da Silva and Paraboni

*Ivandré Paraboni

Av Arlindo Bettio, 1000. São Paulo, Brazil 03828-000.

# Text and author-level political inference using heterogeneous knowledge
representations

Samuel Caetano da Silva  Ivandré Paraboni  School of Arts Sciences and
Humanities, University of São Paulo, São Paulo, Brazil  School of Arts
Sciences and Humanities, University of São Paulo, São Paulo, Brazil
<EMAIL_ADDRESS>
(26 April 2016; 6 June 2016; 6 June 2016)

###### Abstract

[Summary] The inference of politically-charged information from text data is a
popular research topic in Natural Language Processing (NLP) at both text- and
author-level. In recent years, studies of this kind have been implemented with
the aid of representations from transformers such as BERT. Despite
considerable success, however, we may ask whether results may be improved even
further by combining transformed-based models with additional knowledge
representations. To shed light on this issue, the present work describes a
series of experiments to compare alternative model configurations for
political inference from text in both English and Portuguese languages.
Results suggest that certain text representations - in particular, the
combined use of BERT pre-trained language models with a syntactic dependency
model - may outperform the alternatives across multiple experimental settings,
making a potentially strong case for further research in the use of
heterogeneous text representations in these and possibly other NLP tasks.

###### keywords:

Natural Language Processing, political bias, ideology, political alignment,
stance, hyperpartisan news detection, author profiling

††articletype: Article Type00footnotetext: Abbreviations: NLP, natural
language processing; LSTM, long short-term memory networks; CNN, convolutional
neural networks; BERT, Bidirectional Encoder Representations from
Transformers, LIWC, Linguistic Inquiry and Word Count

##  1 Introduction

Inferring politically-charged information from text data is a popular research
topic in Natural Language Processing (NLP), with a wide range of applications
to predict individuals’ political views 1, 2, 3 and behaviour 4, 5, 6.
Existing work in the field often draws a distinction between two main tasks:
the issue of political bias, and political ideology in general. Following 5
and others, political bias is presently defined as any extreme one-sided (or
hyperpartisan) discourse that, in a political context, clearly leans towards a
liberal or conservative agenda, and which may be deliberately produced as a
means to convince or gather support. This contrasts with several other more
nuanced forms of political expression, hereby called ideology, in which
arguments tend to be more balanced, and which do no explicit promote a
particular political agenda. These include expressions of political
orientation (e.g., being left- or right-leaning) and political stance in
general (e.g., being for or against a political party, a principle, or an
individual), among others.

From a computational perspective, both bias and ideology inference from text
data may be further divided into two problem definitions, hereby called text-
and author-level political inference. Text-level inference is more closely
related to sentiment analysis 7, 8, 9 and stance classification 10, 11, 3, and
it is intended to determine the meaning of an input text (e.g., whether the
text expresses a liberal or conservative view.) Less-known author-level
inference, by contrast, is an instance of computational author profiling 12,
13, 14, 15, 16, 17, 18, that is, the task of inferring an individual’s
demographics (e.g., their political leaning) based on samples of text that
they have authored, and which may or may not convey politically-charged
information explicitly.

In recent years, both text- and author-level inference have been implemented
with the aid of representations from transformers such as BERT 19 and others.
Models of this kind - which may be seen as large, pre-trained language models
- are able to capture deep contextual relations between words, and have been
shown to significantly improve downstream task results 20, 21. Despite the
benefits afforded, however, in this paper we hypothesise that the use of pre-
trained language models for political inference from text may be improved even
further with the aid of additional text representations. More specifically, we
ask how we may combine transformed-based text representations with both
syntactic information and psycholinguistics-motivated features, and ask which
of these so-called heterogeneous knowledge representations may have an impact
on different political inference tasks.

To shed light on these issues, the present work takes the form of a series of
experiments in supervised machine learning addressing a number of text- and
author-level tasks alike. As in much of the existing work in the field, some
of these experiments will make use of English text data but, in addition to
that, we will also address a number of tasks based on Portuguese text data as
well, and we will introduce a novel dataset for this particular language. Our
main contributions are summarised as follows.

  * i

A neural architecture that combines transformer-based language models,
syntactic dependencies and psycholinguistics-motivated features for political
bias and ideology inference from text.

  * ii

Text- and author-level formulations of the general political bias and ideology
inference tasks.

  * iii

Experiments involving both mainstream English and less-studied Portuguese text
data.

  * iv

A novel, large dataset of Twitter text data labelled with political stance
information.

The reminder of this paper is structured as follows. Section 2 reviews
existing work in political inference from text, and Section 3 describes the
computational tasks to be addressed in this work. Section 4 presents our main
approach to using heterogeneous knowledge representations. Section 5 summaries
our experiment results, which are further discussed in Section 6. Finally,
Section 7 presents conclusions and future work.

##  2 Related work

Table 1 presents an overview of recent NLP work on political bias and ideology
inference from text data. All selected studies happen to be devoted to the
English language. Further details are discussed below.

Table 1: Related work in political bias (top) and political ideology (bottom) inference from text. For each study, we report task category as either ‘bias’ (e.g., hyperpartisan news detection) or ‘ideology’ (political ideology, stance, and alignment), label granularity (t = text-level, a = author-level), main learning features (text or network relations), learning methods (e.g., RNN = recurrent networks, U = stylometry, CNN = convolutional networks, LogReg = logistic regression, SVM = Support Vector Machines, RGC = graph networks, NPOV=neutral point of view), and text genre (D = discourse/debate, N = news, T = Twitter, W = Wikipedia.) Study | Category | Labelling | Features | Method | Genre
---|---|---|---|---|---
4 | bias | t,a | text | U | N
2 | bias | t,a | text | CNN | N
22 | bias | t,a | text | LogReg | N
23 | bias | t,a | text | BERT | N
20 | bias | t,a | text | BERT | N
24 | bias | t,a | text | SVM, LogReg | N
25 | bias | t | text | NPOV | N
6 | bias | t | text | biLSTM | N
26 | ideology | t | text | RNN | D
27 | ideology | t | text | LogReg | N
28 | ideology | t | text,graph | CNN | N
21 | ideology | t | text | LSTM, BERT | N,T
29 | ideology | t | text,graph | FastText | T
30 | ideology | a | graph | RGC | W

###  2.1 Political bias

Extremely one-sided political bias has largely focused on the issue of
hyperpartisan news detection. The work in 4, which is among the first
prominent NLP studies in this field, analyses a corpus of extremely one-sided
news and presents a stylometry-based approach to distinguish biased and
neutral news, fake news and satire. Among other findings, results suggest that
stylometry is of limited use in fake news detection, and that left- and right-
wing news share a significant amount of stylistic similarities.

Some of the results from 4 were taken as the basis for the influential
SemEval-2019 shared task on hyperpartisan news detection in 5. The task
comprised two formulations of the problem, each of them based on a different
dataset. The by_article dataset contained 1,273 manually labelled texts, and
the by_publisher dataset contained 754,000 articles labelled via distant
supervision (based on the publishing source of each article.) Results reported
in 5 suggest that the by_publisher task was generally more challenging than
the by_article task.

Among the participant systems at SemEval-2019, the work in 2 reported the
overall highest accuracy in the by_article task. The system makes use of a
pre-trained ELMo 31 language model to encode news texts as input features to a
CNN classifier. This approach will be taken as a baseline to our own
experiments described in the next sections.

The work in 22 makes use of a logistic regression classifier to detect
hyperpartisan news with the aid of hand crafted features (e.g., bias scores
obtained from a bias lexicon, article- and sentence-level polarity,
subjectivity and modality scores etc.) and Universal Sentence Encoder
embeddings, among other alternatives. The system obtained the overall highest
F1 score in the by_article task at SemEval-2019.

The studies in 23 and 20 are among the first to attempt using pre-trained BERT
language models for hyperpartisan news detection. In both cases, however,
results remain below those obtained by several more traditional approaches in
both by_article and by_publisher tasks.

The work in 24 reported the overall highest accuracy in the by_publisher task
using a Logistic Regression classifier with a bag-of-words text
representation, outperforming a wide range of more complex models based on
deep neural networks and others.

The work in 25 takes a more application-oriented approach to hyperpartisan
bias detection by presenting a real-time system that flags political bias on
news articles, and then recommends similar articles from alternative sources.
To this end, the system makes use of a bias lexicon and unsupervised methods
for clustering articles by topic similarity.

Finally, the work in 6, although not an original participant system at
SemEval-2019, uses the SemEval by_article dataset to address the hyperpartisan
news detection task as well. The work makes use of a heterogeneous knowledge
representation consisting of BERT pre-trained model enriched with social and
political information and linguistically-motivated features alike, and obtains
results comparable to the top-performing systems at SemEval-2019 with the aid
of a multihead Bi-LSTM architecture.

###  2.2 Political ideology

In addition to extremely one-sided bias, natural language text may convey many
other more nuanced forms of political view, which are presently labelled as
‘ideology’ for conciseness. The work in 26 is among the first of this kind,
addressing the issue of political ideology (defined as left, right, or neutral
leaning) detection in text. In what nowadays may be seen as a standard
approach to the task, the work uses a recurrent neural network model and word
embeddings built from left- and right-leaning data to detect ideology in US
congressman debates. Results suggest that this approach outperforms a range of
logistic regression baseline systems using bag-of-words and word embeddings
representations.

Also in the US congressman debates domain, the work in 27 introduces a
sentiment-oriented model to identify political ideology in text, the
underlying assumption being that sentiment words may be revealing of an
individual’s political leaning (e.g., conservatives may arguably express more
positive sentiment towards the free-market topic etc.) To investigate this
issue, potentially relevant topics were selected from a debate corpus,
including issues related to health care, US military program and others, and
topic-specific sentiments were computed as a probability distribution over
ordinal polarity classes ranging from strongly positive to strongly negative.
Results suggest that a logistic regression classifier based on sentiment
features outperforms the use word embeddings and others.

The work in 28 addresses the issue of political ideology detection in news
text using a so-called multi-view approach. In this approach, document-level
features (e.g., the news headline and contents) and a network of links
exhibited in the text are regarded as being complementary properties in the
sense that authors may refer to links that reinforce their political views.
The study is carried out using a corpus of 120k politically-related news in
English, and results suggest that a multi-view approach based on convolutional
networks outperforms a range of baseline alternatives including the use of
logistic regression classifiers and hierarchical attention models, among
others.

The work in 21 addresses the task of detecting political ideology in news
texts from previously unseen media sources, which prevents models from
learning the text source rather than the ideology proper. The work makes use
of complementary knowledge obtained from Twitter and Wikipedia sources, and
uses adversarial adaptation and triplet loss pre-training (TLP) with both LSTM
and BERT models. Results suggest that combining TLP with additional Twitter
information outperforms a range of alternatives, including the use of pre-
trained transformer models alone, and those with access to additional
Wikipedia information.

The work in 29 addresses the task of characterising the general political
leaning of online media and influencers by using unsupervised learning to
determine the stance of Twitter users towards a polarising topic based on
their retweet behaviour, and then performing label propagation to take the
resulting user stance information as training data for media political leaning
detection. Results suggest that a combination of User-to-Hashtag and User-to-
Mention graph embeddings with BERT models built from both article titles and
contents outperforms the use of these individual strategies in isolation.

