelty, good presentation and reasonable technique of our work. We also appreciate the reviewer's suggestion about giving more discussion on  public opinion field effect. We respond carefully to the reviewer’s questions and hope our answers could address your concerns.\n\n**[W1&Q1&L1]: More Discussion about Public Opinion Field Effect**\n\nMany thanks to the reviewer for your insightful questions. In this paper, we focus on the allocation of people's attention when multiple trending topics coexist. Therefore, we choose the three effects that are most relevant to attention allocation without considering the other effects. For a more detailed explanation, please refer to **[Common Q1]** in the global response.\n\n**However, we would like to clarify that our model is not fixed, rather it can be easily extended to some common known effects**. As we stated in **[Common Q1]**, the $\\textbf{\\textit{Broken Window Effect}}$ is similar to the $\\textbf{\\textit{Negative Bias Effect}}$ and the $\\textbf{\\textit{Snowball Effect}}$ is similar to the $\\textbf{\\textit{Popularity Dominance Effect}}$. Therefore, our model can be easily extended to these effects that are similar in meaning.\n\nIn addition, our model can be easily extended to some effects that do not apply to attention allocation. An example is the $\\textbf{\\textit{Primacy Effect}}$ (People have inherent stereotypes about certain groups of people). If we want to investigate the effect of stereotypes on information diffusion, we can make the following changes based on the model in this paper:\n1. Certain nodes in the public opinion network are classified into groups using known information or graph clustering techniques.\n2. Representative features of each group are obtained using topic extraction or other relevant techniques. For example, the spread of fake news in social networks makes people no longer trust the news media, and many people label the news media as \"fake\". Through feature extraction, we can get the overall \"fake\" features of the news media group.\n3. In the representation learning stage, in addition to aggregating the features of the public opinion field where the neighbor nodes are located, **the user will also aggregate the features of the group where the neighbor nodes are located, in order to simulate the user's inherent impression of the neighbor**, i.e., the $\\textbf{\\textit{Primacy Effect}}$.\n\nIn summary, since we only study the problem of attention allocation, we only consider the three effects mentioned in the paper. However, our model has a good scalability. In the future, we will consider incorporating other effects into our model."}, {"review_id": "CWosGVXYE1", "reviewer": "Reviewer_1ymS", "summary": "In this paper, the public opinion field effect is fused into a representation learning framework for trending topics diffusion. The proposed algorithm includes representation learning for both topic propagation and social circle influence. Experimental results on public opinion concern prediction and event classification demonstrate the effectiveness of the proposed algorithm. \n\n\n", "questions": "NA", "limitations": "NA", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The universality analysis and the ablation study in this paper provide insights such as the proposed algorithm is applicable to academic field in DBLP, and topic propagation plays a major role in the event diffusion. \n\n2. The complexity analysis shows the proposed representation learning algorithm is efficient. \n\n3. This is the first work to consider these public opinion field  effects in representation learning for trending topic diffusion, and the ideas to incorporate “Attention Competition Effect”, “Popularity Dominance Effect” and “Negative Bias Effect” in representation learning are novel. \n\n", "weaknesses": "1. Are the comparison results in Table 2, 3, 4 statistically significant? T-tests can be conducted. \n\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the recognition of the novelty and importance of our work. We also appreciate the positive comment on the effectiveness and efficiency of our model. We respond carefully to the reviewer’s questions and hope our answers could address your concerns.\n\n**[W1]: Significance Test**\n\nMany thanks to the reviewer for the suggestion. As stated by the reviewer, in order to make our experimental results more credible, we perform T-tests on multiple sets of experimental results. Specifically, we use the **test_rel()** function in the scipy package to calculate the p-value of the result array of our model and the result array of the baseline model, and determine whether the difference between our model and the comparison model is statistically significant by whether the p-value is less than 0.05.