# Predicting Hate Intensity of Twitter Conversation Threads

Qing Meng  Southeast UniversityNanjingChina<EMAIL_ADDRESS>,  Tharun Suresh
IIIT-DelhiDelhiIndia<EMAIL_ADDRESS>,  Roy Ka-Wei LEE  Singapore
University of Technology and DesignSingapore and  Tanmoy Chakraborty  IIIT-
DelhiDelhiIndia<EMAIL_ADDRESS>
###### Abstract.

Tweets are the most concise form of communication in online social media,
wherein a single tweet has the potential to make or break the discourse of the
conversation. Online hate speech is more accessible than ever, and stifling
its propagation is of utmost importance for social media companies and users
for congenial communication. Most of the research barring a recent few has
focused on classifying an individual tweet regardless of the tweet
thread/context leading up to that point. One of the classical approaches to
curb hate speech is to adopt a _reactive strategy_ after the hate speech
postage. The ex-post facto strategy results in neglecting subtle posts that do
not show the potential to instigate hate speech on their own but may portend
in the subsequent discussion ensuing in the post’s replies.

In this paper, we propose DRAGNET++, which aims to predict the intensity of
hatred that a tweet can bring in through its reply chain in the future. It
uses the semantic and propagating structure of the tweet threads to maximize
the contextual information leading up to and the fall of hate intensity at
each subsequent tweet. We explore three publicly available Twitter datasets –
_Anti-Racism_ contains the reply tweets of a collection of social media
discourse on racist remarks during US political and Covid-19 background;
_Anti-Social_ presents a dataset of 40 million tweets amidst the COVID-19
pandemic on anti-social behaviours with custom annotations; and _Anti-Asian_
presents Twitter datasets collated based on anti-Asian behaviours during
COVID-19 pandemic. All the curated datasets consist of structural graph
information of the Tweet threads. We show that DRAGNET++ outperforms all the
state-of-the-art baselines significantly. It beats the best baseline by an 11%
margin on the Person correlation coefficient and a decrease of 25% on RMSE for
the Anti-Racism dataset with a similar performance on the other two datasets.

Hate intensity prediction, Twitter reply chain, online social media, hate
speech, graph neural network

##  1\. Introduction

Motivation. The proliferation of social media has enabled users to share and
spread ideas at a prodigious rate. While the information exchanges in social
media platforms may improve an individual’s social connectedness with online
and offline communities, these platforms are increasingly plagued with rampant
onslaught of provocative and toxic content. One such highly toxic content is
‘hate speech’, which is defined by the Cambridge dictionary as “public speech
that expresses hate or encourages violence towards a person or group based on
something such as race, religion, sex, or sexual orientation .” Hate speech on
social media has created dissension among online communities and culminated in
offline violent hate crimes (Müller and Schwarz, 2018). Therefore, it is
critical to address the spread of hate speech on social media.

Major social media platforms such as Facebook and Twitter have made
significant efforts to combat the spread of hate speech on their platforms
(Times, 2019; Bloomberg, 2019). For example, the platforms have established
clear policies regarding hateful conduct (Facebook, 2022; Twitter, 2022),
implemented mechanisms for users to report hate speech, and employed content
moderators to detect hate speech. However, such approaches are labor-
intensive, time-consuming, and thus not scalable or sustainable in the long
run (Waseem and Hovy, 2016; Gambäck and Sikdar, 2017). Traditional machine
learning and deep learning methods have also been proposed to automatically
detect hate speech in online social media (Schmidt and Wiegand, 2017; Fortuna
and Nunes, 2018; Poletto et al., 2021). However, most of the existing methods
are limited to classifying hate speech at the individual post level, ignoring
the network and propagation effects of hateful content on social media (Liu et
al., 2018).

Figure 1. An example of a tweet propagation. The hateful tweets are
highlighted in red.

Ideally, social media content moderators would want to identify hateful posts
and monitor posts and threads that are more likely to incite hatred. Consider
the example of tweet propagation showed in Figure 1. The initial source tweet
is a benign tweet that reports the Russian invasion on Ukraine. However, as
time evolves, we observe hateful content justifying the Russian invasion and
promoting violence against the Ukrainians. Existing automated hate speech
detection methods could help content moderators detect hateful tweets.
Nonetheless, content moderators could significantly improve the effectiveness
and efficiency of moderation by prioritizing those posts that are likely to
generate a large number of hateful tweets in their retweet or reply threads.
This a challenging problem as the post that induces hateful content may not be
hateful itself (e.g., source tweet in Figure 1). Early detection of tweets
that are likely to generate a large amount of hateful content becomes a
critical real-world issue.

A very few studies examined hate intensity of Twitter conversation threads for
early hate speech detection. Lin et al. (2021) manually categorize Twitter
conversation threads into different level of hatred, and proposed a deep
learning model to forecast and classify tweets into the pre-defined hatred
levels. Recently, we Sahnan et al. (2021) introduced the hate intensity
prediction task and proposed DRAGNET, a deep stratified learning framework,
which predicted the intensity of hatred that a root tweet can fetch through
its subsequent replies. Nevertheless, DRAGNET assumes a linear sequence for
the conversation thread in its model, in which tweets in a conversation
threads are arranged in a chronological sequence. This neglects the tree
structural information inherently present in a conversation thread; there
could be multiple branches in a conversation threads similar to the example
shown in Fig. 1. The structural information may be important features that
could better inform and improve hate intensity prediction. For instance, we
may notice a heated debate along the branches of the conversation threads;
therefore, modeling the dynamics of the tree structure of the conversation
thread may aid us in better predicting the eventual hate intensity of the
conversation thread.

Research Objectives. In this paper, we aim to fill this research gap and
extend our earlier model, DRAGNET (Sahnan et al., 2021) by proposing DRAGNET++
that models multifaceted information to forecast the hate intensity of a
Twitter conversation thread. Specifically, we define our problem statement as
follows – _given a root tweet and a few of its initial replies, can we predict
the hate intensity of the subsequent replies of the tweet_? To model this
problem, we first quantify hate intensities of tweets in the conversation
thread and express them as a series of hate intensities, which essentially
transforms the task into a time-series problem. At a high level, DRAGNET++
adopts a similar stratified learning framework as suggested in (Sahnan et al.,
2021) to model the hate intensity profiles of Twitter conversation threads and
categorizes them into clusters of varying hate intensity. In addition to the
content sentiment and temporal information, DRAGNET++ also captures structural
information of the conversation thread. Specifically, DRAGNET++ adopts Graph
Neural Networks (GNN) to learn the conversation thread semantic and
propagation structure.

As the prediction of hate intensity in conversation threads is a relatively
new research problem, we conduct thorough experiments and analyses to evaluate
DRAGNET++. We collate three publicly available real-world datasets – _Anti-
Racism_ with $3.5k$ root tweets, _Anti-Social_ with $668k$ root tweets, and
_Anti-Asian_ with $218k$ root tweets. We perform an extensive analysis of
these datasets to examine the hate intensities of real-world Twitter
conversation threads. We benchmark DRAGNET++ against DRAGNET and six other
baselines on the hate intensity task. Finally, we examine case studies and
conduct ablation studies to explain the advantages and limitations of
DRAGNET++.

Contributions. We summarize our contributions below:

  * •

We analyze the hate intensity in three large-scale real-world Twitter
datasets. This is the first large-scale study that examines hate intensity in
Twitter conversation threads.

  * •

We propose DRAGNET++, a stratified learning framework with structural graph
augmentation to perform hate intensity prediction.