Finally, the work in 30 combines socially- and politically-related features to
address the issue of entity stance prediction, an which may be regarded as an
instance of author-level inference as discussed in Section 1. Examples of
entities under consideration include US presidents, parties, and states. The
study builds a heterogeneous information network from Wikipedia articles, in
which nodes are social entities and edges are relations between them (e.g.,
party affiliation, home state etc.) The network is combined with the Wikipedia
text summary of each entity using a RoBERTa transformer 32 in a gated
relational graph convolutional network for representation learning. Results
suggest that the approach outperforms a wide range of baseline alternatives,
including bag-of-words, average word embeddings, transformers and graph-based
models alike.

##  3 Task definitions

The present work addresses two text-level political inference tasks (T1,T2)
and three author-level tasks (T3,T4,T5) using data from three sources: the
SemEval-2019 Hyperpartisan news corpus 5, the BRmoral essay corpus 33 and a
novel dataset, hereby called GovBR corpus, to be introduced in Section 4.1.
These tasks are summarised in Table 2 and discussed individually in the next
sections.

Table 2: Text- and Author-level political inference tasks according to annotation level, target problem, class definition, corpus, dataset, and language. Task | Level | Target | Classes | Corpus | Dataset | Language
---|---|---|---|---|---|---
T1 | text | hyperpartisan news | hyperpartisan, neutral | SemEval | by_articles | English
T2 | text | political orientation | left, (centre), right | BRmoral | by_opinion | Portuguese
T3 | author | hyperpartisan news | hyperpartisan, neutral | SemEval | by_publisher | English
T4 | author | political orientation | left, (centre), right | BRmoral | by_author | Portuguese
T5 | author | political stance | for, against | GovBR |  | Portuguese

####  3.0.1 Text-level tasks (T1,T2)

Text-level tasks concern the inference of politically-charged information
directly associated with the meanings of the input texts, in which case class
labels are annotated at the individual text level. As discussed in Section 1,
this is analogous to sentiment analysis, stance classification and related
tasks.

Task T1 addresses the issue of text-level hyperpartisan news detection based
on the SemEval by_articles dataset 5. This consists of a binary classification
task intended to distinguish ‘hyperpartisan’ from ‘neutral’ information, as in
the following examples.

  * •

Hyperpartisan: ‘Trump can’t get Congress to repeal Obamacare, he’s making
changes that will penalize low-income people’

  * •

Neutral: ‘Colin Kaepernick told a CBS reporter that he would represent the
national anthem if he was hired by an NFL team’

Task T2 addresses the issue of text-level political orientation detection
based on the BRmoral corpus 33 by_opinion dataset following both binary
(‘left’ / ‘right’) and ternary (‘left’ / ‘centre’ / ‘right’) class definitions
(to be further discussed in Section 4.1.2.) Examples taken from short essays
related to the issue of same-sex marriage are illustrated as follows
(translated from the original texts in Portuguese.)

  * •

Left-leaning: ‘Agreed, same-sex people must have their marriages valid, as
they pay taxes and have the same civil obligations, so they should also have
the same rights as the other.’

  * •

Centre: ‘It’s not up to the State to forbid this. However if a person asks me
if I’m in favour, I’ll say no, although I respect (their choice).’

  * •

Right-leaning: ‘From the perspective of the civil institution, I do not see
problems in marriage, however, the Christian doctrine makes it clear that the
family consists of a man and a woman.’

####  3.0.2 Author-level tasks (T3,T4,T5)

Author-level tasks concern the inference of politically-charged information
related to the individual who wrote the input texts rather than to the literal
meaning of the text. In this case, class labels are annotated at the author
(or publisher) level. As discussed in Section 1, this is analogous to NLP
author profiling.

Task T3 is the author-level version of previous task T1, addressing the issue
of author-level hyperpartisan news detection based on the SemEval by_publisher
dataset 5. Once again, this consists of a binary classification task intended
to distinguish ‘hyperpartisan’ from neutral’ information, but using weakly
labelled data determined by the source of information rather than individually
annotated texts. Thus, for instance, all texts produced by a publisher deemed
to be a hyperpartisan source are labelled as ‘hyperpartisan’ news regardless
of their actual contents.

Task T4 is the author-level version of previous task T2, addressing the issue
of author-level political orientation detection based on the BRmoral 33
by_author dataset following both binary (‘left’ / ‘right’) and ternary (‘left’
/ ‘centre’ / ‘right’) class definitions. To this end, all texts are weakly
labelled with the self-reported political orientation of their authors
regardless of the actual text contents. Thus, for instance, opinions that are
annotated (at text-level) as ‘left-leaning’ for the purpose of previous Task
T2 may nevertheless be assigned a (author-level) ‘right-leaning’ label if
their authors happen to identify themselves as right-leaning individuals.

Finally, task T5 addresses the issue of author-level stance classification
based on the GovBR corpus to be described in the next section. This consists
of a binary classification task intended to distinguish Twitter users who are
‘for’ or ‘against’ the current president of Brazil. In this case, tweets are
weakly labelled with for/against stance information derived from popular
hashtags. Thus, for instance, all tweets accompanied by a #RespectThePresident
hashtag are assumed to be favourable to the president (the actual hashtags are
not included in the data.) Examples of both classes are as follows.

  * •

For: ‘THIS IS MY PRESIDENT’

  * •

Against: ‘This misgovernment is formed by indecent, immoral, ignorant, stupid
and perverse people.’

##  4 Materials and method

The goal of the present study is to investigate the use of heterogeneous
knowledge representations - based on transformer-based language models,
syntactic dependencies, and psycholinguistics-motivated features - for
political bias and ideology inference from text as discussed in the previous
section. In what follows we describe the data for each task, the classifier
models to be investigated, and evaluation procedure.

###  4.1 Data

The following sections discuss the three corpora to be taken as train and test
data for our experiments, and present descriptive statistics.

####  4.1.1 SemEval-2019 hyperpartisan news corpus (tasks T1 and T3)

For the hyperpartisan news detection tasks T1 and T3, we will make use a
subset of the SemEval-2019 Hyperpartisan news corpus 5 in the English
language. The SemEval-2019 corpus consists of political news organised in two
datasets called by_articles and by_publisher, both of which annotated with
‘hyperpartisan’ or ‘neutral’ labels. Hyperpartisan news convey extreme one-
sided information of either liberal or conservative nature alike. The full
corpus data - whose train subset is presently used in our experiments -
originally conveys 645 news articles in the by_articles set, and 750 million
articles in the by_publisher set.

As discussed in the previous section, by_articles texts are labelled
individually according to their contents, and will be taken as an input to
text-level hyperpartisan news detection (task T1). by_publisher texts, by
contrast, are weakly labelled according to their media source, and will be
taken as the input for author-level hyperpartisan news detection (task T3).
Despite using well-known shared task data, however, we notice that we do not
presently seek to outperform the existing SemEval benchmark, but rather
compare a number of novel computational strategies among themselves.

For the purpose of the present work, the original train portions of both
datasets were randomly split into development (80%) and test (20%) sets. Table
3 presents the resulting class distribution.

Table 3: SemEval-2019 by_articles and by_publisher class distribution in development and test sets. |  by_articles |  by_publisher
---|---|---
Set | hyperpartisan | neutral | Total | hyperpartisan | neutral | Total
Development | 332 (64.3%) | 184 (35.7%) | 516 | 1235 (49.4%) | 1265 (50.6%) | 2500
Test | 75 (58.1%) | 54 (41.9%) | 129 | 492 (49.2%) | 508 (50.8%) | 1000

####  4.1.2 BRmoral essay corpus (tasks T2 and T4)

For the political orientation detection tasks T2 and T4, we will make use of
the BRmoral essay corpus 33 in the Portuguese language. This consists of short
essays about eight topics of liberal and conservative nature alike (same-sex
marriage, gun possession, abortion, death penalty, drug legalisation, lowering
of criminal age, racial quotas, and tax exemptions for churches) labelled with
both stance scores (from ‘totally against’ to ‘totally for’ each topic) and
authors’ demographics, including their self-reported political orientation
from ‘extreme left’ to ‘extreme right’. The full corpus data conveys 4080
essays written by 510 crowd-sourced volunteers 33.

The dual labelling scheme in the BRmoral corpus (i.e., either based on
individual stances or author’s own political orientation) gives rise to two
dataset definitions, hereby called by_opinion and by_author for analogy with
the SemEval by_articles and by_publisher datasets discussed in the previous
section. Both by_opinion and by_author are labelled with ‘left’, ‘right’ and,
depending on the task under consideration (see below), also with ‘centre’
information.

by_opinion takes as labels the liberal and conservative stance information
available from the corpus to determine, albeit indirectly, a text’s likely
political leaning. More specifically, texts expressing an opinion against so-
called liberal topics (same-sex marriage, abortion, drug legalisation, and
racial quotas), or those expressing opinions in favour of so-called
conservative topics (death penalty, gun possession, lowering of criminal age,
and tax exemptions for churches), are labelled as ‘right’, and so forth. This
dataset will be taken as an input to text-level political orientation
detection (task T2).

The by_author dataset, by contrast, takes as labels the actual authors’
political orientation information available from the corpus, in what may be
seen as an instance of weakly labelling not unlike the SemEval by_publisher
labels discussed in the previous section. BRmoral by_author texts will be
taken as an input to author-level political orientation detection (task T4).

Both datasets were randomly split into development (80%) and test (20%) sets.
Table 4 presents the resulting class distribution.

Table 4: BRmoral by_opinion and by_author class distribution in development and test sets. |  by_opinion |  by_author
---|---|---
Set | left | centre | right | Total | left | centre | right | Total
Development | 1201 (36.8%) | 685 (21.0%) | 1378 (42.2%) | 3264 | 1210 (37.1%) | 1158 (35.5%) | 896 (27.4%) | 3264
Test | 299 (36.6%) | 176 (21.6%) | 341 (41.8%) | 816 | 310 (38.0%) | 282 (34.5%) | 224 (27.5%) | 816

####  4.1.3 GovBR political stance corpus (task T5)

Finally, for the political stance task T5, we created a novel language
resource based on Twitter data in the Portuguese language, hereby called the
GovBR corpus. GovBR comprises a collection of tweets written by users who
expressed a clear stance towards the current president of Brazil. The corpus
was built by selecting two disjoint sets of users - supporters and opponents
of the said president - according to the use of a number of popular
politically-charged hashtags (e.g., #RespectThePresident or #NotHim. The full
corpus data - from which non-political tweets were filtered out as discussed
below - conveys 13.5 million tweets written by 5452 unique users.

For each selected user, all their publicly available tweets (i.e.,
disregarding their retweets) were downloaded. Users who simultaneously
promoted supportive and opposing hashtags were discarded, and so were all
hashtags and all messages shorter than five words. Finally, tweets that did
not convey a minimal level of political content were also discarded. To this
end, we computed a TF-IDF representation of the political section of the Folha
de SP newspaper111https://www.kaggle.com/marlesson/news-of-the-site-folhauol,
and kept only the tweets conveying a minimum degree of similarity to the
political news texts. After the removal of non-political tweets, we obtained
approximately 25 tweets per user.