\n\nWe present the experimental results in **Tables 1-3 in the PDF** file of the global responses. **\"+\"** in the table indicates that the p-value is less than 0.05, i.e., it is acceptable that our model significantly outperforms the baseline models. **The experimental results show that our model significantly outperforms all the baseline models**.\n"}, {"review_id": "TLV9XFcUjK", "reviewer": "Reviewer_aU4Y", "summary": "The seminal models of opinion dynamics as information cascades on networks, such as DJ Watts 2002 or Watts and Dodds 2007, uses homogeneous graphs in which the nodes (representing people) are characterized by just one or two numbers (such as a bias number and a Boolean on adoption). This line of research provided a way to quantify the observation that some people are more influential than others, but the simplifying assumptions also limited its success in making predictions. This paper introduces a heterogeneous network setup (with users, events, and sources). It operationalizes three observations about the spread of opinions: an attention competition effect, an effect of popularity on the attention of individual users, an an attentional bias towards negative information. It evaluates the model using user-user link prediction and user-event link prediction on datasets drawn from BuzzFeed, PolitiFact and Twitter, and also with an event-classification task. The authors POFD model achieves very high AUC values for these tasks, improving on a number of older and SOTA baselines. ", "questions": "line 104 onwards. Can you substantiate the assumption that the users breadth of attention is constant?  The total volume of posts of a social media channel fluctuates in response to emergencies and unusual events, indicating that the total attention people pay to public matters may also fluctuate.\n\nline 150 Can you explain why normalized degree centrality is the appropriate measure? For information-propagation problems, eigencentrality may be more relevant. cf SP Borgatti (2005) “Centrality and network flow”, Borgatti and Everett (2006) “A graph-theoretic perspective on centrality”. \n\nline 215 The assumptions about the similarity of users sharing the same opinion seem excessively strong. In other domains, such as marketing, socio-demographic characteristics are only moderate predictors of opinions. Please offer further justification, or admit that this assumption is a limitation of the study.\n\nSection 4.1 Experimental Setup\n\nAre these datasets balanced or not if not, how unbalanced are they? What are the properties of the graphs they define (eg connectivity, distribution of node degrees…)\n\nlihe 277 What’s the justification for these parameter settings? Were the parameters systematically hypertuned? If so, how?\n\nline 311 In what way does research domain classification of authors shed light on the propagation of opinions or topics in research? \n", "limitations": "The authors clearly state in their last sentence that the study does  not consider the dynamics of the PON (the public opinion network). The author(s) indicate an intention to pursue this issue in future research. This is the primary limitation of the study, which should have been represented as study on the coherence or cohesiveness of public opinions (considered as a static problem). The study does not actually address trending, diffusion, or virality of opinions. \n\nThe study's general research area is very well established, and presents relatively few societal risks.  Algorithms relating to fake news detection do have the potential for societal harm, if deployed by platform moderators or in government surveillance, because both false negatives and false positives can be very harmful (by allowing fake news to spread, or suppressing legitimate free speech). The authors do not discuss this potential harm. The work does not risk this harm any more than the large body of related work, however. ", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "Finding ways to work with heterogenous graphs is an important research area. The definition of the heterogeneous network structure appears well-grounded. It offers an insightful treatment of how opinions promulgated by different opinion leaders can compete for people's attention. Very high performance is achieved on the tasks used in the experiments. ", "weaknesses": "This is a very technical paper that is written in non-native English, and