  * •

We conduct extensive experiments and show that DRAGNET++ consistently
outperforms state-of-the-art methods in the early prediction of hateful
conversation threads. Specifically, DRAGNET++ outperforms the best baseline by
at least 34% on Pearson Correlation Coefficient (PCC), reduction of at least
200% on Root Mean Square Error (RMSE), and 7% lower on Mean Forecast Error
(MFE) across the datasets. Comparing the performance of DRAGNET++ with DRAGNET
shows an average improvement of 8.33% on PCC, and an average reduction of
16.07%, and 18.20% on RMSE and MFE, respectively.

  * •

Our case studies demonstrate the viability of predicting hate speech early to
prevent the propagation of hateful content.

Organization of the paper: We start by presenting the developments until
recently related to hate speech detection and time series forecasting in
Section 2. Following this, we define the formulation of hate intensity
profiles appropriate to our problem statement in Section 3. We then move on to
detailing our model in Section 4. Further, we analyze the various datasets and
present their statistics and observations in Section 5. We discuss a brief
overview of various baselines in Section 6.1. In Section 6.2, we present a
detailed comparison, analysis of the model performance, and the effect of
various parameters used to fine-tune the model. We conclude the paper in
Section 7.

Reproducibility. The source codes of DRAGNET++ and all the baselines, and the
dataset are available at the following link:
https://github.com/LCS2-IIITD/Predicting-Hate-Intensity.

##  2\. Related Work

###  2.1. Hate Speech Detection in Social Media

Industry and academics have paid close attention to the work on hate speech
detection. Early research (Dinakar et al., 2011; Sood et al., 2012b) focuses
mostly on list-based methods that extract profane and offensive terms from
predetermined lexicons. These approaches struggle to handle words not found in
curated lexicons. Sood et al. (Sood et al., 2012a) developed an edit distance
metric to catch more obscene terms as a result. To differentiate offensive
language on Twitter, Davidson et al. (Davidson et al., 2017a) introduced the
multi-class classifier, which combines different features (e.g., TF-IDF,
grammatical structure, sentiment lexicon, etc.). Based on the word embedding
algorithm, some studies (Djuric et al., 2015; Nobata et al., 2016) proposed to
learn embedding features of words or sentences in hate speech detection. Other
studies (Djuric et al., 2015; Nobata et al., 2016) proposed learning embedding
properties of words or phrases in hate speech detection based on the word
embedding technique (Mikolov et al., 2013; Le and Mikolov, 2014).

With the advancement deep learning, neural language processing systems that
can automatically extract features from the text have seen a lot of success
(Kim, 2014; Sutskever et al., 2014; Vaswani et al., 2017). This opens up new
possibilities for hate speech detection (Mehdad and Tetreault, 2016; Badjatiya
et al., 2017; Zhang et al., 2018; Arango et al., 2019; Founta et al., 2019).
Gamback et al. (Gambäck and Sikdar, 2017), for example, used Convolutional
Neural Networks (CNN) to classify hate speech by extracting word similarities.
Similar research was done by Park et al. (Park and Fung, 2017), who presented
the HybridCNN model to investigate word and character combination patterns in
order to detect hate speech. Del et al. (Del Vigna12 et al., 2017), on the
other hand, used Long Short Term Memory (LSTM) to record the long-term
dependencies of words in phrases in order to differentiate hatred remarks.
Badjatiya et al. (Badjatiya et al., 2017) evaluated the use of the LSTM model
in conjunction with the Gradient-Boost Decision Tree (GBDT) in the task of
hate speech identification and found that it greatly enhanced performance.
Zhang et al. (Zhang et al., 2018) presented a CNN+GRU network architecture to
investigate word dependency for recognizing hate speech tweets, combining the
benefits of CNN-based models and Gate Recurrent Unit (GRU)-based models.
However, most research focus on learning a particular textual property while
ignoring other valuable data. Cao et al. (Cao et al., 2020a) introduced
DeepHate, a deep learning-based hate speech detection algorithm for mining
multi-faceted textual representations. Lee et al. (Lee et al., 2021) later
developed DisMultiHate, a hateful meme classification model that can learn
both textual and visual information.

Pre-trained language models such as BERT (Devlin et al., 2018) and GPT
(Radford et al., 2018) can extract external information from massive volumes
of text data. These models have also been used in hate speech detection models
with promising results (Mozafari et al., 2019; Awal et al., 2021). Awal et al.
(Awal et al., 2021), for example, used the pre-trained BERT model as a shared
layer and created AngryBERT, a multi-task learning model that can jointly
detect hate speech and classify sentiment. Nonetheless, most previous research
works have focused on categorizing hate speech. A few research looked into how
hate speech spreads through social media. In a recent discussion, Dahiya et
al. (Dahiya et al., 2021) discussed the necessity of anticipating the hatred
intensity of tweets. Lin et al. (Lin et al., 2021) classified the tweets into
different levels of hatred and suggested the HEAR model track posts that are
likely to cause hate speech. Closer to our work is DRAGNET (Sahnan et al.,
2021), which is a deep stratified learning framework that predicts the hate
intensity of a conversation thread based on what a root tweet can fetch
through its subsequent replies. DRAGNET models the linear sequence for the
conversation thread chain where the tweets are arranged chronologically. Such
a modeling approach ignores the conversation thread’s inherent structural
information propagation information. We address this limitation and propose
DRAGNET++which considers the Twitter conversation thread’s structural
information to improve hate intensity prediction

###  2.2. Times Series Forecasting Modeling

Time series models are designed to predict values or trends over time in the
future and have been extensively studied in many fields such as
transportation(Ma et al., 2020), finance(Andersen et al., 2005), event
forecasting, (Ding et al., 2019) and disease transmission (Matsubara et al.,
2014). The hatred intensity prediction problem can be reduced to a time series
prediction task, where we forecast the hate intensity of the conversation
thread in the future. Therefore, we also introduce the existing studies of
time series forecasting (TSF) models.

Traditional TSF methods, such as ARMA (Rojas et al., 2008), exponential
smoothing (Gardner Jr, 1985), and linear space models, have been the basis of
much work and achieved better performance. With the rapid development of deep
learning technology in recent years, more and more end-to-end TSF models have
been proposed. Compared to traditional methods, deep learning-based models
such as CNN, RNN, and LSTM can automatically extract features from the input
without domain expertise, which is widely accepted in many fields. For
example, Oord et al. (Oord et al., 2016) adopted CNN in raw audio generation
and proposed the WaveNet model. Based on WaveNet, Borovykh et al. (Borovykh et
al., 2017) utilized CNN to perform conditional time series forecasting tasks.
The model shared filter weights assuming that the hidden patterns are time-
invariant at each step. In addition, the RNN contains an internal memory
state, which is also able to retain information about previous time steps (Wei
et al., 2021). However, due to vanishing gradients, the performance of
classical RNN-based models degrades as the sequence length increases. Later,
the LSTM model overcomes the long-term dependency problem to some extent.
Elsworth et al. (Elsworth and Güttel, 2020) used LSTM for TSF tasks, improving
performance and robustness.

However, most of the above models only focus on one-step predictions. Some
recent studies (Mariet and Kuznetsov, 2019; Fan et al., 2019) generalize
sequence-to-sequence (Seq2Seq) models and propose them for multi-step time
series forecasting methods. Fan et al. (Fan et al., 2019) exploited attention
mechanisms to capture the temporal context information extracted by the RNN
encoder. Combined with a bidirectional LSTM decoder, the model can generate
multiple future horizons simultaneously. Later, researchers proposed new
architectures (Sen et al., 2019; Li et al., 2019) to reduce error accumulation
in multi-step prediction. For instance, Sen et al. (Sen et al., 2019) combined
global matrix factorization models and local temporal networks to capture
latent patterns in time series. In recent years, the Transformer architecture
has been proposed for natural language processing tasks and has also achieved
success on time series data (Li et al., 2019; Oreshkin et al., 2019).
Moreover, some studies (Yuan and Kitani, 2019; Salinas et al., 2020) proposed
models to estimate the probability distribution of future time series. For
example, Yuan et al. (Yuan and Kitani, 2019), and Koonchli et al. (Koochali et
al., 2019b) employ Generative Adversarial Networks (GANs) to predict future
values. Salinas et al. (Salinas et al., 2020) proposed a DeepAR model for
probabilistic prediction based on auto-regressive recurrent networks.