GovBR politically-related tweets will be taken as the input for author-level
political stance detection (task T5). In our current work, we use a balanced
subset of this data consisting of 4000 randomly selected tweets. These were
randomly split into development (80%) and test (20%) sets as illustrated in
Table 5

Table 5: GovBR class distribution in development and test sets. Set | against | for | Total
---|---|---|---
Development | 1600 (49.9%) | 1608 (50.1%) | 3208
Test | 405 (50.5%) | 397 (49.5%) | 802

###  4.2 Models

As a means to investigate the issue of political inference from text (tasks
T1-T5 described in the previous sections), in what follows we propose
combining heterogeneous knowledge representations into a convolutional neural
network architecture. An overview of this architecture is presented in Section
4.2.1, and its individual components are described in Section 4.2.2.

####  4.2.1 Architecture

We envisaged a convolutional neural network for political inference from text
that combines three kinds of text representation: (i) pre-trained language
models provided by Bidirectional Encoder Representations from Transformers
(BERT) 19, hereby called bert; (ii) syntactic bigram counts computed from
dependency graphs 34, hereby called sngram, and (iii) psycholinguistics-
motivated features obtained from Linguistic Inquiry and Word Count (LIWC) 35
and from the Medical Research Council (MRC) database 36, hereby called psych.
This architecture is illustrated in Figure 1 and further discussed below.

Figure 1: General architecture.

Given a set of input documents (bottom left of the figure), we use a text
classifier model that takes as an input both standard text features
represented as contextual embeddings bert (top left), and engineered features
(bottom centre) that combine the alternative text representations based on
syntactic dependencies sngram and psycholinguistics-motivated features psych.
In this approach, bert embeddings are taken as an input to five convolutional
layers (Conv1-Conv5) followed by batch normalisation, a max pooling and a 0.5
dropout layers, whereas engineered features are processed in parallel by a
kernel of size 1, also followed by a normalisation layer and max pooling.
Finally, the output of the operations Conv1-Conv5 is concatenated with the
engineered feature vector followed by a 0.5 dropout, and a softmax activation
function produces the class predictions.

The full model architecture, hereby called bert+sngram+psych, will be
evaluated against a number of baseline systems, and also against some of its
individual components as discussed in Section 4.3.

####  4.2.2 Text representations

In the bert+sngram+psych model, input texts are to be represented as
contextual embeddings (our bert component), syntactic bigram counts sngram,
and psycholinguistics-motivated features (psych). These components are
described as follows.

Bidirectional Encoder Representations from Transformers (BERT) 19 are now
mainstream in NLP and related fields, and are the basis for our bert
architectural component as well. This consists of pre-trained BERT language
models fine-tuned for each of our classification tasks T1-T5. For the English
language models (tasks T1 and T3), we use base-uncased BERT, and for the
Portuguese language (tasks T2, T4, and T5) we use multilingual-base-uncased
BERT.

The sngram component explores the use of text structural information to enrich
our classifier models by computing syntactic bigram counts from dependency
graphs. To this end, we first compute a syntactic dependency graph from the
input text using SpaCy222https://spacy.io/usage/linguistic-
features#dependency-parse, and then generate a TF-IDF bigram model as
suggested in 34. For the English language models (tasks T1 and T3), we use the
en_core_web_sm pipeline, and for the Portuguese language (tasks T2, T4, and
T5) we use the pt_core_news_sm pipeline. Finally, we perform univariate
feature selection using F1 as a score function in order to keep only the $k$
best features. Optimal $k$ values for each task were obtained through grid
search on development data.

The psych component makes use of psycholinguistics-motivated features computed
with the aid of both LIWC 35 and MRC 36 lexicons. Examples of LIWC word
categories include those related to attention focus (e.g., pronouns and verb
tense), affective or emotional processes (positive and negative emotions,
anxiety, fear etc.), social relationships (e.g., family, friends etc.) and
others. Similarly, MRC categories cover lexical features such as concreteness,
age of acquisition, and others. For the English language models (tasks T1 and
T3), we use the 93-feature LIWC-2015 lexicon 37 and the 9-feature MRC database
36. For the Portuguese language (tasks T2, T4, and T5) we use 64-feature LIWC-
BR 38 and the 6 MRC-like features from 39.

Both LIWC and MRC text representations consist of word category counts
normalised by document size, in which words that belongs to more than one
category update all related counts (e.g., ‘she’ is a pronoun and also a
feminine word etc.) Both representations are concatenated as a single vector
of size $93+9=101$ features for English, or $64+6=70$ features for Portuguese.
As in the case of the syntactic features discussed above, we once again
perform univariate feature selection with F1 as a score function to obtain the
$k$ best features for each task.

###  4.3 Procedure

We conducted a series of experiments focused on tasks T1-T5 introduced in
Section 3 to assess the use of the bert+sngram+psych model and some of its
subcomponents, namely, bert, sngram, psych alone, and also the two BERT-based
pairs bert+sngram and bert+psych. More specifically, our goal is to
investigate how each of these alternatives compare to two baseline systems,
namely, the Bertha von Suttner model described in 2, which was the overall
best-performing system at SemEval-2019 Hyperpartisan news detection shared
task 5, and the use of BERT alone as a classifier, hereby called
BERT.baseline.

All models were trained in 30 epochs using a development dataset partition,
and then evaluated using a previously unseen test data as described in Section
4.1. For BERT-based models, additional pre-processing was performed to remove
all non-alphabetic characters, links and HTML tags. All input documents were
limited to their first 300 tokens, and shorter documents were completed with
the [PAD] token. This representation was taken as the input to a BERT model of
size 768, resulting in text embeddings of size $300\times 768$.

sngram and psych features are concatenated as a single vector, and a z-score
function is applied to obtain standardised value ranges. Table 6 summarises
the actual number of features considered by each models and for each corpus.

Table 6: Number of features used in psych and sngram vectors in each corpus. Corpus | psych | sngram
---|---|---
SemEval by_articles | 37 | 13,107
SemEval by_publisher | 78 | 38,220
BRmoral by_opinion | 55 | 13,466
BRmoral by_author | 22 | 13,399
GovBR | 25 | 6,998

Evaluation proper was carried out by (i) measuring Accuracy (Acc), macro
$F_{1}$ ($F_{1}$), Precision (P) and Recall (R) scores, (ii) by assessing
statistical significant differences between models, and (iii) by providing
model prediction explanations. To this end, statistical significance is
assessed by using the McNemar test 40 in the case of binary classifiers, and
by using the Stuart-Maxwell test 41, 42 for ternary classifiers. For each
task, two kinds of significance tests are conducted. First, we identify those
models that are statistically superior to the reference model in 2. Second, we
identify the groups of models that are statistically distinguishable from
others. Finally, we performed eli5 prediction
explanation333https://eli5.readthedocs.io/en/latest/ to compute the word
features more strongly correlated with each class and task, as discussed in
Section 6.

##  5 Results

This section presents results of the full model bert+sngram+psych and its
subcomponents (bert, sngram, psych, bert+sngram, and bert+psych) compared
against those obtained by the work in 2 and by BERT alone as a classifier
(bert.baseline).

Results are to be reported as Accuracy (Acc), $F_{1}$, Precision (P) and
Recall (R) scores divided into three groups: (1) on the top row baselines from
2 and bert.baseline, (2) following by model components bert, sngram, psych,
bert+sngram, and bert+psych, and (3) on the bottom row the full model
bert+sngram+psych. In all scenarios, best accuracy scores are highlighted, and
also marked as * when found to be statistically superior to the baseline
system in 2. Finally, in addition to the main results report for each task,
models are also depicted in statistically significant clusters ($p<0.05$)
according to their accuracy scores.

###  5.1 Task T1: Text-level hyperpartisan news detection

Results for task T1 - text-level hyperpartisan news detection - using the
SemEval corpus by_articles dataset are summarised in Table 7 and further
discussed below.

Table 7: Text-level hyperpartisan news detection results.  Model | Acc | $F_{1}$ | P | R
---|---|---|---|---
Jiang et. al. | 0.72 | 0.65 | 0.69 | 0.61
BERT.baseline | 0.68 | 0.65 | 0.61 | 0.71
bert | 0.75 | 0.69 | 0.73 | 0.65
sngram | 0.69 | 0.69 | 0.70 | 0.69
psych | 0.47 | 0.46 | 0.45 | 0.47
bert+sngram | 0.78* | 0.77 | 0.78 | 0.78
bert+psych | 0.74 | 0.71 | 0.66 | 0.76
bert+sngram+psych | 0.67 | 0.64 | 0.67 | 0.67

Based on these results, we notice that the best-performing model is
bert+sngram. The difference between this and the baseline in 2 is
statistically significant ($\chi=5.161$, $\alpha$ = 0.05, $p$ < 0.05). The
full model bert+sngram+psych, by contrast, ranks considerably lower. To
further illustrate this outcome, the models were clustered into homogeneous
groups (A,B,C) by statistical significance according to their accuracy scores
as illustrated in Table 8.

Table 8: Text-level hyperpartisan news detection homogeneous groups.  Model | Acc | Groups
---|---|---
bert+sngram | 0.78* | A |  |
bert | 0.75 | A |  |
bert+psych | 0.74 | A |  |
Jiang et al. | 0.72 |  | B |
sngram | 0.69 |  | B |
BERT.baseline | 0.68 |  | B |
bert+sngram+psych | 0.67 |  | B |
psych | 0.47 |  |  | C

We notice that, in addition to the best-performing bert+sngram model, both
bert and bert+psych obtain, to a lesser extent, statistically similar results
within group A. The full model and the reference baseline in 2, by contrast,
are both members of group B.

###  5.2 Task T2: Text-level political orientation detection

Results for task T2 - text-level political orientation detection - using the
BRmoral corpus by_opinion dataset for both binary (left, right) and ternary
(left,centre,right) classification are summarised in Table 9 and further
discussed below.

Table 9: Text-level political orientation detection results. | Binary classification | Ternary classification
---|---|---
Model | Acc | $F_{1}$ | P | R | Acc | $F_{1}$ | P | R
Jiang et. al. | 0.76 | 0.76 | 0.77 | 0.76 | 0.62 | 0.61 | 0.61 | 0.62
BERT.baseline | 0.57 | 0.57 | 0.57 | 0.57 | 0.43 | 0.36 | 0.43 | 0.43
bert | 0.75 | 0.75 | 0.76 | 0.75 | 0.60 | 0.56 | 0.59 | 0.60
sngram | 0.70 | 0.70 | 0.71 | 0.70 | 0.55 | 0.53 | 0.55 | 0.55
psych | 0.68 | 0.68 | 0.68 | 0.68 | 0.52 | 0.50 | 0.49 | 0.52
bert+sngram | 0.78 | 0.78 | 0.78 | 0.78 | 0.64 | 0.62 | 0.63 | 0.64
bert+psych | 0.76 | 0.76 | 0.77 | 0.76 | 0.60 | 0.59 | 0.59 | 0.60
bert+sngram+psych | 0.73 | 0.73 | 0.74 | 0.73 | 0.58 | 0.58 | 0.58 | 0.58

Once again, the best-performing model for both binary and ternary
classification is bert+sngram. However, differences between this and others,
including the baseline in 2, were not found to be statistically significant.
To further illustrate this outcome, homogeneous groups related to the binary
classification task are shown in Table 10, and groups related to ternary
classification are shown in Table 11.