it is difficult to follow in some places. Having read the paper several times, I conclude that there is a mismatch between the framing of the work and the work itself. The paper succeeds at a static link-prediction task (eg hiding links and then predicting them) and at static event or research topic classification. A dynamic prediction would involve using the state of the network up to a time t_i and using that to predict the state at time t_(i+1) -- possible predictions could be which links are added or which nodes change their state in some other manner. This is a more difficult problem and the paper does not appear to address the growing body of research on the topic. \n\nThe paper makes a number of unsubstantiated assumptions, see questions below.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for positive comments on the novelty and high performance  of our work. We respond carefully to the questions and hope our answers could address your concerns.\n\n**[W1&L1]: Dynamic of trending topic diffusion**  \n\nThanks a lot for your insightful suggestion for considering dynamic of trending topic. As mentioned by reviewer, the information diffusion prediction is always based on information cascade, which is to identify potential users who are likely to participate in information sharing at next time. It is a dynamic process. However, the main objective of this work is not to study the cascade representation but to investigate users’ representation by considering public opinion field effect. We study the influence of users’ attention distribution in our representation model when several trending topics coexist in public opinion space at the same time. **In practice, the trending topics do not alternate frequently in a short period of time and thus the existence of trending topics is relatively stable. Our users’ representation can be utilized as part of cascade-based prediction model for dynamic information diffusion**. Information diffusion prediction is a downstream task and our representation model can help existing methods to significantly improve the performance of prediction. \n\nThe “dynamics of the PON” we mentioned in last sentence means **the popularity change of trending topics in public opinion space**. Every trending topic has the process of breaking out, developing and extinction. The popularity of trending topic always changes and interacts with users’ participation. We will study the effect of popularity dynamic in our future work. It is a very difficult but interesting problem and we hope this paper could inspire more researchers pay attention to this problem.\n\n**[Q1]: Attention is Constant**\n\nWe sincerely thank you for reading our paper carefully and it is a very good question. Several studies [1-3] on social media substantiate the attention amount is limited and thus we introduce “Attention competition effect” in our representation learning model to reflect that how is users’ attention distributed when several hot topics coexist in social networks. We agree with that when an emergency or unusual event happens, it will attract a large amount of attention from people. On one hand, if there is no other hot topic in public opinion space, our model can handle this case by considering that there is only one POF of this emergency or unusual event. On the other hand, if there have existed some other hot topics before this emergency or unusual event happening, the attention will be distracted from previous hot topics. Our model also can handle this case by considering several POFs. One of the main contributions of this work is to investigate how to obtain a high-quality representation when there are several coexisting hot topics in public opinion space. We are sorry about this point is not clarified clearly and we will give more discussion in revised paper.\n\n[1] Limited individual attention and online virality of low-quality information. Nature Human Behaviour, 2017\n\n[2] The spread of true and false news online. Science, 2018\n\n[3] Accelerating dynamics of collective attention. Nature communications, 2019\n\n**[Q2]: Degree Centrality and Eigenvector Centrality**\n\nWe sincerely thank you for your insightful suggestion. Actually, influence measure $\\lambda_i$ can be considered as an input of our model. As we mentioned in line 90 and 150, existing studies have proposed various influence measures. For ease of understanding $\\lambda_i$, we explain it and use normalized degree centrality as influence measure in this paper, because intuitively a blogger has more influence if he/she has more fans. We also agree with the reviewer's suggestion that eigenvector centrality is better and we add new experiments in **Table 5** to investigate performance under different kinds of influence measure. We will explain it more clearly in revision.