##  3\. Preliminaries

Table 1. Important notations and denotations. Symbol |  Definition
---|---
$\varphi$ |  Root tweet
$c_{i}^{\varphi}$ |  $i^{th}$ reply to root tweet $\varphi$
$R_{p,q}$ |  Hate value set of $q$ reply tweets of the $p^{th}$ root tweet
$R^{*}_{p,q}$ |  The set of hate values for the $q$ reply tweets of the $p^{th}$ root tweet predicted by the autoencoder
$S_{s(1,n)}$ |  Cosine similarity set between root tweet and $n$ reply tweets
$R_{s(1,n)}$ |  Set of hate intensity profiles
$j$ |  Number of clusters
$\delta$ |  Window size
$t_{h}$ |  Number of replies in history
$t_{f}$ |  Index of the last reply tweet in the conversation thread
$n$ |  Maximum length of the conversation thread
$s$ |  Total number of conversation threads
$N_{X_{h}}$ |  Dimension of encoded history latent vector
$N_{X_{f}}$ |  Dimension of encoded future latent vector
$\mathcal{X}$ |  Latent vector of $R_{p,q}$
$\mathcal{X}^{*}$ |  Latent vector of $R^{*}_{p,q}$
$C_{c}$ |  List of cluster centers
$\mathcal{P}(C_{ci})$ |  Likelihood of belongingness to $i^{th}$ cluster identified with $C_{ci}$
$\mathcal{P}^{*}(C_{ci})$ |  Predicted weight for $i^{th}$ cluster centre $C_{ci}$ to calculate $\mathcal{X}_{c}$
$\mathcal{X}_{d}$ |  Pre-processed prior vector
$\mathcal{X}_{h}$, $\mathcal{X}_{f}$ |  The representation of historical and future conversation threads
$\mathcal{X}_{h}^{c}$, $\mathcal{X}_{f}^{c}$ |  The representation of pseudo historical and pseudo future conversation threads
$\mathcal{E}_{h}(\cdot)$ |  The encoder model of historical conversation threads
$\mathcal{E}_{f}(\cdot)$ |  The encoder model of future conversation threads
$\mathcal{GM}(\cdot)$ |  Clustering model
$\mathcal{PR}(\cdot)$ |  Classification model
$\mathcal{FP}(\cdot)$ |  Prediction model
$\mathcal{FP}_{d}(\cdot)$ |  $1^{st}$ segment of prediction model
$\mathcal{FP}_{p}(\cdot)$ |  $2^{nd}$ prediction model
$\mathcal{D}(\cdot)$ |  The decoder model
$\mathcal{TE}(\cdot)$ |  The tree encoder

Hate Intensity Definition. Table 1 summarizes the denotations of the important
notations. Let an ordered sequence of first $t$ replies to a root tweet
$\varphi$ be
$\mathcal{T}_{1,t}^{\varphi}=<c_{1}^{\varphi},c_{2}^{\varphi},\cdots,c_{t}^{\varphi}>$,
where $c_{i}^{\varphi}$ refers to the $i^{th}$ reply. As the replies in the
original dataset have no ground-truth hate intensity, we quantify the hate
intensity of each reply using a weighted sum of two measures as suggested in
(Dahiya et al., 2021):

(1) $\mathcal{H}=w\mathcal{H}_{c}(c)+(1-w)\mathcal{H}_{l}(c),$

where $\mathcal{H}_{c}$ indicates the probability that the reply is hateful,
and it is calculated by a state-of-the-art hate speech detection model (we
will elaborate it in Section 6.2). $\mathcal{H}_{l}$ is the average score for
all words in a reply from a model-independent hate lexicon that comprises
2,895 words as proposed in (Wiegand et al., 2019). $w\in[0,1]$ is a hyper-
parameter that balances two quantities of the hate intensity score. As
$\mathcal{H}_{c}\in[0,1]$ and $\mathcal{H}_{l}\in[0,1]$, the final hate
intensity score of a reply $\mathcal{H}$ is still between 0 and 1. Therefore,
each conversation thread $\mathcal{T}$ can be mapped to a sequence of hate
intensity scores,

(2)
$\mathcal{H}(\mathcal{T}_{1,t}^{\varphi})=<\mathcal{H}(c_{1}^{\varphi}),\mathcal{H}(c_{2}^{\varphi}),\cdots,\mathcal{H}(c_{t}^{\varphi})>$

To avoid noise and drastic fluctuations that are not in line with reality, we
further smooth the hate intensity sequence by utilizing a rolling average
operation with window size $\delta$ (Dahiya et al., 2021). A window consists
of $\delta$ consecutive replies, and the window that starts from the $k$th
reply is denoted by $\mathcal{T}_{k,k+\delta}^{\varphi}$. Finally, the hate
intensity of a window for the tweet $\varphi$ is measured as,

(3) $\displaystyle\mathcal{H}(\mathcal{T}_{k,k+\delta}^{\varphi})$
$\displaystyle=\sum_{c\in\mathcal{T}_{k,k+\delta}^{\varphi}}\mathcal{H}(c)=w\sum_{c\in\mathcal{T}_{k,k+\delta}^{\varphi}}\mathcal{H}_{c}(c)+(1-w)\sum_{c\in\mathcal{T}_{k,k+\delta}^{\varphi}}\mathcal{H}_{l}(c),$

where $\mathcal{H}(\mathcal{T}_{k,k+\delta}^{\varphi})\in[0,\delta]$, and
$\delta$ is the window size.

Sentiment Features. The emotional feedback of users is reflected in the
sentiment features of reply posts, which provide both for and against
arguments of the original tweet. Therefore, we use the cosine similarity
between the sentiment embedding of the root tweet ($\varphi$) and its
accompanying replies ($c^{\varphi}_{1},c^{\varphi}_{2},\cdots$) to capture the
sentiment context of a conversation thread, denoted as
$\mathcal{CS}(c_{i})=CosineSim(Embed(c^{\varphi}_{i}),Embed(\varphi))$. The
sentiment embedding is the second last fully-connected layer from the pre-
trained XLNet model (Yang et al., 2019) for sentiment classification. To
smooth the value and eliminate the effect of noise, we also apply the rolling
average operation to the sentiment context sequences
$\mathcal{CS}(\mathcal{T}^{\varphi}_{1,t})$ with the same window size $\delta$
as performed on $\mathcal{H}(\mathcal{T}_{1,t}^{\varphi})$.

Problem Definition. Given (i) a root retweet $\varphi$, (ii) its last $t_{h}$
historical replies
$\mathcal{T}_{1,t_{h}}^{\varphi}=\\{c_{1}^{\varphi},c_{2}^{\varphi},\cdots,c_{t_{h}}^{\varphi}\\}$,
(iii) the corresponding hate intensity sequence
$\\{\mathcal{H}(\mathcal{T}_{k,k+\delta}^{\varphi})|k\in[1,2,\cdots,t_{h}-\delta]\\}$,
and (iv) $G_{\varphi}=(V,E)$ referring to the adjacency matrix of the
propagation tree, where
$V=\\{\varphi,c_{1}^{\varphi},c_{2}^{\varphi},\cdots,c_{t}^{\varphi}\\}$, and
$e_{ij}\in\\{0,1\\}$ denote the retweeting/reply relationships between tweets
(i.e., root tweet or replies), we aim to predict the hate intensity of the
upcoming replies $c_{t^{\prime}}^{\varphi}$ in the propagation tree of the
root tweet $\varphi$. However, in corresponding to the historical hate
intensity sequence, we consider to predict the hate intensity for each window
of $c_{t^{\prime}}^{\varphi}$, denoted by
$\mathcal{H}(\mathcal{T}_{t^{\prime},t^{\prime}+\delta}^{\varphi})$, instead
of directly predicting the hate intensity of each reply.