Table 10: Binary text-level political orientation detection homogeneous groups.  Model | Acc | Groups |
---|---|---|---
bert+sngram | 0.78 | A |  |  |
Jiang et. al. | 0.76 | A |  |  |
bert+psych | 0.76 | A |  |  |
bert | 0.75 | A |  |  |
bert+sngram+psych | 0.73 |  | B |  |
sngram | 0.70 |  | B |  |
psych | 0.68 |  |  | C |
BERT.baseline | 0.57 |  |  |  | D
Table 11: Ternary text-level political orientation detection homogeneous groups.  Model | Acc | Groups |
---|---|---|---
bert+sngram | 0.64 | A |  |  |
Jiang et. al. | 0.62 | A |  |  |
bert | 0.60 | A |  |  |
bert+psych | 0.60 |  | B |  |
bert+sngram+psych | 0.58 |  | B |  |
sngram | 0.55 |  | B |  |
psych | 0.52 |  |  | C |
BERT.baseline | 0.43 |  |  |  | D

In both binary and ternary classification tasks, although bert+sngram still
obtains the highest accuracy scores, its simpler bert sub-component (i.e., the
combination of a fine-tuned BERT model with a CNN classifier, as discussed in
Section 4) is statistically similar. The full model, bert+sngram+psych,
composes the group B in both classification tasks, ranking lower than the
reference system 2.

###  5.3 Task T3: Author-level hyperpartisan news detection

Results for task T3 - author-level hyperpartisan news detection - using the
SemEval corpus by_publisher dataset are summarised in Table 12 and further
discussed below.

Table 12: Author-level hyperpartisan news detection results.  Model | Acc | $F_{1}$ | P | R
---|---|---|---|---
Jiang et. al. | 0.56 | 0.62 | 0.55 | 0.71
BERT.baseline | 0.54 | 0.60 | 0.51 | 0.75
bert | 0.58 | 0.67 | 0.55 | 0.85
sngram | 0.57 | 0.55 | 0.57 | 0.57
psych | 0.53 | 0.53 | 0.53 | 0.53
bert+sngram | 0.57 | 0.54 | 0.59 | 0.57
bert+psych | 0.61* | 0.67 | 0.58 | 0.80
bert+sngram+psych | 0.55 | 0.52 | 0.50 | 0.55

Based on these results, we notice that the best-performing alternative is
bert+psych. The difference between this and the baseline in 2 is statistically
significant ($\chi$ = 6.715, $\alpha$ = 0.05, $p$ < 0.01). Models were
clustered into homogeneous groups by statistical significance according to
their accuracy scores as illustrated in Table 13.

Table 13: Author-level hyperpartisan news detection homogeneous groups.  Model | Acc | Groups
---|---|---
bert+psych | 0.61* | A |
bert | 0.58 | A |
bert+sngram | 0.57 | A |
sngram | 0.57 |  | B
Jiang et al. | 0.56 |  | B
bert+sngram+psych | 0.55 |  | B
BERT.baseline | 0.54 |  | B
psych | 0.53 |  | B

According to Table 13, group A includes most alternatives that are based on
BERT language models, and once again the difference between the full model
bert+sngram+psych and the reference baseline in 2, both of which in group B,
is not statistically significant.

###  5.4 Task T4: Author-level political orientation detection

Results for task T4 - author-level political orientation detection - using the
BRmoral corpus by_author dataset for both binary (left, right) and ternary
(left,centre,right) classification are summarised in Table 14 and further
discussed below.

Table 14: Author-level political orientation detection results. | Binary classification | Ternary classification
---|---|---
Model | Acc | $F_{1}$ | P | R | Acc | $F_{1}$ | P | R
Jiang et al. | 0.61 | 0.61 | 0.61 | 0.61 | 0.38 | 0.37 | 0.37 | 0.38
BERT.baseline | 0.56 | 0.55 | 0.55 | 0.56 | 0.37 | 0.31 | 0.37 | 0.37
bert | 0.53 | 0.53 | 0.58 | 0.53 | 0.41 | 0.37 | 0.41 | 0.41
sngram | 0.56 | 0.56 | 0.57 | 0.56 | 0.38 | 0.37 | 0.37 | 0.38
psych | 0.59 | 0.56 | 0.57 | 0.59 | 0.37 | 0.35 | 0.35 | 0.37
bert+sngram | 0.63 | 0.63 | 0.63 | 0.63 | 0.41 | 0.37 | 0.40 | 0.41
bert+psych | 0.60 | 0.53 | 0.59 | 0.60 | 0.36 | 0.30 | 0.44 | 0.36
bert+sngram+psych | 0.59 | 0.59 | 0.61 | 0.59 | 0.42 | 0.41 | 0.41 | 0.42

The best-performing model for binary classification is bert+sngram, and for
ternary classification is bert+sngram+psych. However, the differences between
these and the baseline in 2 were not found to be significant. Homogeneous
groups for the binary task are illustrated in Table 15, and groups for the
ternary task are illustrated in Table 16.

Table 15: Binary author-level political orientation detection homogeneous groups.  Model | Acc | Groups
---|---|---
bert+sngram | 0.63 | A |
Jiang et al. | 0.61 | A |
bert+psych | 0.60 | A |
psych | 0.59 | A |
bert+sngram+psych | 0.59 | A |
BERT.baseline | 0.56 | A |
sngram | 0.56 |  | B
bert | 0.53 |  | B
Table 16: Ternary author-level political orientation detection homogeneous groups.  Model | Acc | Groups
---|---|---
bert+sngram+psych | 0.42 | A |
bert+sngram | 0.41 | A |
bert | 0.41 | A |
Jiang et al. | 0.38 | A |
sngram | 0.38 | A |
psych | 0.37 |  | B
BERT.baseline | 0.37 |  | B
bert+psych | 0.36 |  | B

In both binary and ternary classification tasks, we notice that several models
turned out to obtain statistically equivalent results. This outcome, which is
similar to what has been observed in the text-level political orientation task
(cf. Section 5.2) based on the same corpus, will be further discussed in
Section 6.

###  5.5 Task T5: Author-level political stance detection

Results for task T5 - author-level political stance detection - using the
GovBR corpus are summarised in Table 17 and further discussed below.

Table 17: Author-level political stance detection results.  Model | Acc | $F_{1}$ | P | R
---|---|---|---|---
Jiang et. al. | 0.58 | 0.55 | 0.62 | 0.58
BERT.baseline | 0.53 | 0.52 | 0.54 | 0.53
bert | 0.61 | 0.59 | 0.64 | 0.61
sngram | 0.53 | 0.53 | 0.53 | 0.53
psych | 0.52 | 0.51 | 0.52 | 0.52
bert+sngram | 0.62 | 0.62 | 0.62 | 0.62
bert+psych | 0.60 | 0.60 | 0.60 | 0.60
bert+sngram+psych | 0.59 | 0.58 | 0.59 | 0.59

Once again, the best-performing model is bert+sngram, but others, including
the baseline in 2, were found to be similar. The corresponding homogeneous
groups are illustrated in Table 18.

Table 18: Author-level political stance detection homogeneous groups.  Model | Acc | Groups
---|---|---
bert+sngram | 0.62 | A |
bert | 0.61 | A |
bert+psych | 0.60 | A |
bert+sngram+psych | 0.59 | A |
Jiang et. al. | 0.58 | A |
BERT.baseline | 0.53 |  | B
sngram | 0.53 |  | B
psych | 0.52 |  | B

As in some of the previous experiments, although bert+sngram still obtains the
highest accuracy among the alternatives, some of its simpler sub-components
(as bert, in this case) were found to be statistically similar. Moreover, the
full model bert+sngram+psych is once again statistically similar to the
reference baseline in 2.

##  6 Discussion

In what follows we summarise our main results (Section 6.1) and report
prediction explanations for the main classification tasks.

###  6.1 Results summary

Table 19 shows the tasks in which each of the models under evaluation ranks
among the top-performing alternatives (i.e., belonging to cluster A in each of
the homogeneous groups illustrated in the previous section.)

Table 19: Models that rank in the top-performing cluster (A) for each task. | Text-level tasks | Author-level tasks
---|---|---
Model | Wins | T1 | T2.bin | T2.ter | T3 | T4.bin | T4.ter | T5
Jiang et al. | 5 |  | A | A |  | A | A | A
BERT.baseline | 1 |  |  |  |  | A |  |
bert | 6 | A | A | A | A |  | A | A
sngram | 1 |  |  |  |  |  | A |
psych | 1 |  |  |  |  | A |  |
bert+sngram | 7 | A | A | A | A | A | A | A
bert+psych | 5 | A | A |  | A | A |  | A
bert+sngram+psych | 3 |  |  |  |  | A | A | A

From these results, a number of observations are warranted. First, we notice
that there is a large number of statistically-similar models in the author-
level tasks (on the right of the table), particularly in the case of the essay
(tasks T4) and Twitter (task T5) domains. This was to some extent to be
expected as the information to be learned from author-level inference is less
explicit in the input texts, making these tasks possibly more challenging than
text-level inference in general.

Second, we notice that the full model, comprising the main CNN architecture
and bert, sngram and psycho sub-components, is generally not the best choice,
being often outperformed by simpler alternatives and/or by the reference
baseline system in 2.

Regarding the role of individual sub-components of the main architecture, we
notice that using psych or sngram alone is clearly insufficient, and that even
the use of the bert component alone generally fails to deliver optimal
results. This outcome suggests that using fine-tuned BERT and the CNN
architecture alone, as in the present bert model (not to be mistaken by the
standard BERT.baseline model in the second row from the top, which does not
use a CNN classifier) explains much of the best results obtained across our
experiments, but not all of them. In fact, it is the combination of BERT and
sngrams in the CNN architecture (represented by the bert+sngram model) that
generally obtains the best results among these alternatives, being the top-
performing model in 5 out of 7 tasks. This outcome may be partially explained
by the simultaneous use of two representations of the input text (i.e.,
linearly ordered tokens and count-based syntactic bigram features), but we
notice that larger models using this strategy (e.g., including
psycholinguistics-motivated features) are not necessarily better.

Finally, we notice that the baseline in 2 remains highly competitive and,
although seldom obtaining the highest accuracy, it is often found within the
group of top-performing alternatives.

###  6.2 Feature importance

As a means to illustrate the word features more strongly correlated with each
class and task, we performed eli5 model explanation to obtain word weights
representing the change (decrease/increase) of the evaluation score when a
given feature is shuffled.

Table 20 presents the most important features associated with the
hyperpartisan (i.e., non-neutral) class in the SemEval tasks T1 (by_articles)
and T3 (by_publisher) datasets.