\n\n**[Q3]: Reasonability of the Similarity Assumption**\n\nThanks for your question. The similarity we mentioned here means that **people who surrounding the same poc node has the similar preference to participate in the discussion or propagation of the corresponding trending topic but not they have the same opinion**. For example, the fans of an idol are willing to discuss the hot topic about this idol. **We reinforce similarity only to better predict users' willingness to engage in something, not to reinforce the overall similarity among users**. We add new ablation experiments about this similarity. From **Figure 1** in the PDF, we find that the similarity assumption within POF can indeed improve the accuracy of the model. We are sorry about the misunderstanding caused by this “similarity”, we will give more details in revised paper. \n\n**[Q4]: Attributes of Datasets**\n\nThank you for your suggestions. **Table 4 and Figure 2** in PDF file depict the **average degree, connectivity, average clustering coefficients, and degree distributions** for the datasets. We will give more details about the three datasets in the revision.\n\n**[Q5]: Experimental Parameter Settings**\n\nThank you for your suggestions. We give details of the parameter settings in **[Common Q2]** of the global response and we will add these details in revised paper.\n\n**[Q6]: DBLP**\n\nThanks for your suggestion. We would like to demonstrate through DBLP experiments that **the field effect does not just exist in social networks, but is ubiquitous**. For DBLP dataset, conference nodes may form an academic field to compete researchers' attention, and author nodes outside the field will connect themselves to the conference topic through paper nodes inside the field, which can be used to infer the authors' research interest. Therefore, it is not for topic propagation prediction but research interest inference on DBLP dataset. We will explain it more clearly in the revision.\n"}, {"review_id": "s2LNJDXWzQ", "reviewer": "Reviewer_kWLJ", "summary": "This paper proposes to model the public opinion field effect in representation learning of social networks. The authors propose to model social networks as heterogeneous graphs and incorporate three effects into a neural architecture. Experiments on three datasets demonstrate that the proposed approach outperform several baselines across two classification settings.", "questions": "please see above", "limitations": "There is a brief discussion in Section 6.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "+ modeling public opinion on social networks is an important research question\n+ the connection to media and communications literature is good", "weaknesses": "- \"studying the diffusion and prediction of trending topics can effectively help governments ... discover potential public opinion crisis and deal with it to avoid their reputation ... losses\". This framing in lines 23-24 potentially has great ethical concerns regarding the task and problem.\n\n- In definition 2.3, I understand that only one-hop neighborhood of a center node could contribute to its energy. Why wouldn't 2-hop or more distant entities on social networks contribute to the popularity of certain issues or opinion leaders? They might not directly follow them, but may offer commentary on their own account. That being said, I wonder if the authors have good reasons for why only considering the 1-hop proximity is enough.\n\n- I suggest moving Figure 1 from the appendix to the main paper. It is usually a good idea to present a high-level illustration of the proposed approach.\n\n- My greatest concern is about the selection of baselines. While 9 baselines approaches, mostly GNNs or heterogenous GNNs, are considered, they are somewhat outdated. For example, the most recent baseline is HGT proposed back in 2020. If the authors agree that the field of heterogeneous GNNs or modeling social networks with GNNs have advanced since 2020, it is advised to compare with more recent approaches. Also, the baselines considered in this work are mostly generic GNNs, while more domain-specific methods on misinformation [1], Twitter [2], other social media [3], and more might also be considered or at least discussed.\n\n- I suggest adding statistical significance tests to results in Tables 2-4, especially given that some of the numbers are close.