##  4\. Methodology

This section presents our proposed hate intensity prediction method,
DRAGNET++. It is a deep stratified learning (Hastings et al., 2016) method
that splits heterogeneous data points (in this case, Twitter conversations)
into homogeneous clusters/strata before training a deep regressor on each
stratum to predict hate intensity. Figure 2 illustrates the overall
architecture of DRAGNET++.

The training set of window-wise hate intensity profile and sentiment context
value sequences is formed by the two-dimensional vector.

(4) $\displaystyle\mathcal{R}_{s(1,n)}$
$\displaystyle=\\{\mathcal{R}_{(p,q)}:1\leq p\leq s,1\leq q\leq n\\}$
$\displaystyle\mathcal{R}_{(p,q)}$
$\displaystyle=\\{\mathcal{H}(\mathcal{T}^{\varphi_{p}}_{k,k+\delta}):1\leq
k\leq q-\delta\\}$ $\displaystyle\mathcal{S}_{s(1,n)}$
$\displaystyle=\\{\mathcal{S}_{(p,q)}:1\leq p\leq s,1\leq q\leq n\\}$
$\displaystyle\mathcal{S}_{(p,q)}$
$\displaystyle=\\{\mathcal{CS}(\mathcal{T}^{\varphi_{p}}_{k,k+\delta}):1\leq
k\leq q-\delta\\}$

where $s$ is the total number of conversations, and $n$ is the maximum length
of the conversation. The elements $\mathcal{R}_{(p,q)}\in\mathcal{R}_{s(1,n)}$
and $\mathcal{S}_{(p,q)}\in\mathcal{S}_{s(1,n)}$ are the $p$th data point,
whose conversation thread is of length $q$ ($\varphi_{p}$ represents the $p$th
root tweet). The model begins by utilising an autoencoder to learn low-
dimensional latent representations for the hate intensity profile of
conversation threads (of irregular lengths). In this situation, we learn two
alternative latent representations: $\mathcal{X}_{h}$, which represents the
first few replies and is viewed as history, and $\mathcal{X}_{f}$, which
represents the future hatred trend for the remaining replies. Then, in an
unsupervised setting, we use a fuzzy clustering technique to give cluster
membership probabilities $\mathcal{P}(C_{c1},C_{c2},\cdots,C_{cj})$ and
cluster centres $(C_{c1},C_{c2},\cdots,C_{cj})$ to each conversation thread,
where $j$ is a hyper-parameter indicating the number of clusters. Following
this, we train a new deep neural network unit to predict cluster membership
probabilities given $\mathcal{X}_{h}$ and $\mathcal{S}_{s(1,t_{h})}$, which
assign cluster centres for a new conversation thread. Finally, using
$\mathcal{X}_{h}$ and $\mathcal{P}(C_{c1},C_{c2},\cdots,C_{cj})$, a novel deep
regressor predicts the latent representation of the future hate trend
$\mathcal{X}_{f}$, which, when coupled with $\mathcal{X}_{h}$, is transformed
to the whole hate trend by the decoder trained during the autoencoder phase.

Figure 2. The overall framework of DRAGNET++. The autoencoder is trained on
hate intensity profiles of entire conversation thread. Using the trained
autoencoder, the history and future latent representations are concatenated
and clustered using the fuzzy clustering algorithm. In the Prior Model
$\mathcal{PR(\dot{)}}$, graph representations and sentiment features are
concatenated to generate the Prior Knowledge vector. On inference, (a) the
history latent representation, (b) sentiment similarity features of the
history, and (c) the graph representation of the conversation thread are used
to predict the future hate intensity profile.

###  4.1. Time-series Representative Learning

The vector of the conversation thread $\mathcal{R}_{s(1,n)}$ can be viewed as
a collection of irregularly lengthening time series (window-wise hatred
intensity profiles). The Dynamic Time Warping (DTW) distance metric and its
derivatives are used to group comparable trends together in state-of-the-art
approaches for clustering irregular time series (Niennattrakul and
Ratanamahatana, 2007). DTW’s precision in mapping time series similarity is
beneficial, but the noisy and volatile character of the data points in the
present research prevents it from showing high efficiency in clustering
comparable hatred patterns into a single stratum. We propose an autoencoder to
translate each conversation thread $\mathcal{R}_{(p,q)}$ in
$\mathcal{R}_{s(1,n)}$ to a low-dimensional latent representation in order to
capture a more suitable representation of the time series. We also propose a
multi-encoder strategy, as proposed in (Sun et al., 2021), instead of a single
encoder-decoder design.

###  4.2. Proposed Autoencoder

To capture the hate intensity series, the autoencoder module seeks to learn a
low-dimensional representation. In DRAGNET++, we specifically construct two
encoders and a single decoder. The model can learn the representations of both
historical and future hate intensity sequences separately thanks to the two
encoders. The decoder then uses the representations to reconstruct the
original hate intensity sequence.

####  4.2.1. Encoder

Several studies provide models for both univariate and multivariate (Yang et
al., 2018; Ismail Fawaz et al., 2020) time series in order to mine the hidden
patterns of various sequences. We use a state-of-the-art Inception-Time
(Ismail Fawaz et al., 2020) module to automatically extract features and
represent hate intensity sequences, denoted as:

(5) $\mathcal{X}_{m}=\mathcal{E}_{t}(\mathcal{R}_{s_{(1,n)}}),$

where $\mathcal{X}_{m}\in\mathbb{R}^{s\times n\times 4}$ is the multivariate
intermediate representation of $\mathcal{R}_{s_{(1,n)}}$. The Inception-Time
module is denoted by $mathcalEt(cdot)$. We flatten $\mathcal{X}_{m}$ after the
Inception-Time module and use multilayer perceptrons as the classification
stage. Finally, the representations are written down as follows:

(6) $\displaystyle\mathcal{X}_{o}=\mathcal{E}_{lt}(flatten(\mathcal{X}_{m})),$

Here, $\mathcal{X}_{m}$ is transformed into a one-dimensional vector using
$flatten(\cdot)$. $\mathcal{E}_{lt}(\cdot)$ denotes multilayer perceptrons
that have been trained to learn the best representation of the hate intensity
sequence.

We develop the history encoder ($\mathcal{E}_{h}$) and the future encoder
($\mathcal{E}_{f}$) on the basis of Equations (5) and (6) to encode hate
intensity sequences of both historical and future conversation threads:

(7) $\displaystyle\mathcal{X}_{h}$
$\displaystyle=\mathcal{E}_{h}(\mathcal{R}_{s(1,t_{h})})$
$\displaystyle\mathcal{X}_{f}$
$\displaystyle=\mathcal{E}_{f}(\mathcal{R}_{s(t_{h+1},t_{f})})$

where $\mathcal{X}_{h}\in\mathbb{R}^{s\times N_{\mathcal{X}_{h}}}$ and
$\mathcal{X}_{f}\in\mathbb{R}^{s\times N_{\mathcal{X}_{f}}}$ denote the
historical and future latent representations, respectively.
$N_{\mathcal{X}_{h}}$ and $N_{\mathcal{X}_{f}}$ represent the length of
$\mathcal{X}_{h}$ and $\mathcal{X}_{f}$, respectively.