Table 20: Text-based (left) and author-based (right) hyperpartisan news detection most important features. T1: Text-level | T3: Author-level
---|---
weight | feature | weight | feature
10.467 | cnn | 6.02 | window
10.169 | american | 5.585 | bush
10.069 | it | 5.542 | mr
9.905 | women | 5.149 | that
9.708 | hillary | 4.833 | iraq
9.536 | her | 4.367 | nyse
9.507 | now | 4.089 | billion
… | … | … | …
-6.754 | million | -4.699 | reuters
-6.756 | muslim | -4.829 | percent
-6.952 | rally | -5.025 | globalpost
-7.46 | donald | -5.463 | mexico
-7.531 | isis | -5.629 | california
-7.895 | <BIAS> | -6.268 | albuquerque
-8.17 | mr | -6.921 | ap

Table 21 presents the most important features associated with the left/right
classes in the BRmoral corpus tasks T2 and T4 (by_opinion and by_author
datasets, respectively.)

Table 21: Text-level (left) and author-level (right) political orientation detection most important features. T1: Text-level | T3: Author-level
---|---
left orientation | right orientation | left orientation | right orientation
weight | feature | weight | feature | weight | feature | weight | feature
2.533 | remove | 2.743 | black | 0.902 | women | 0.628 | favour
2.388 | guns | 2.526 | choice | 0.805 | about | 0.618 | mine
2.385 | institution | 2.493 | love | 0.739 | lay | 0.618 | be (present)
2.29 | am | 2.278 | marriage | 0.668 | society | 0.6 | since
2.234 | churches | 2.195 | wed | 0.654 | more | 0.587 | acts
1.86 | money | 2.174 | couple | 0.643 | body | 0.549 | should
1.807 | god | 2.154 | abortion | 0.625 | population | 0.54 | be (subjunctive)
1.751 | youth | 1.977 | alcohol | 0.603 | while | 0.533 | freedom
1.727 | life | 1.965 | traffic | 0.596 | alcohol | 0.481 | they
1.696 | for | 1.944 | gender | 0.595 | think | 0.465 | I
… | … | … | … | … | … | … | …
-1.677 | black | -1.738 | reduce | -0.515 | defend | -0.483 | she
-1.698 | child | -1.746 | innocent | -0.515 | mine | -0.494 | country
-1.851 | law | -1.817 | church | -0.516 | they | -0.494 | are
-1.857 | crimes | -1.953 | remove | -0.528 | crimes | -0.507 | population
-1.984 | favour | -2.111 | although | -0.546 | because | -0.523 | this_way
-2.017 | consciousness | -2.114 | have | -0.572 | same | -0.526 | women
-2.029 | alcohol | -2.138 | institution | -0.59 | hideous | -0.551 | some
-2.083 | hideous | -2.394 | churches | -0.633 | colour | -0.621 | or
-2.285 | prohibition | -2.505 | guns | -0.703 | am | -0.621 | public
-2.416 | freedom | -3.19 | perhaps | -0.755 | be | -0.658 | lay

Finally, Table 22 presents the most important features associated with
political stance in GovBR task T5.

Table 22: Political stance detection most important features. weight | feature | weight | feature
---|---|---|---
5.826 | supreme_court | -4.087 | came
5.709 | jair_bolsonaro | -4.138 | let’s_go
5.159 | communists | -4.161 | some
4.875 | visit | -4.201 | poor
4.789 | senator | -4.235 | human
4.694 | criminal | -4.33 | (president, derogatory)
4.653 | red | -4.399 | out
4.589 | care | -4.662 | sportive
4.561 | call | -4.687 | damn
4.507 | thinks | -4.899 | political

##  7 Final remarks

This paper has addressed the issue of how to combine transformed-based text
representations, which are main stream in NLP and related fields, with both
syntactic dependency information and psycholinguistics-motivated features for
political inference from text data. In doing so, we considered both text- and
author-level task definitions in both English and Portuguese languages, and
introduced a novel dataset devoted the latter.

As expected in experiments involving a range of tasks, datasets and languages,
our present results vary considerably across evaluation settings and, although
BERT remains a robust baseline for many of these tasks, in most cases it was
possible to obtain significant improvements by making use of additional
representations. This is not to say, however, that combining all current three
text representations (BERT, syntax and psycholinguistics) into a single model
is the best option. In particular, it was a subset of our original CNN
architecture combining only BERT and the syntactic dependency model that
obtained overall best results in most tasks.

The current work leaves a number of opportunities for further research. First,
we notice that political bias and ideology are relatively broad terms that may
actually include a wide range of distinct politically-related phenomena, and
that future NLP studies may benefit from more fine grained task definitions.

We notice also that many other pre-trained language models have been made
available in recent years, including ELMo 31, XLNet 43, RoBERTa 32, GPT-3 44.
Whether any of these may outperform BERT when combined with other text
representations (as in the present work) remains an open research question.

Finally, the present use of text representations is only a first step towards
more informed models that may ultimately combine BERT with many other text-
and author-level features. In particular, the present architecture may be
expanded with, for instance, sentiment or emotion-related information, or even
with author demographics (e.g., gender, age, personality traits, moral
foundations etc.) obtained with the aid of author profiling classifiers 16.
These and many other related possibilities are also left as future work.

### Author contributions

Samuel Caetano da Silva: Conceptualisation, Methodology, Software, Validation,
Formal analysis, Investigation, Writing - original draft, reviewing and
editing. Ivandré Paraboni: Conceptualisation, Writing - review and editing,
supervision.

### Financial disclosure

The first author received support from the Brazilian Foundation CAPES -
Coordination for the Improvement of Higher Education Personnel, under grant
88882.378103/2019-01.

### Conflict of interest

The authors declare no potential conflict of interests.

## References

  * 1 Santos Wesley Ramos, Paraboni Ivandré. Moral Stance Recognition and Polarity Classification from Twitter and Elicited Text. In: :1069–1075; 2019; Varna, Bulgaria.
  * 2 Jiang Ye, Petrak Johann, Song Xingyi, Bontcheva Kalina, Maynard Diana. Team Bertha von Suttner at SemEval-2019 Task 4: Hyperpartisan News Detection using ELMo Sentence Representation Convolutional Network. In: :840–844Association for Computational Linguistics; 2019; Minneapolis, Minnesota, USA.
  * 3 Pavan Matheus Camasmie, Santos Wesley Ramos, Paraboni Ivandré. Twitter Moral Stance Classification using Long Short-Term Memory Networks. In: :636–647Springer; 2020.
  * 4 Potthast Martin, Kiesel Johannes, Reinartz Kevin, Bevendorff Janek, Stein Benno. A Stylometric Inquiry into Hyperpartisan and Fake News. In: :231–240Association for Computational Linguistics; 2018; Melbourne, Australia.
  * 5 Kiesel Johannes, Mestre Maria, Shukla Rishabh, et al. SemEval-2019 Task 4: Hyperpartisan News Detection. In: :829–839Association for Computational Linguistics; 2019; Minneapolis, Minnesota, USA.
  * 6 Li Chang, Goldwasser Dan. Using Social and Linguistic Information to Adapt Pretrained Representations for Political Perspective Identification. In: :4569–4579Association for Computational Linguistics; 2021; Online.
  * 7 Zhang Lei, Wang and Bing Liu. Deep learning for sentiment analysis: A survey. WIREs Data Mining and Knowledge Discovery. 2018;8(4):e1253.
  * 8 Berka Petr. Sentiment analysis using rule-based and case-based reasoning. Journal of Intelligent Information Systems. 2020;55:51–66.
  * 9 Singh Loitongbam Gyanendro, Singh Sanasam Ranbir. Empirical study of sentiment analysis tools and techniques on societal topics. Journal of Intelligent Information Systems. 2021;56:379–407.
  * 10 Mohammad Saif M., Sobhani Parinaz, Kiritchenko Svetlana. Stance and sentiment in tweets. ACM Transactions on Internet Technology on Argumentation in Social Media. 2017;17(3).
  * 11 Siddiqua Umme Aymun, Chy Abu Nowshed, Aono Masaki. Tweet Stance Detection Using an Attention based Neural Ensemble Model. In: :1868–1873; 2019; Minneapolis, USA.
  * 12 Vijayaraghavan Prashanth, Vosoughi Soroush, Roy Deb. Twitter Demographic Classification Using Deep Multi-modal Multi-task Learning. In: :478–483Association for Computational Linguistics; 2017; Vancouver.
  * 13 Preotiuc-Pietro Daniel, Liu Ye, Hopkins Daniel, Ungar Lyle. Beyond Binary Labels: Political Ideology Prediction of Twitter Users. In: :729–740Association for Computational Linguistics; 2017; Vancouver.
  * 14 Takahashi Takumi, Tahara Takuji, Nagatani Koki, Miura Yasuhide, Taniguchi Tomoki, Ohkuma Tomoko. Text and Image Synergy with Feature Cross Technique for Gender Identification. In: :12; 2018; Avignon, France.
  * 15 Pizarro Juan. Using N-grams to detect Bots on Twitter. In: Cappellato Linda, Ferro Nicola, Losada David E., Müller Henning, eds. CLEF 2019 Labs and Workshops, Notebook Papers, :10CEUR-WS.org; 2019.
  * 16 Rangel Francisco, Rosso Paolo, Zaghouani Wajdi, Charfi Anis. Fine-grained analysis of language varieties and demographics. Natural Language Engineering. 2020;:1–21.
  * 17 Polignano Marco, Gemmis Marco, Semeraro Giovanni. Contextualized BERT Sentence Embeddings for Author Profiling: The Cost of Performances. In: :135–149Springer; 2020; Cham.
  * 18 Price Samantha, Hodge Abigail. Celebrity Profiling using Twitter Follower Feeds. In: CLEF and CEUR-WS.org; 2020; Thessaloniki, Greece.
  * 19 Devlin Jacob, Chang Ming-Wei, Lee Kenton, Toutanova Kristina. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. In: Burstein Jill, Doran Christy, Solorio Thamar, eds. Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, NAACL-HLT 2019, Minneapolis, MN, USA, June 2-7, 2019, Volume 1 (Long and Short Papers), :4171–4186Association for Computational Linguistics; 2019.
  * 20 Lee Nayeon, Liu Zihan, Fung Pascale. Team yeon-zi at SemEval-2019 Task 4: Hyperpartisan News Detection by De-noising Weakly-labeled Data. In: :1052–1056Association for Computational Linguistics; 2019; Minneapolis, Minnesota, USA.
  * 21 Baly Ramy, Martino Giovanni Da San, Glass James, Nakov Preslav. We Can Detect Your Bias: Predicting the Political Ideology of News Articles. In: :4982–4991Association for Computational Linguistics; 2020; Online.
  * 22 Srivastava Vertika, Gupta Ankita, Prakash Divya, Sahoo Sudeep Kumar, R.R Rohit, Kim Yeon Hyang. Vernon-fenwick at SemEval-2019 Task 4: Hyperpartisan News Detection using Lexical and Semantic Features. In: :1078–1082Association for Computational Linguistics; 2019; Minneapolis, Minnesota, USA.
  * 23 Drissi Mehdi, Segura Pedro Sandoval, Ojha Vivaswat, Medero Julie. Harvey Mudd College at SemEval-2019 Task 4: The Clint Buchanan Hyperpartisan News Detector. In: :962–966Association for Computational Linguistics; 2019; Minneapolis, Minnesota, USA.
  * 24 Bestgen Yves. Tintin at SemEval-2019 Task 4: Detecting Hyperpartisan News Article with only Simple Tokens. In: :1062–1066Association for Computational Linguistics; 2019; Minneapolis, Minnesota, USA.
  * 25 Patankar Anish, Bose Joy, Khanna Harshit. A Bias Aware News Recommendation System. In: :232–238IEEE; 2019.
  * 26 Iyyer Mohit, Enns Peter, Boyd-Graber Jordan, Resnik Philip. Political Ideology Detection Using Recursive Neural Networks. In: :1113–1122Association for Computational Linguistics; 2014; Baltimore, Maryland.
  * 27 Bhatia Sumit, P Deepak. Topic-Specific Sentiment Analysis Can Help Identify Political Ideology. In: :79–84Association for Computational Linguistics; 2018; Brussels, Belgium.
  * 28 Kulkarni Vivek, Ye Junting, Skiena Steve, Wang William Yang. Multi-view Models for Political Ideology Detection of News Articles. In: :3518–3527Association for Computational Linguistics; 2018; Brussels, Belgium.
  * 29 Stefanov Peter, Darwish Kareem, Atanasov Atanas, Nakov Preslav. Predicting the Topical Stance and Political Leaning of Media using Tweets. In: :527–537Association for Computational Linguistics; 2020; Online.
  * 30 Feng Shangbin, Chen Zilong, Yu Peisheng, Luo Minnan. Encoding Heterogeneous Social and Political Context for Entity Stance Prediction. arXiv preprint arXiv:2108.03881. 2021;.
  * 31 Peters Matthew E., Ammar Waleed, Bhagavatula Chandra, Power Russell. Semi-supervised sequence tagging with bidirectional language models. In: :1756–1765Association for Computational Linguistics; 2017; Vancouver, Canada.
  * 32 Liu Yinhan, Ott Myle, Goyal Naman, et al. RoBERTa: A Robustly Optimized BERT Pretraining Approach. CoRR. 2019;abs/1907.11692.
  * 33 Pavan Matheus Camasmie, Santos Vitor Garcia, Lan Alex Gwo Jen, et al. Morality Classification in Natural Language Text. IEEE transactions on Affective Computing. 2020;.
  * 34 Sidorov Grigori, Velasquez Francisco, Stamatatos Efstathios, Gelbukh Alexander, Chanona-Hernández Liliana. Syntactic n-grams as machine learning features for natural language processing. Expert Systems with Applications. 2014;41(3):853–860.
  * 35 Pennebaker J. W., Francis M. E., Booth R. J.. Inquiry and Word Count: LIWC.  Mahwah, NJ: Lawrence Erlbaum; 2001.
  * 36 Coltheart Max. The MRC psycholinguistic database. The Quarterly Journal of Experimental Psychology Section A: Human Experimental Psychology. 1981;33(4):497–505.
  * 37 Pennebaker James W., Boyd Ryan L., Jordan Kayla, Blackburn Kate. The development and psychometric properties of LIWC2015. : University of TexasAustin, Texas, USA; 2015.
  * 38 Balage Filho Pedro P., Aluísio Sandra M., Pardo T.A.S.. An Evaluation of the Brazilian Portuguese LIWC Dictionary for Sentiment Analysis. In: :215–219; 2013; Fortaleza, Brazil.
  * 39 Santos Leandro Borges, Duran Magali Sanchez, Hartmann Nathan Siegle, Junior Arnaldo Candido, Paetzold Gustavo Henrique, Aluísio Sandra Maria. A Lightweight Regression Method to Infer Psycholinguistic Properties for Brazilian Portuguese. In: Springer; 2017.
  * 40 McNemar Quinn. Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika. 1947;12(2):153–157.
  * 41 Stuart Alan. A test for homogeneity of the marginal distributions in a two-way classification. Biometrika. 1955;42(3/4):412–416.
  * 42 Maxwell Albert Ernest. Comparing the classification of subjects by two independent judges. The British Journal of Psychiatry. 1970;116(535):651–655.
  * 43 Yang Zhilin, Dai Zihang, Yang Yiming, Carbonell Jaime G., Salakhutdinov Ruslan, Le Quoc V.. XLNet: Generalized Autoregressive Pretraining for Language Understanding. In: :5753–5763Curran Associates, Inc.; 2019; Vancouver, Canada.
  * 44 Brown Tom B., Mann Benjamin, Ryder Nick, et al. Language Models are Few-Shot Learners. CoRR. 2020;abs/2005.14165.