\n\n- I suggest adding an ethics statement / broader impact section since modeling and monitoring public opinions could have ethical concerns and dual use scenarios.\n\n[1] Nguyen, Van-Hoang, et al. \"Fang: Leveraging social context for fake news detection using graph representation.\" Proceedings of the 29th ACM international conference on information & knowledge management. 2020.\n\n[2] Feng, Shangbin, et al. \"TwiBot-22: Towards graph-based Twitter bot detection.\" Advances in Neural Information Processing Systems 35 (2022): 35254-35269.\n\n[3] Qian, Yiyue, et al. \"Distilling meta knowledge on heterogeneous graph for illicit drug trafficker detection on social media.\" Advances in Neural Information Processing Systems 34 (2021): 26911-26923.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for the positive comments on the novelty and importance of our research. We also appreciate the reviewer's suggestion on ethics statement, $k$-hop neighborhood, and more baseline models. We respond carefully to the reviewer’s questions and hope our answers could address your concerns.\n\n**[W1&W6]: Ethical Concerns**  \n\nThanks for your invaluable suggestion. We do understand the reviewer's concern. We have provided a detailed response to this issue in **[Common Q4]** of the global response.\n\n**[W2]: k-hop Neighbors**  \n\nThanks for your insightful suggestions. The main reason of considering 1-hop neighbors is **they are the closest neighbor to the poc node**. For example, people who directly post comments on a hot event or the followers of a famous public figure. These people are the most active ones prefer to participate in the trending topic about their corresponding poc node (e.g., hot event or public figure). There are also indeed someone know a trending topic indirectly or post their comments on a retweeted content. **This phenomenon has been taken account into our social circle influence representation in Section 3.2**. \n\nMoreover, our model can be easily extended to handle multi-hop neighbors by the following equation $E(P_i^{(k)})=\\sum_{t=1}^k\\sum_{d_{i,j}=t}w_{i,j}\\tau_{i, j}$, where $d_{i,j}$ denotes the distance between nodes $v_i$ and $v_j$. We also add a new set of experiments to evaluate the performance by varying $k$ from 1 to 4. As shown in **Table 6** in PDF file, the experimental results show that using multi-hop neighbors does not improve the performance. We are sorry about that we did not explain this point clearly and will give more detailed discussion in our revised paper. \n\n**[W3]: Framework of POFD**  \n\nThanks a lot for your invaluable suggestion. Due to space limitation, we only give the figure to illustrate the public opinion field effect (i.e., Fig.1 in the original paper) and put the figure of framework of the model into supplementary material. We will add the framework diagram of the model in the final version of the paper.\n\n**[W4]: More Baseline Models**  \n\nThanks a lot for your invaluable suggestions.  We add **FANG[1]** and **MetaHG[2]** as baseline models in our experiments. In addition, we also add the latest heterogeneous graph neural network, **HALO[3]**, in our comparison model. We perform a grid search on the parameters of all three models to get the best performance. The experimental results are shown in **Tables 1-3** in the PDF file, which validates that our models outperform the best known models. Since **TwiBot-22[4]** is a public dataset standard rather than a model, we do not add it in our baseline model. \n\n**[W5]: Significance Test**  \n\nThanks a lot for your invaluable suggestion. We conduct T-tests experiments as we mentioned in **[Common Q3]** of the global response. The experimental results validate the superiority of our model. We will add discussion about significance test in revised paper.\n\n**References**  \n\n[1] Nguyen, Van-Hoang, et al. \"Fang: Leveraging social context for fake news detection using graph representation.\" Proceedings of the 29th ACM international conference on information & knowledge management. 2020.\n\n[2] Qian, Yiyue, et al. \"Distilling meta knowledge on heterogeneous graph for illicit drug trafficker detection on social media.\" Advances in Neural Information Processing Systems 34 (2021): 26911-26923.\n\n[3] Ahn, Hongjoon, et al. \"Descent steps of a relation-aware energy produce heterogeneous graph neural networks.\" Advances in Neural Information Processing Systems 35 (2022): 38436-38448.\n\n[4] Feng, Shangbin, et al. \"TwiBot-22: Towards graph-based Twitter bot detection.\" Advances in Neural Information Processing Systems 35 (2022): 35254-35269."}]