####  4.2.2. Decoder.

Although we use two encoders to convert the hate intensity of each
conversation thread into two latent representations, $\mathcal{X}_{h}$ and
$\mathcal{X}_{f}$, we only employ one decoder, $\mathcal{D}(\cdot)$ to return
the latent representation to the original input. The decoder is trained to
reconstruct the original hate intensity profile per conversation thread by
concatenating the two latent representations. The decoder’s operation can be
summarised as follows:

(8)
$\mathcal{R}^{*}_{(s(1,n)}=\mathcal{D}([\mathcal{X}_{h}\oplus\mathcal{X}_{f}]),$

where $\mathcal{R}^{*}_{(s(1,n)}$ is the reconstructed hate intensity sequence
containing both historical and future hate intensity sequence.

###  4.3. Fuzzy Associations

The hate intensity profiles of conversation threads in our dataset are noisy,
volatile, and lack a discernible pattern, as mentioned in Section 4.1. Our
goal is to group similar profiles together using low-dimensional latent
representations of data obtained by autoencoder (as explained in Section 4.2).
Recent research that supports this technique attests to the validity of deep
learning-based models’ effectiveness in learning hidden features from time-
series data for various applications (Cui et al., 2016; Ziat et al., 2017). To
aggregate heterogeneous hate intensity profiles into (near-) homogeneous
clusters, we apply a clustering strategy over the latent representations.
Finding meaningful correlations in data is unduly dependent on the number of
clusters $j$ and the cluster centres in this unsupervised context. As a
result, rather than restricting each profile to a single cluster, we apply a
fuzzy clustering approach and use the membership probabilities as a feature
embedding.

We define the combined latent space $\mathcal{X}$ as,

(9) $\mathcal{X}=\mathcal{X}_{h}\oplus\mathcal{X}_{f}.$

Rather than using a hard clustering strategy, in which each profile’s
association to the nearest cluster is fixed, we instead use cluster membership
probability using a fuzzy clustering approach. The membership probability
vector, denoted by $P$($C_{c1},C_{c2},\dots,C_{cj}$), reflects the associative
probabilities of each cluster with the provided chain, where $C_{ci}$ denotes
the cluster centre of the $i$th cluster.

####  4.3.1. Fuzzy Clustering

We cluster on the combined latent representation $\mathcal{X}$ because our
goal is to uncover correlations between each hate intensity profile and
homogeneity groupings. To locate the clusters $C_{c}$, which is the collection
of cluster centres, we use a state-of-the-art fuzzy clustering model
(Reynolds, 2009), indicated by $\mathcal{GM}(\cdot)$:

(10) $C_{c}=\mathcal{GM}(\mathcal{X})=(C_{c1},C_{c2},\cdots,C_{cj}).$

where $j$ is the pre-defined number of clusters, and $C_{ci}$ is the cluster
centre of the $i$th cluster.

(a) The tree encoder $\mathcal{TE}(\cdot)$

(b) The Node Embedding Module

Figure 3. The tree encoder $\mathcal{TE}(\cdot)$ for generating graph-level
representations for each conversation thread.

###  4.4. Tree Encoder

Twitter conversation threads typically contain numerous replies (i.e., tweets)
with various propagation topological structures. These propagation structures
capture the relationships between the tweets; modeling the topological
structures would enrich the conversation thread’s representation for
downstream machine learning tasks (Cao et al., 2020b; Bian et al., 2020). For
our hate intensity prediction task, we design a tree encoder to fuse the
information of tweet content and the structural information to represent the
conversation tree. The tree encoding process is presented in Fig 3(a).
Specifically, to learn a conversation thread’s representation, we first learn
the node embedding by designing a sub-module to learn the tweet’s
representation using a hate intensity prediction task. Next, we leverage a
Graph Neural Network (GNN) (Scarselli et al., 2008) to learn the conversation
tree embedding by fusing the conversation tree structural information and the
node embedding.

Learning Node Embedding. We adopt tweet-level hate intensity prediction task
as the supervised signal for learning the node (i.e., tweet) embedding. We
first leverage pre-trained Word2Vec (Mikolov et al., 2013) word embedding to
represent the words in individual tweets. Next, we use a two-layer
bidirectional gated recurrent unit (BiGRU) to learn the individual post’s
representation, and the tweet-level hate scores are used as training signals.
Specifically, the post representations are fed into a two-layer MLP classifier
to predict the post’s hate label. The model is formulated as follows:

(11) $\displaystyle\bm{w}_{i}$
$\displaystyle=Bi\text{-}GRU(<w_{0},w_{1},\cdots,w_{N}>),$
$\displaystyle\bm{\hat{p}}_{k}$
$\displaystyle={Att}(<w_{0},w_{1},\cdots,w_{N}>),$ $\displaystyle\hat{y}_{k}$
$\displaystyle={MLP}(\bm{\hat{p}}_{k}),$

where $\hat{y}_{k}$ is the predicted hate score for the $k$ tweet. With the
loss function below and the Adam optimizer, we can train the parameters of the
model. We can then obtain the tweet-level embedding $\bm{p}_{k}$. The loss
function ($\mathcal{L}_{h}$) is defined as follows:

(12) $\mathcal{L}_{h}=\sum_{k=1}^{N}(y_{k}-\hat{y}_{k})^{2}+reg(\Theta)$

where $N$ is the number of tweets in all conversation threads, $reg(\cdot)$ is
a regularization function to alleviate overfitting, and $\Theta$ is a
parameter for the fine-tuning model.

Learning Tree Embedding. The goal of learning the tree embedding of the
conversation thread is to leverage useful propagation structural information
to perform early hate intensity prediction. Working towards this goal, we
leverage GNNs to model the tree structure in the conversation threads.
Specifically, GNNs model the conversation thread structural information as a
directed graph with the node represented using the node embeddings learned
from the previous section:

(13)
$\bm{P}^{(l)}=\bm{W}^{(l-1)}\bm{P}^{(l-1)}\bm{D}^{-1/2}\bm{A}\bm{D}^{-1/2}$

where $\bm{W}$ is the trainable parameter,
$\bm{P}^{(l-1)}\in\mathbb{R}^{n\times d}$ is the representation of all tweets,
and $\bm{A}$ is the adjacency matrix of the conversation thread tree
structure. Finally, using the average pooling operation, we can obtain the
graph-level embedding of the reply tree, denoted $\bm{T}_{i}$.

###  4.5. Boosting Prediction with Prior Knowledge

The task of predicting the hate intensity of upcoming replies, provided
limited history $\mathcal{R}^{*}_{(s(1,t_{h})}$, is strenuous even for state-
of-the-art deep learning models due to the noisy, volatile and heterogeneous
nature of the time-series hate intensity profiles. To address this, we
introduce the notion of prior knowledge to the prediction component of our
pipeline as the weighted sum of the cluster centres, where the weights
correspond to the cluster membership probabilities for the new chain, denoted
by $\mathcal{P}^{*}(C_{c1},C_{c2},\dots,C_{cj}$). We define prior knowledge as
follows:

(14) $\displaystyle\mathcal{X}_{c}$ $\displaystyle=\sum_{i\in(0\leq i\leq
j)}C_{ci}\dot{P}^{*}(C_{ci})$

Note that $C_{c}$ is calculated over $\mathcal{X}$, i.e., the combined latent
representation. Therefore, to calculate the complete membership probability
vector for a new chain, we cannot use the fuzzy clustering model
$\mathcal{GM}(\cdot)$ directly. Rather, we construct a prior model
$\mathcal{PR}(\cdot)$ with the aim of predicting the membership probabilities
for new chains using only the latent representation of the history
$\mathcal{X}_{h}$ and sentiment feature $\mathcal{S}_{s(1,t_{h})}$.