## Author Biography

Samuel Caetano da Silva. Graduate student of Information Systems at the
University of São Paulo.

Ivandré Paraboni. PhD in Computer Science (Univ. of Brighton, UK, 2003), and
associate professor at the University of São Paulo.


# Optimal model-based beamforming and independent steering for spherical
loudspeaker arrays

Boaz Rafaely and Dima Khaykin
Department of Electrical and Computer Engineering, Ben-Gurion University of
the Negev
Beer-Sheva 84105, Israel<EMAIL_ADDRESS>6 February 2011

###### Abstract

Spherical loudspeaker arrays have been recently studied for directional sound
radiation, where the compact arrangement of the loudspeaker units around a
sphere facilitated the control of sound radiation in three-dimensional space.
Directivity of sound radiation, or beamforming, was achieved by driving each
loudspeaker unit independently, where the design of beamforming weights was
typically achieved by numerical optimization with reference to a given desired
beam pattern. This is in contrast to the methods already developed for
microphone arrays in general and spherical microphone arrays in particular,
where beamformer weights are designed to satisfy a wider range of objectives,
related to directivity, robustness, and side-lobe level, for example. This
paper presents the development of a physical-model-based, optimal beamforming
framework for spherical loudspeaker arrays, similar to the framework already
developed for spherical microphone arrays, facilitating efficient beamforming
in the spherical harmonics domain, with independent steering. In particular,
it is shown that from a beamforming perspective, the spherical loudspeaker
array is similar to the spherical microphone array with microphones arranged
around a rigid sphere. Experimental investigation validates the theoretical
framework of beamformer design.

111Copyright (c) 2010 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to<EMAIL_ADDRESS>
##  I Introduction

Spherical loudspeaker arrays, composed of a set of loudspeaker units mounted
on the surface of a sphere, operating as a multiple-channel sound source, have
been recently studied for applications such as electro-acoustic music
performance, synthesizing the radiation pattern of musical instruments [1, 2],
and active control of sound [3]. A physical model of the loudspeaker array has
been developed [4, 3], as a rigid sphere with vibrating caps mounted on its
surface, employing spherical harmonics to describe caps vibration and sound
radiation [5]. At low frequencies, array directivity can be represented as a
linear combination of spherical harmonics basis functions [6], and by
additionally including models of the loudspeaker units [7], array weights can
be designed to achieve a desired direcitivity function. A comprehensive review
of previous work concerning spherical loudspeaker arrays has been presented
recently [6].

Although useful in generating spherical harmonics based beam patterns, the
methods presented in previous work posses the following shortcomings:

  1. 1.

Typically, beam-pattern matching was the sole design objective, and so
robustness against noise and uncertainty was not introduced, which can degrade
performance in practical systems.

  2. 2.

No simple steering of the beam pattern was presented, and so re-calculation of
the beam pattern is typically required to realize steering.

  3. 3.

Alternative design approaches to the one previously presented, i.e. numerical
fitting to a desired directivity function, may be of interest. These include
multiple-objective designs; optimal designs; and analytical designs that
produce closed-form expressions for the beamforming weights. However, a
framework to apply these designs to spherical loudspeaker array was not
presented.

This paper presents a beamforming design framework for spherical loudspeaker
arrays that overcomes the shortcoming presented above. The design framework is
based on a physical model of the spherical loudspeaker array, presented in
section II. In this model the spherical loudspeaker array is represented by a
rigid sphere with a set of caps mounted on its surface, representing the
vibration of the diaphragm of the loudspeaker units, which is then further
simplified to a spherical source with radial velocity represented in the
spherical harmonics domain. This model is then used to develop the fundamental
beamforming equations in section III, both in the space domain by weighting
caps velocities, and more generally in the spherical harmonics domain. Section
IV presents the beamforming formulation for far-field, axis-symmetric
radiation, which is central to this paper. It is shown that the resulting
beamforming problem is almost identical to the beamforming problem of a
spherical microphone array with microphones arranged around a rigid sphere.
The latter has been recently introduced [8], has been studied extensively
since, with well investigated analysis of performance [9], and with a range of
beamforming methods developed [10]. The novel result of the similarity between
the two arrays leads directly to the development of a beamforming design
method for spherical loudspeaker arrays that is based on the framework
developed for spherical microphone arrays. A formulation of measures for array
directivity index and robustness are presented in section V, after which
optimal beamformers with simple steering for the spherical loudspeaker array
are developed in section VI, including maximum directivity, maximum
robustness, and Dolph-Chebyshev, as examples. Experimental investigation of
beamforming with a real array having 12 loudspeaker units, measured in an
anechoic chamber, concludes the paper.

##  II Sound radiation from spherical sources

Sound radiation from spherical sources is reviewed in this section. A
spherical source is modeled as a rigid sphere of radius $r_{0}$ with $L$
spherical caps, representing loudspeaker units, positioned on its surface at
locations $(\theta_{l},\phi_{l})$, each imposing a constant radial surface
velocity of $v_{l},\ l=1,...,L$, at the surface segment they cover [3, 11].
Here $\theta_{l}$ represent elevation angle, measured down from the z-axis,
and $\phi_{l}$ represent azimuth angle, measured on the x-y plane away from
the x-axis towards the y-axis, defining a spherical coordinate system [12].
The radial velocity of the sphere surface at wave number $k$,
$u(k,r_{0},\theta,\phi)$, is composed of contributions from all $L$ caps. The
spherical Fourier transform of the radial velocity, $u_{nm}(k,r_{0})$, is
defined as [12]:

$u_{nm}(k,r_{0})=\int_{0}^{2\pi}\int_{0}^{\pi}u(k,r_{0},\theta,\phi)[Y_{n}^{m}(\theta,\phi)]^{*}\sin\theta
d\theta d\phi$ (1)

with $Y_{n}^{m}(\cdot,\cdot)$ the spherical harmonics of order $n$ and degree
$m$. After deriving the spherical Fourier transform of the radial velocity due
to a single cap and adding the contributions from all $L$ caps, Eq. (1)
reduces to [3]:

$u_{nm}(k,r_{0})=g_{n}\sum_{l=1}^{L}v_{l}(k)[Y_{n}^{m}(\theta_{l},\phi_{l})]^{*}$
(2)

with

$g_{n}\equiv\frac{4\pi^{2}}{2n+1}\left[P_{n-1}(\cos\alpha)-P_{n+1}(\cos\alpha)\right],$
(3)

and with $P_{n}(\cdot)$ the Legendre polynomial, and $\alpha$ the aperture
angle of each spherical cap.