Author rebuttal:
We would like to thank all the reviewers for their insightful and invaluable comments, which really help to improve the quality of our paper. We also appreciate five reviewers' positive comments about the novelty and well-organization of our paper.  Here, we response to four common questions and hope our answers could address reviewers' concerns. **All the tables and figures involved in rebuttal are summarized in PDF file**, which can be downloaded at the bottom of the global response.

**[Common Q1]: More Discussion about Public Opinion Field Effect**  

We investigate how to incorporate public opinion field effect in representation learning for trending topic diffusion. The trending topic diffusion problem essentially is an information diffusion prediction problem, which is an important and fundamental task in social networks and has been extensively studied. The existing works regard information diffusion is an independent process. However, in real world, there are always several trending topics in the social network at the same time. These topics compete for people’s attention and thus information diffusion process will be affected. The existing works neglect the influence of coexisting trending topics. To solve this problem, we introduce three well-known and important public opinion field effects, “Attention Competition Effect”, “Popularity Dominance Effect” and “Negative Bias Effect”, which are most closely related to the allocation of people’s attention in media and communication studies, to investigate how is people’s attention affected by these coexisting trending topics in public opinion field and thus trending topic diffusion can be predicted more accurately.

As the reviewers are concerned, there are some other effects in the real world. However these effects are not closely relevant to the influence of coexisting trending topics on information diffusion. For example, two following effects reflect what are the people’s opinion and emotion:

$\textbf{\textit{Empathy Effect:}}$ People are prone to identify and empathize with events or people similar to themselves.

$\textbf{\textit{Primacy Effect:}}$ People habitually put labels on certain events or groups.

In addition, there also are some other effects, e.g., “$\textbf{\textit{Broken Window Effect}}$”, “$\textbf{\textit{Snowball Effect}}$” and “$\textbf{\textit{Herd Effect}}$” in media and communication studies, but the meaning behind these effects are very similar to three effects introduced in this paper and thus we do not discuss them. 

In summary, we study three most closely relevant effects in our representation learning model. There indeed exist various effects in public opinion space, and we cannot discuss all of them in one paper due to our knowledge limitation. **We hope this work can inspire more researcher pay attention to studying public opinion field effect in information diffusion prediction task.**

**[Common Q2]: Experimental Parameter Settings**  

Both reviewers NVSH and aU4Y have questions about the details of the parameter settings and the fairness of the experiment. Firstly we apologise for not providing a more detailed description of the parameter settings in the original paper. We have expressed the steps of parameter setting in the experiment as follows, and promise to add this section in the final version.

For all models appearing in the experiments, **we perform a hyperparameter search and select the parameters that perform best on the validation set as the final parameters to ensure that the experiments are fair and comparable**. In particular, we report the best results for all metapaths in mp2vec. For all neural network models, in order to ensure that the experiments are comparable, we set the basic parameters such as number of layers and hiding size to be the same for all models, and then perform a grid search on the other parameters of the models to ensure that we get the optimal performance.

**[Common Q3]: Significance Test**   

The reviewers NVSH, 1ymS and kWLJ suggest us to perform some statistical analyses of the experimental results in order to better demonstrate the superiority of our model. We are very grateful to the three reviewers for their suggestions. We conduct t-tests on multiple sets of experimental results, and the results are displayed in **Tables 1-3** in the PDF file. The test results demonstrate that our model significantly outperforms all of the comparative models.

**[Common Q4]: Ethical Concerns**  

We greatly appreciate the reviewer’s reminders about ethical concerns that this study could be used to prevent the spread of information which is inconvenient to some organizations. Actually, our study is used for trending topic diffusion. Trending topic diffusion essentially is the problem of information diffusion prediction, which is a fundamental task in social networks and has been extensively studied in recent years. Different from previous studies, we consider public opinion field effects in representation learning model for the first time to make it more applicable to real world. An important application of information diffusion prediction is fake news controlling. For example, wiping out $130 billion in stock value after a false tweet claimed that Barack Obama was injured in an explosion [1]. We are sorry about that the last sentence of first paragraph in introduction leads to the misunderstanding on our study. Our intention behind this sentence is that studying trending topic diffusion can help timely discover potential crises caused by fake news and clarify the truth with evidence as soon as possible to avoid unnecessary losses. We will revise this statement in the revision.

[1] K. Rapoza, “Can ‘fake news’ impact the stock market?” Forbes, 26 February 2017

**The following attached pdf file includes the tables and figures involved in rebuttal.**

Meta-review: This paper proposed a heterogeneous representation learning framework to incorporate public opinion field effect and social circle influence effect. The consideration of the two effects in representation learning for trending topics diffusion is interesting. Experiments were performed on multiple datasets and the proposed method outperforms existing methods. The reviewers raised a few concerns, e.g., unclear technical details or experimental details, lack of significance test, and ethical concerns. The authors made good clarifications in the rebuttal and most reviewers slightly increased the scores. I think most of the issues raised in the reviews are relatively minor issues regarding paper writing, which can be well addressed in the revised version.
Decision: Accept (poster)