(15)
$\mathcal{PR}(\mathcal{E}_{h}(\mathcal{R}_{s(1,t_{h})}),\mathcal{S}_{s(1,t_{h})})=\mathcal{P}^{*}(C_{c1},C_{c2},\cdots,C_{cj})$

The precision of the predictions by the prior regression model is measured by
comparing $\mathcal{P}^{*}(C_{c1},C_{c2},\dots,C_{cj}$) against
$\mathcal{P}(C_{c1},C_{c2},\dots,C_{cj}$).

####  4.5.1. Estimating Latent Representation of Upcoming Conversation Threads

The designed decoder needs the latent representations of both historical
conversation threads and future conversation threads to reconstruct the
complete hate intensity profile. However, our primary objective is to predict
the future hate intensity profile on the basis of historical information. To
provide the decoder with the ability to perform prediction, we propose a
future representation predictor that uses historical information to estimate
the latent representation of future hate intensity profile $\mathcal{X}_{f}$.
Then, combined with the latent representation of historical conversation
threads, the output can be fed into the decoder.

Specifically, we utilize the prior knowledge extracted by the fuzzy clustering
module, and the latent representation $\mathcal{X}_{c}$ of the historical
conversation threads. To avoid the estimation problem being unduly influenced
by prior knowledge, we design the predictor in two steps. In the first step,
for each conversation thread, the prior latent representation of historical
conversation threads $X_{h}^{c}$ contains the required information to predict
the latent representation of future conversation threads. And we have the
expected latent representation $\mathcal{X}_{h}$ encoded from the initial
historical replay chains. As a result, we use the difference operator on the
expected ($\mathcal{X}_{h}$) and estimated priors ($\mathcal{X}^{c}_{h}$) of
the historical conversation threads to evaluate the deviation of these two
representations. Secondly, a single-layer perceptron $\mathcal{FP}_{d}(\cdot)$
is used to learn the representation ($X_{d}$) in a hidden space, indicating
the dissimilarity between the prior knowledge and the history conversation
threads.

(16) $\displaystyle\mathcal{X}_{s}$
$\displaystyle=\mathcal{X}_{h}\ominus\mathcal{X}^{c}_{h}$
$\displaystyle\mathcal{X}_{d}$
$\displaystyle=\mathcal{FP}_{d}(\mathcal{X}_{s})$

We finally obtain the $X_{hc}$ vector by concatenating the provided input
$X_{h}$, the pre-processed prior $X_{d}$ and $X^{c}_{f}$ as,
$X_{hc}=X_{h}\oplus X_{d}\oplus X^{c}_{f}$. The second stage is the deep
linear transformation model $\mathcal{FP}_{p}(\cdot)$ that predicts the
upcoming hate intensity in the latent space $X^{*}_{f}$ as follows:

(17) $\mathcal{X}^{*}_{f}=\mathcal{FP}_{p}(\mathcal{X}_{hc})$

###  4.6. Decoding the future

We use the decoder module trained in Section 4.2.2 to forecast entire hate
intensity profiles (i.e., $\mathcal{R}^{*}_{s(1,n)}$) based on the expected
latent representation of the upcoming hate intensity $\mathcal{X}^{*}_{f}$. In
particular, we concatenate the original latent representation
($\mathcal{X}_{h}$) of historical hate intensity sequences with the expected
future representation ($\mathcal{X}^{*}_{f}$), denoted as:

(18) $\mathcal{X}^{*}=\mathcal{X}_{h}\oplus\mathcal{X}^{*}_{f}$

where $\mathcal{X}^{*}$ is the predicted hate intensity profile of the
upcoming conversation thread in the latent space. The decoder is designed to
be a mirror of the encoder. The decoder is defined as follows:

(19) $\mathcal{R}^{*}_{s(1,n)}=\mathcal{D}(\mathcal{X}^{*})$

where $\mathcal{R}^{*}_{s(1,n)}$ denotes the expected hate intensity profile
for the next future conversation thread. Finally, we compare the predicted and
original hate intensity score sequences (i.e., $\mathcal{R}_{s(1,n)}$) to
evaluate and report the performance on several metrics.

###  4.7. Comparison with DRAGNET

From the modeling standpoint, DRAGNET++ has advanced DRAGNET (Sahnan et al.,
2021) on two aspects: DRAGNET++ exploits the tweet-level semantics information
and the conversation-level structural information to improve hate intensity
prediction. DRAGNET had leveraged sentiment features, calculated as each
tweet’s similarity in the conversation threads to the root tweet. However,
this approach largely ignores the complex relationships among the tweets in
the conversation threads. Furthermore, as illustrated in our earlier example
in Fig. 1, the root tweet might be benign, and anchoring the sentiment
features computation base on the root tweet may not provide an accurate
forecast of the sentiment of the subsequent tweets in the conversation
threads. Therefore, DRAGNET++ addressed this limitation by modeling the
tweets’ semantics with an additional hate intensity prediction task at the
tweet level, and the conversation thread structure with GNNs as the tree
encoder. The intuition is that by learning the node (i.e., tweets) and tree
(i.e., conversation thread) representations using GNNs, we are able to capture
the dependency among the tweets in the conversation threads and extract unique
structural patterns that could improve the prediction of hate intensity for
conversation thread.

##  5\. Datasets

We evaluate DRAGNET++ on three publicly available large Twitter datasets.
These datasets contain large amount of Twitter conversation threads, which
were originally collected for other hate speech related studies. Table 2 shows
the statistics of the datasets.

Dataset | #Conversation threads | Conversation thread length | #Tweets | #Unique users
---|---|---|---|---
Min. | Max. | Avg.
Anti-Racism | 3,500 | 1 | 582 | 200 | 750,235 | 620,437
Anti-Social | 668,082 | 1 | 20014 | 31 | 40,385,257 | 4,980,160
Anti-Asian | 218,790 | 1 | 2822 | 35 | 206,348,565 | 23,895,911
Table 2. The statistics of the three datasets used in our experiments.

In the _Anti-Racism_ dataset (Sahnan et al., 2021), the authors manually
identified various real-world events by using a hashtag-based matching via the
Twitter API. During the tumultuous year of 2020, many topics polarised the
discussion, such as the 2020 US Presidential election, the Brexit referendum
in the UK, and extending similar political issues across the US, the UK, and
India. Adding to the diversity of the dataset, _sinophobic_ tweets attributing
coronavirus to China are also curated in the dataset, with most mentions (in
tweets) as “China virus”. The final dataset consists of 3500 Twitter
conversation threads with over 750K tweets.

In the _Anti-Social_ dataset (Awal et al., 2020), the COVID-19 related tweets
were collected from the Twitter platform. The authors performed query
searchers using a bunch of case-sensitive keywords such as “covid-19”,
“COVID-19”, “Coronavirus”, “coronavirus” and “corona”. Leveraging the Twitter
Streaming API, the authors collected the conversations related to these
queried tweets. Using this approach, the authors collected over $650K$ Twitter
conversations with over $40M$ tweets published between March 17 and 2020 to
April 28, 2020.

In the _Anti-Asian_ dataset (He et al., 2021), the authors focused on the
Asian hate speech surrounding the COVID-19 discussions. They followed a
similar keyword-based approach but as a two-step process. The _covid-19
keywords_ are used to narrow the COVID-19 related tweets, following which
_hate keywords_ about anti-Asian hate is used to segregate the tweets as
defined by the collection for the dataset. Finally, _counter-speech keywords_
are keywords and hashtags used to counter the hate speech and support Asians.
It comprised of 42 keywords. The authors used a combination of Twitter
Streaming API and Twitter Search API to collect real-time tweets between
January 15, 2020 and March 26, 2021. The dataset comprises over $210K$ Twitter
conversation threads with more than $206M$ tweets.