Given the radial velocity over the sphere surface, the sound pressure
$p(k,r,\theta,\phi)$ away from the source, is computed by [5]:

$p(k,r,\theta,\phi)=i\rho_{0}c\sum_{n=0}^{\infty}\sum_{m=-n}^{n}\frac{h_{n}(kr)}{h_{n}^{{}^{\prime}}(kr_{0})}u_{nm}(k,r_{0})Y_{n}^{m}(\theta,\phi),$
(4)

with $c$ the speed of sound, $\rho_{0}$ air density, $i=\sqrt{-1}$, and
$h_{n}(\cdot)$ and $h^{\prime}_{n}(\cdot)$ are the spherical Hankel function
of the first kind of order $n$, and it’s derivative, respectively [12]. Now,
the spherical Fourier transform of the sound pressure, $p_{nm}(k,r)$, can be
written as:

$p_{nm}(k,r)=i\rho_{0}c\frac{h_{n}(kr)}{h^{\prime}_{n}(kr_{0})}u_{nm}(k,r_{0})$
(5)

Equations (4), (2) and (3) can now be used to represent the sound pressure
radiated by the spherical source, given the velocity of each spherical cap, or
loudspeaker unit. It is worth noting that with $L$ spherical caps constructing
the source, only $L$ spherical harmonics in $u_{nm}$ and $p_{nm}$ can be
independently controlled, typically taking the first $(N+1)^{2}$ harmonics,
such that

$(N+1)^{2}\leq L$ (6)

with $n\leq N$, and $-n\leq m\leq n$. Also note that by controlling the radial
velocity of $L$ caps, and assuming control over spherical harmonics of orders
$n\leq N$, the higher order harmonics $N+1$ and above cannot be controlled.
However, sufficiently away from the source, at distances that satisfy $kr>>N$,
the higher order harmonics are significantly attenuated by the term
$h_{n}(kr)/h^{\prime}_{n}(kr_{0})$, and can be neglected [3]. This means that
although in practice source control is achieved through control over caps
velocity, one can also assume a direct control over $u_{nm}$ at orders $n\leq
N$, with good accuracy.

##  III beamforming with a spherical source

Beamforming with spherical sources is employed with the aim of controlling the
directivity pattern of the sound radiated from the source. This is achieved by
weighting the source signal $s(k)$ with weights $w_{l}(k)$ before driving the
caps velocity, or loudspeaker units in practice, such that,

$v_{l}(k)=w_{l}(k)s(k),\,l=1,...,L$ (7)

Now, repeating the derivation in Eqs. (1), (2) and (3), but this time with
$w_{l}(k)$, $w_{nm}(k)$ and $w(k,\theta,\phi)$ replacing $v_{l}(k)$,
$u_{nm}(k,r_{0})$ and $u(k,r_{0},\theta,\phi)$, respectively, and using Eq.
(7), the following holds:

$w_{nm}(k)=g_{n}\sum_{l=1}^{L}w_{l}(k)[Y_{n}^{m}(\theta_{l},\phi_{l})]^{*}$
(8)

and

$u_{nm}(k,r_{0})=s(k)w_{nm}(k)$ (9)

with $w(k,\theta,\phi)$ representing the beamforming weight function as a
continuous function over the sphere surface. Following the same argument as
presented in section II, one can assume control over $w_{nm}(k)$, although in
practice beamforming is achieved through a direct control over $w_{l}(k)$.

Now, the pressure away from the source can be written in terms of the
beamforming weights by substituting Eq. (9) in Eq. (4),

$p(k,r,\theta,\phi)=i\rho_{0}cs(k)\sum_{n=0}^{\infty}\sum_{m=-n}^{n}\frac{h_{n}(kr)}{h_{n}^{{}^{\prime}}(kr_{0})}w_{nm}(k,r_{0})Y_{n}^{m}(\theta,\phi).$
(10)

Following Eqs. (10) and (8), beamforming design requires the computation of
weights, $w_{nm}(k)$ or $w_{l}(k)$, such that the radiated sound pressure
maintains some given design criterion. These equations, or measured versions
of them, have been previously employed in a numerical design framework, for
computing beamforming weights for spherical sources. The next section presents
some further derivations, that will facilitate an analytical, rather than
numerical design of beamformers for spherical sources, in a manner similar to
spherical microphone arrays.

##  IV Axis-symmetric far-field beamforming

An efficient formulation for far-field beamforming is derived in this section
by constraining the radiated far-field sound pressure to be rotationally
symmetric around the look direction, similar to the approach taken for
spherical microphone array beamforming [8]. We first assume that a far-field
beam pattern is required, which is the case in most applications involving
sound radiated into large rooms, such as music halls and video conferencing
rooms. Far-field in the context of this work means that $kr>>N$, where $N$ is
the highest order controlled by the source. In this case the following large-
argument approximation can be employed [5]:

$h_{n}(kr)\approx(-i)^{n+1}\frac{e^{ikr}}{kr}$ (11)

Also, we introduce the Wronskian relation [5]:

$j_{n}(kr)h^{\prime}_{n}(kr)-j^{\prime}_{n}(kr)h_{n}(kr)=\frac{i}{(kr)^{2}}$
(12)

which is rearranged as follows:

$\frac{1}{h^{\prime}_{n}(kr)}=-i(kr)^{2}\left[j_{n}(kr)-\frac{j^{\prime}_{n}(kr)}{h^{\prime}_{n}(kr)}h_{n}(kr)\right]$
(13)

We further denote for notation simplicity:

$b_{n}(kr)\equiv
i\rho_{0}ckr^{2}(-i)^{n}\left[j_{n}(kr)-\frac{j^{\prime}_{n}(kr)}{h^{\prime}_{n}(kr)}h_{n}(kr)\right]$
(14)

Substituting Eqs. (11), (13) and (14) into Eq. (10), the far-field sound
pressure can be written as:

$p(k,r,\theta,\phi)=\frac{e^{ikr}}{r}s(k)\sum_{n=0}^{\infty}\sum_{m=-n}^{n}b_{n}(kr_{0})w_{nm}(k,r_{0})Y_{n}^{m}(\theta,\phi).$
(15)

In the next step of this derivation, we remove the dependance on $r$ by
considering the directivity function, or beam pattern $B$, computed by
normalizing the far-field sound pressure with a factor of $re^{-ikr}$ [5], and
assuming a unit input signal $s(k)=1$,

$B(k,\theta,\phi)=\sum_{n=0}^{\infty}\sum_{m=-n}^{n}b_{n}(kr_{0})w_{nm}(k,r_{0})Y_{n}^{m}(\theta,\phi).$
(16)

We now make a further simplification by considering axis-symmetric beam
patterns, in a way similar to spherical microphone array beamforming [9], by
selecting weights as follows:

$w_{nm}(k)=\frac{d_{n}(k)}{b_{n}(kr_{0})}[Y_{n}^{m}(\theta_{0},\phi_{0})]^{*}$
(17)

where $d_{n}(k)$ is the one-dimensional axis-symmetric beamforming weighting
function, and $(\theta_{0},\phi_{0})$ is the look direction, forming the axis
of symmetry. By substituting Eq. (17) in Eq. (16), and using the spherical
harmonics addition theorem [12], the far-field directivity function can be
rewritten as:

$B(k,\Theta)=\sum_{n=0}^{N}d_{n}(k)\frac{2n+1}{4\pi}P_{n}(\cos\Theta)$ (18)

where $\Theta$ is the angle between the look direction $(\theta_{0},\phi_{0})$
and the direction of radiated sound, $(\theta,\phi)$, defined as:

$\cos\Theta=\cos\theta_{0}\cos\theta+\cos(\phi_{0}-\phi)\sin\theta_{0}\sin\theta.$
(19)

Several interesting observations can be made regarding the derivation in this
section:

  * •

Eq. (18) representing the beam pattern for the spherical source is exactly the
same as the beam pattern equation for spherical microphone arrays [9]. A wide
range of analytical beam pattern design methods have been developed for the
latter, and will be proposed in this paper for beamforming with the spherical
source.

  * •

The term $b_{n}$ in Eq. (14) is very similar to the same term derived for
spherical microphone arrays designed around a rigid sphere. In both cases,
$b_{n}$ represents the dynamics of sound propagation around a rigid sphere,
such that a division by $b_{n}$ turns the beam pattern independent on the
spherical array configuration. It is therefore expected that beamforming with
a spherical loudspeaker array as formulated in this paper will poses a similar
behavior to beamforming with a spherical microphone array with a rigid sphere
configuration.

  * •

The weights $w_{l}$ are assumed to control caps velocity, $v_{l}$. In
practice, the weights will control the signal driving the loudspeaker units,
i.e. voltage input rather than velocity input. For typical moving-coil
loudspeakers, operating above the mechanical cut-off frequency and below the
radiation cut-off, the voltage is proportional to the frequency times the
velocity [13], such that in practice $ks(k)$ can be considered as directly
proportional to the voltage signal if $s(k)$ is the velocity signal, and so
the dependance on $k$ in Eqs. (14), (15) and (16) is removed, making the
system models for the spherical loudspeaker and microphone arrays even more
similar.

##  V Directivity index and robustness

Beamformer design typically involves achieving a desired directivity, while
maintaining necessary robustness constraints [14]. A common measure for array
performance is the directivity factor, calculated as the directivity at the
look direction, relative to the directional average of the directivity
function [14]:

$Q=\frac{\left|B(k,\theta_{0},\phi_{0})\right|^{2}}{\frac{1}{4\pi}\int_{0}^{2\pi}\int_{0}^{\pi}\left|B(k,\theta,\phi)\right|^{2}\sin\theta
d\theta d\phi}$ (20)

The directivity factor for the spherical source can be derived by substituting
Eq. (18) into Eq. (20). Note that Eq. (18) is identical to the directivity
function of the spherical microphone array [15]. The directivity factor, as
derived in [15], is therefore:

$Q=\frac{\left|\sum_{n=0}^{N}d_{n}(k)(2n+1)\right|^{2}}{\sum_{n=0}^{N}\left|d_{n}(k)\right|^{2}(2n+1)}$
(21)

The Directivity Index (DI) is now defined as $10\log_{10}Q$.

Another important measure is array robustness, which is a measure of the
system sensitivity to noise, errors, uncertainties and perturbations. A common
measure of robustness relates to the inverse of the 2-norm of the array
weights, assuming the direcitvity function in the look direction is unity. The
latter constraint is referred to as distortionless response. This measure is
exactly the white-noise gain for sensor arrays, but is also considered as a
general measure for robustness [14]. We adopt the same measure for the
spherical source. We use the term white-noise gain (WNG) although in the
context of this work it refers to general robustness. The WNG can be
calculated by normalizing the 2-norm of the coefficients $w_{nm}$ to satisfy
the distortionless response constraint with reference to Eq. (16):

$\mathrm{WNG}=\frac{\left|\sum_{n=0}^{\infty}\sum_{m=-n}^{n}b_{n}(kr_{0})w_{nm}(k,r_{0})Y_{n}^{m}(\theta_{0},\phi_{0})\right|^{2}}{\sum_{n=0}^{N}\sum_{m=-n}^{n}|w_{nm}(k)|^{2}}$
(22)

Substituting Eq. (17), and using the spherical harmonics addition theorem, we
get:

$\mathrm{WNG}=\frac{\left|\sum_{n=0}^{\infty}d_{n}(k)(2n+1)\right|^{2}}{\sum_{n=0}^{N}\frac{|d_{n}(k)|^{2}}{|b_{n}(kr_{0})|^{2}}(2n+1)}$
(23)

This result is equivalent to the WNG calculated for spherical microphone
arrays [15], although the function involved, e.g. $b_{n}(kr_{0})$ are only
equivalent up to some frequency-dependant constant, as discussed above.