(a) Anti-Racism (b) Anti-Social

(c) Anti-Asian

Figure 4. Distribution of number of conversation threads vs length of each
conversation thread and the number of unique users in respective conversation
threads for all three datasets. Note that for the _Anti-Social_ and _Anti-
Asian_ datasets, the x-axis ticks start from 10 and ends earlier than the
maximum length as described in Table 2 to show the distribution more clearly.

##### Length of Conversation Threads:

Figure 4(a) shows the length of conversation threads over the number of
conversation threads for the _Anti-Racism_ dataset. The average length of the
conversation threads is concentrated at around $200$, with the maximum length
being $582$. On the other hand, Figures 4(b) and 4(c) show a clipped version
of the entire graph for better visualization of the distribution. Most of the
tweets constitute lengths less than or equal to $100$. To understand the full
picture, the numerical statistics of _Anti-Social_ and _Anti-Asian_ is
represented in Table 2. The maximum length in the _Anti-Social_ dataset goes
as high as $20014$. However, the average length of the dataset is around 31.
Along the similar lines, the _Anti-Asian_ dataset also touches a maximum
conversation thread length of $2822$ with an average length of $35$ across the
tweet threads.

##### Number of Unique Users:

Figure 4 also highlights the number of unique users per reply thread. For the
_Anti-Racism_ dataset, it can be observed that the unique users and the
lengths follow a similar distribution. The increased number of unique users
can be attributed to limited re-engagement by the same users for a particular
thread. Furthermore, both the _Anti-Social_ and _Anti-Asian_ datasets exhibit
a high variation in the length of the threads with a consistent presence of
threads in almost all lengths. Correspondingly, the unique users touch about
$65$ for about 225 threads in case of _Anti-Social_ , whereas $70$ unique
users for about $240$ threads in _Anti-Asian_.

##### Number of Conversation threads and Tweets:

The conversation threads and the total number of tweets are present in Table
2. Compared to the _Anti-Racism_ dataset, the other two datasets possess a
vast number of conversation threads, forming the ideal datasets to test the
performance of the models. However, the number of tweets is $206M$ for _Anti-
Asian_ , whose conversation threads are less in number as compared to _Anti-
Social_ , which has about $40M$ tweets in total. This shows the variation in
conversation thread length for different datasets and the corresponding unique
users overall, adding diversity to the datasets.

##  6\. Experiments

###  6.1. Baselines

There are just a few studies that predict hate intensity profiles in Twitter
conversations (Sahnan et al., 2021; Dahiya et al., 2021). As a result, we use
time-series forecasting and temporal pattern model based on both conventional
and deep learning as baselines.

  * •

LSTM (Elsworth and Güttel, 2020): Long short-term memory is a neural network
architecture with feedback connections that is very effective. LSTMs, unlike
RNNs, perform better on long-range predictions, such as time-series problems.
As suggested by Elsworth and Güttel (2020), we employ a stacked LSTM. We use
ReLU as the activation function for each layer to forecast the hate intensity
profile.

  * •

CNN (Mehtab et al., 2020): A convolutional neural network considers the time
information of the hate intensities in order to better profile the tweet’s
upcoming replies. We employ a 1-D CNN architecture with ReLU activation as the
last layer. The kernel size is 2, and the number of filters employed is 64.

  * •

N-Beats (Oreshkin et al., 2020): Neural Basis Expansion Analysis for
interpretable Time Series forecasting is a deep learning model designed to
tackle the univariate time-series problem. With a very deep stack of fully-
connected layers, it incorporates forward and backward residual linkages.

  * •

DeepAR (Salinas et al., 2020):  It is a supervised learning approach for
forecasting scalar time-series using Recurrent Neural Networks (RNN), which is
achieved by auto-regressively training the RNN on numerous related time-series
data.

  * •

TFT (Lim et al., 2020): Temporal Fusion Transformers are used in conjunction
with multi-horizon forecasting to help the model mix known future inputs and
extract exogenous correlations from the time series’ past input data. The
model employs a self-attention-based architecture to give interpretable time-
series insights.

  * •

ForGAN (Koochali et al., 2019a): Probabilistic forecasting of sensory data
using generative adversarial networks employs an adversarial network to learn
data generating distributions and compute probabilistic forecasts over them.
In a time-series forecasting problem, the model claims to learn the whole
conditional probability distribution of future values, with no quantile
crossing or reliance on the prior distribution.

  * •

DRAGNET (Sahnan et al., 2021): It is a deep stratified learning approach. To
create the latent representation of past and future tweets from the specified
point of reference as hyperparameter, an autoencoder is utilised using the
Inception-Time module (Ismail Fawaz et al., 2020). This is combined with a
fuzzy clustering algorithm to forecast the future hate intensity sequence,
which is reinforced with sentiment features to determine the correlation of
each tweet with the root tweet.

###  6.2. Experimental Setup

The hyperparameters used for all the experiments are as follows: $\delta$ =
10, $w=0.6$, $t_{h}=25$, $t_{f}=275$, $n=300$, $j=15$, $N_{X_{h}}=32$,
$N_{X_{f}}=128$. In the auto-encoder step, DRAGNET++ is implemented with the
Inception-Time module (Ismail Fawaz et al., 2020) for transformation with
variable kernel sizes – 5,7, and 9. Sentiment characteristics, history
encodings from the auto-encoder, and graph structure information are fed into
fully-connected layers in the prior model. A Gaussian mixture model with full
covariance is utilised for fuzzy clustering. Davidson model (Davidson et al.,
2017b) is the default hate-speech classifier. We utilise the _Adam_ optimizer
with an _lr_ = $0.001$ for faster convergence, and the training and test split
is set at $80-20$.

Three evaluation metrics for this task are used: (i) Pearson correlation
coefficient (PCC), where higher value is better, (ii) Root Mean Square Error
(RMSE), and (iii) Mean Forecast Error (MFE), where lower values are better.

###  6.3. Experimental Results and Analysis

The overall performance of DRAGNET++ and baselines on the three datasets are
shown in Table 3. Across all datasets, we find that DRAGNET++ outperforms the
baselines. Specifically, for the _Anti-Racism_ dataset, DRAGNET++ outperforms
the best baseline (N-Beats) by 40% on PCC. Other assessment parameters show a
similar trend, with a 100% reduction in RMSE and a $9\times$ reduction in MFE
when compared to N-Beats. On the contrary, as compared to the baselines on the
_Anti-Asian_ dataset, both DRAGNET and DRAGNET++ perform poorly on PCC. One
possible explanation is the dataset’s restricted chain of responses. DRAGNET++
on the other hand, outperforms N-Beats by more than $3\times$ on RMSE when
optimising the inaccuracies on hate intensity profiles. TFT has a higher MFE
score than _DRAGNET_ , but DRAGNET++ has the highest total score. Along with
LSTM and CNN, ForGAN appears to be one of the worst performers. On the _Anti-
Social_ dataset, DRAGNET++ outperforms the best baseline, TFT, by 0.223,
0.476, and 0.202, respectively, on PCC, RMSE, and MFE. When DRAGNET and
DRAGNET++ are directly compared, the latter performs better on all three
datasets and on all three metrics. This demonstrates how using graph
information inherent in tweet threads can help forecast hate intensity
profiles more accurately. The greatest significant improvement over RMSE is
$22.72\%$ on the _Anti-Social_ dataset, and the highest increase on PCC is
$0.066$ points on the _Anti-Racism_ dataset. On the MFE (_Anti-Racism_
dataset), DRAGNET performs the best, which can be attributed to customised
windowing strategies that reduce forecast error. DRAGNET’s improved
performance does not apply to other datasets, where DRAGNET++ readily
outperforms.

Model | Anti-Racism | Anti-Social | Anti-Asian
---|---|---|---
PCC | RMSE | MFE | PCC | RMSE | MFE | PCC | RMSE | MFE
LSTM | 0.145 | 0.611 | 0.500 | 0.160 | 0.511 | 0.315 | 0.680 | 0.722 | 0.692
CNN | 0.105 | 0.644 | 0.509 | 0.112 | 0.542 | 0.320 | 0.675 | 0.731 | 0.699
DeepAR | 0.310 | 0.484 | 0.065 | 0.180 | 0.490 | 0.275 | 0.682 | 0.748 | 0.708
TFT | 0.469 | 0.437 | 0.076 | 0.376 | 0.630 | 0.333 | 0.562 | 0.866 | 0.125
N-Beats | 0.380 | 0.544 | 0.085 | 0.340 | 0.633 | 0.271 | 0.712 | 0.462 | 0.173
ForGAN | 0.240 | 0.603 | 0.360 | 0.172 | 0.897 | 0.785 | 0.563 | 0.871 | 0.475
DRAGNET | 0.563 | 0.247 | 0.010 | 0.559 | 0.189 | 0.156 | 0.603 | 0.165 | 0.134
DRAGNET++ | 0.629 | 0.218 | 0.008 | 0.599 | 0.154 | 0.131 | 0.641 | 0.147 | 0.116
Table 3. Overall performance of DRAGNET++ and baselines on the three datasets.
The best resutls are bold.

###  6.4. Ablation Study

The prior model $\mathcal{PR}(\cdot)$ in DRAGNET++ makes use of the
propagation graph structure, sentiment information, and fine-tuning operation
to improve the representation of historical discussion threads and establish a
link between historical and future data. To assess the performance of each
component, we remove it one at a time and provide three variants: DRAGNET++
w/o graph structure, DRAGNET++ w/o sentiment, and DRAGNET++ w/o fine-tune.
Then, using three datasets, we run experiments to see how the alternative
models perform in the end, and the findings are displayed in Fig 5.

Figure 5. Ablation study: The Effectiveness of components in prior model
$\mathcal{PR}(\cdot)$ on three datasets.

The performance of the model degrades for each of the versions, as seen in Fig
5. It indicates that each component contributes differently to the prediction
of conversation thread labels, resulting in improved hate intensity prediction
results. Across all three datasets, DRAGNET++ w/o graph structure performs the
worst among the four variations. The diffusion patterns and informative
material are present in the propagation graph structures of conversation
threads; therefore, this is reasonable. Capturing earlier responses and
projecting future patterns would help the data. When comparing DRAGNET++ w/o
sentiment to DRAGNET++, the performance drops slightly, but not as much as
when comparing DRAGNET++ w/o graph structure. It is possible that the
reasoning is because each tweet’s sentiment is assessed in relation to the
root tweet. The structural graph information, on the other hand, is a more
advanced method of recording hate intensity distribution. Furthermore,
DRAGNET++ outperforms DRAGNET++ w/o fine-tuning. It suggests that using the
fine-tune technique, word embedding can precisely capture hate intensity
information.

###  6.5. Parameter Analysis

We further analyze the parameters of DRAGNET++ to better understand its
superiority and limitations. Throughout this study, we compare DRAGNET++ and
DRAGNET.

####  6.5.1. The impact of different window sizes.

The window size utilised in the average rolling process is represented by the
hyperparameter $\delta$. It is possible that the smaller window size would
result in more pronounced hate intensity profiles. We chose the window size in
$\\{5,10,15,20\\}$ to analyse the influence of different window sizes, and the
experimental findings are displayed in Fig 6. Across all three datasets, we
observe that increasing the value of $\delta$ improves the performance of both
DRAGNET++ and DRAGNET. A bigger window size ($\delta$) smooths the values in
hate intensity sequences, making it easier for the models to learn the hidden
hate intensity pattern. Furthermore, DRAGNET++ consistently outperforms
DRAGNET across all window size settings, demonstrating its efficacy.

(a) Anti-Racism (b) Anti-Social

(c) Anti-Asian

Figure 6. Performance comparison based on window size ($\delta$) of hate
intensity profiles.

####  6.5.2. The impact of history sizes.

The beginning history size $t_{h}$ is the amount of data needed to estimate
the whole hate intensity profile for a new conversation thread. The value of
the Pearson correlation coefficient for DRAGNET++ shows relatively little
change as $t_{h}$ increases, as seen in Fig 7. We can observe that DRAGNET++
outperforms DRAGNET. The model’s capacity to generate early predictions
decreases as the number of initial responses submitted to the model grows. As
a result, in the experiments, we used $t_{h}$=25 to predict hate intensity.

(a) Anti-Racism (b) Anti-Social

(c) Anti-Asian

Figure 7. Performance of DRAGNET++ on three datasets based on changes to tweet
history length at input.

####  6.5.3. The impact of different numbers of clusters.

One of the most important hyperparameters of DRAGNET++ in the fuzzy clustering
step is the number of clusters $j$. As a result, we choose a number of
clusters in the range of $\\{5,10,15,20\\}$ to assess the impact of cluster
size. The outcomes of the experiment are shown in Fig 8. We notice that as the
number of clusters grows, the DRAGNET++’s performance improves and it is
consistently better than DRAGNET. It is difficult to discern between different
types of conversation threads when we use a small number of clusters. However,
beyond a certain number of clusters, the performance begins to deteriorate.
One probable explanation is that grouping conversation threads into too many
clusters produces noise, making it harder for the prior model to detect the
correct cluster labels with minimal historical data.

(a) Anti-Racism (b) Anti-Social

(c) Anti-Asian

Figure 8. Performance comparison shown by changing the hyperparameter of
number of clusters in fuzzy clustering algorithm.

####  6.5.4. The impact of different weights in hate intensity score.

Our hate intensity score leverages $w$ to simplify the trade-off between the
hate detection model and the hate lexicon component in Section 3. Our
suggested DRAGNET++ model definitely outperforms DRAGNET for all three values
of $w$ (i.e., 0.45, 0.6, 0.75) on all three datasets, as demonstrated in Fig
9.

(a) Anti-Racism (b) Anti-Social

(c) Anti-Asian

Figure 9. Performance comparison depicted by varying the weight (w) which
optimizes the trade-off between hate detection/lexicon.

####  6.5.5. The impact of hate detection models.

We adopt a hate speech detection model to measure hate intensity scores of
replies during data preprocessing. To investigate the impact of different hate
speech detection models, we adopt three hate speech detection models, proposed
by Davidson et al. (2017a) (default), Founta et al. (2019), and Waseem and
Hovy (2016). Fig 10 shows that different hate speech detection models would
have a subtle impact on the final performance. However, DRAGNET++ has
consistent precedence over DRAGNET across all three hate detection models.

(a) Anti-Racism (b) Anti-Social

(c) Anti-Asian

Figure 10. The impact of different hate detection algorithms on DRAGNET++ and
DRAGNET

##  7\. Conclusion

In this paper, we build on our previous work by using two new datasets: _Anti-
Social_ and _Anti-Asian_. The new datasets gave enough bandwidth to continue
experimenting with the old model DRAGNET to forecast hate intensity profiles.
By adding the structural graph information critical for any Twitter reply
chain, we suggested a new model, DRAGNET++. GNN-augmented DRAGNET++
outperformed all baselines, including DRAGNET, by a large margin. We then used
several ablations to compare DRAGNET and DRAGNET++ in order to figure out why
our model was able to outperform the existing architecture.

In the future, we would like to see if we can build a meaningful association
of hate intensity profiles at the branch level of the reply chain’s tree
structure by using sophisticated structural graph information. We would also
like to look into how user data can be used to predict hate intensity scores.
Human-annotated hate intensity datasets can be included. Our ultimate goal,
sooner or later, would be to stop the spread of hate speech as soon as
possible after the first tweet appears on Twitter.

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