##  VI Optimal beamforming

Having developed expressions for the spherical source concerning directivity
and WNG, in this section some optimal beamforming methods are proposed, which
have analytical, or closed-form solutions, as opposed to most current methods
for spherical source beamforming that use numerical optimization.

###  VI-A Maximum Directivity

This beamforming method aims to find the beamforming weights $d_{n}$ that
maximize the directivity factor of a given spherical loudspeaker array, or
spherical source. First, the problem is formulated in a matrix form and then
the weights are derived that maximize the directivity factor.

The beamforming weights vector at wave number $k$ is defined as:

$\mathbf{d}=\left[d_{0}(k),d_{1}(k),...,d_{N}(k)\right]^{T}$ (24)

The following $(N+1)\times 1$ vector of coefficients, with the $n$-th element
given by $2n+1$, is also defined:

$\mathbf{a}=\left[1,3,...,2N+1\right]^{T}$ (25)

such that the directivity factor, Eq. (21) can be written in a matrix form as:

$Q=\frac{\mathbf{d}^{H}[\mathbf{a}^{T}\mathbf{a}]\mathbf{d}}{\mathbf{d}^{H}[\mathrm{diag}(\mathbf{a})]\mathbf{d}}$
(26)

Equation (26) represents a generalized Rayleigh quotient, with a maximum value
in this case evaluated to be simply [10]:

$\mathbf{d}=\left[1,1,...,1\right]^{T}$ (27)

In the spherical microphone array literature, this is referred to as regular
beam pattern, or plane-wave decomposition, representing directivity functions
having a closed-form expression [10]:

$B(\Theta)=\frac{N+1}{4\pi(\cos\Theta-1)}[P_{N+1}(\cos\Theta)-P_{N}(\cos\Theta)]$
(28)

also referred to as hyper-cardioid beam pattern, with the maximal directivity
factor of $(N+1)^{2}$.

###  VI-B Maximum WNG

In a similar manner, the weights $d_{n}$ that maximize the WNG can also be
computed. Equation (23) can be written in a matrix form as:

$WNG=\frac{\mathbf{d}^{H}[\mathbf{a}^{T}\mathbf{a}]\mathbf{d}}{\mathbf{d}^{H}[\mathrm{diag}(\mathbf{c})]\mathbf{d}}$
(29)

with

$\mathbf{c}=\left[1/b_{0}(kr_{0}),3/b_{1}(kr_{0}),...,(2N+1)/b_{N}(kr_{0})\right]^{T}$
(30)

and with a maximum value in this case achieved with weights given by [10]:

$d_{n}(k)=\frac{4\pi|b_{n}(kr_{0})|^{2}}{\sum_{n=0}^{N}|b_{n}(kr_{0})|^{2}(2n+1)}$
(31)

Again, this is similar to the result obtained for the spherical microphone
array.

###  VI-C Other beam pattern designs

Due to the similarity in the directivity function, directivity factor, and
WNG, between the spherical loudspeaker array presented above and the spherical
microphone array developed elsewhere, a range of beam pattern design methods
can be applied to the spherical loudspeaker array, see, for example [10].
These include, among other, the Dolph-Chebyshev beam pattern, providing
optimal trade-off between main-lobe width and side-lobe level, and other
optimal design methods.

##  VII Experimental study

The aim of this section is to provide an experimental examination of the
beamforming design methods presented in this paper. The examination is based
upon comparison of measured beam patterns and simulated beam patterns. The
simulated beam patterns are generated by using some of the analytical design
method presented in this paper to compute beamforming weights and apply them
to a computer model of a spherical loudspeaker array, as presented in this
paper. The model represents an experimental spherical loudspeaker array
system, and so the same weights are applied to the experimental system to
produce beam patterns evaluated by microphones measuring the sound pressure
away from the spherical loudspeaker array. The measured and simulated beam
patterns are then compared.

The experimental system includes a spherical loudspeaker array of radius
$r_{0}=0.15\,$m, with 12 individual loudspeaker units mounted on it’s surface,
in a dodecahedron arrangement. The loudspeaker array is designed and produced
by the Institute of Technical Acoustics, Aachen university, and includes power
amplifiers to drive each loudspeaker unit individually. The power amplifiers
are connected to a two-channel sound card via a switching circuit, such that
each loudspeaker unit can be separately driven by the sound card.

A microphone attached to a rotating system is used to spatially sample the
sound pressure radiated by the loudspeaker array. The microphone positions
followed the Gaussian sampling scheme [9], with a total of $242$ samples,
positioned at a radius of $r=0.57\,$m, achieving a spherical harmonic order of
$N=10$ at the analysis sphere.

Once the microphone is positioned in place, the impulse response between each
loudspeaker unit and the microphone is measured using a linearly swept-sine
signal of a duration of 4 seconds, in the range of $0-1500\,$Hz. A sampling
frequency $3000\,$Hz was employed by the measurement system. A sound card
connected to a computer running MATLAB was used to play and record the
signals. An entire session includes measuring and saving the impulse response
data for each microphone position and each loudspeaker unit, giving a total of
$242\times 12=2904$ impulse response measurements during a complete session.
The entire experiment was performed at the anechoic chamber, acoustics
laboratory, Ben-Gurion University of the Negev, having inner dimensions of
$2\,$m, certified as anechoic from $300\,$Hz.

At a frequency of $400\,$Hz, the value of $kr_{0}$ is about $1.1$, and the
value of $kr$ is about $4.2$, and so both the spherical loudspeaker array and
the measuring spherical microphone array satisfy $kr_{0}<2$ and $kr<10$,
therefore providing spatial over-sampling in both systems. At a frequency of
$1000\,$Hz, $kr_{0}\approx 2.75$ and $kr\approx 10.45$, above which spatial
aliasing is expected to be significant in both systems.

The design framework presented in this paper was used for the computation of
$d_{n}$, from which $w_{nm}$ was computed using Eq. (17). Then, $w_{l}$, the
weight assigned to each loudspeaker unit was computed from $w_{nm}$, as
detailed below, and applied directly to the measured data to compute the
measured beam pattern. With the aim of calculating $w_{l}$, Eq. (8) can be
written in a matrix form as:

$\mathbf{w_{nm}}=\mathbf{G}\mathbf{Y}\mathbf{w},$ (32)

where the $(N+1)^{2}\times 1$ vector of beamforming weights at wave number $k$
is defined by:

$\mathbf{w_{nm}}=[w_{00}(k),w_{1(-1)}(k),w_{10},w_{11},...,w_{NN}(k)]^{T}.$
(33)

The spherical harmonics matrix $\mathbf{Y}$ of size $(N+1)^{2}\times L$ has
element at row $q$ and column $l$ given by:

$Y_{ql}=[Y_{n}^{m}(\theta_{l},\phi_{l})]^{*},\quad
q=n^{2}+n+m,\,\,n=0,...,N,\,\,m=-n,...,n,\,\,l=1,...,L.$ (34)

Matrix $\mathbf{G}$ of size $(N+1)^{2}\times(N+1)^{2}$ is given by:

$\mathbf{G}=\mathrm{diag}(g_{0},g_{1},g_{1},g_{1},...,g_{N})$ (35)

and the $L\times 1$ vector $\mathbf{w}$ is given by

$\mathbf{w}=[w_{1}(k),w_{2}(k),...,w_{L}(k)]^{T}$ (36)

Having designed $d_{n}$ to achieve a desired beam pattern, Eq. (17) is used to
derive $w_{nm}$ given the look direction $(\theta_{0},\phi_{0})$, from which
the weights assigned to each loudspeaker unit, $w_{l}$, is computed by:

$\mathbf{w}=\mathbf{Y}^{\dagger}\mathbf{G}^{-1}\mathbf{w_{nm}}$ (37)

where $\mathbf{Y}^{\dagger}$ is the pseudo-inverse of $\mathbf{Y}$.

Beamforming weights $d_{n}$ were designed as described above, based on the
maximum WNG method, as in Eq. (31), and the maximum directivity method, as in
Eq. (27). It should be noted that these are only example designs, and other
methods as discussed in this paper could also be used. Figure 1 shows balloon
plots of the simulated and measured beam patterns for a design frequency of
$400\,$Hz, using the maximum WNG method. Figure 2 shows a cross-section along
the azimuth angle $\theta$ for elevation angle $\phi=\pi/2$. Note that because
in this paper the design methods produce axis-symmetric beam pattern, any
cross-section intersecting the look direction can be presented. The figures
show a reasonable similarity between simulated and measured beam patterns,
validating the proposed design framework. Improving the agreement between
simulated and measured beam patterns may require a more accurate matching
between transducers. Also, because the distance of $r=0.57\,$m of the
microphones cannot be considered far-field, the designed weights were modified
to account for this near-field effect according to Eq. (10).

Figures 3 and 4 show similar results for $1000\,$Hz, using the maximum
directivity design method, with a different beam pattern, which has a narrower
main lobe. The measured beam pattern is similar to the simulated one, once
again validating the design framework.

##  VIII Conclusion

This paper presented an efficient beamforming framework for spherical
loudspeaker arrays, facilitating optimal, closed-form beam pattern design,
with independent steering. The paper derives beamforming equations for the
spherical loudspeaker array, showing similarity to spherical microphone arrays
configured around a rigid sphere. This similarity facilitates the use of a
wide range of beamforming methods already developed for spherical microphone
arrays. The design framework is then employed for beamforming with an
experimental spherical loudspeaker array system, validating the theoretical
results. The proposed framework can be used to produce directional radiation
patterns with the spherical loudspeaker array in a wide range of applications.

##  IX Acknowledgement

This work was supported in part by the Ministry of Industry and Trade, grant
no. 40161.

## References

  * [1] O. Warusfel and N. Misdariis, “Directivity synthesis with a 3d array of loudspeakers: application for stage performance,” in _Proceedings of the COSTG-6 Conference on Digital Audio Effects (DAFX-Ol), Limerick, Ireland_ , 2001.
  * [2] R. Avizienis, A. Freed, P. Kassakian, and D. Wessel, “A compact 120 independent element spherical loudspeaker array with programmable radiation patterns,” in _Proceedings of the 120th Audio Engineering Society Convention, Paris_ , no. 6783, 2006.
  * [3] B. Rafaely, “Spherical loudspeaker array for local active control of sound,” _J. Acoust. Soc. Am._ , vol. 125, no. 5, pp. 3006–3017, May 2009.
  * [4] F. Zotter and R. Höldrich, “Modeling of radiation synthesis with spherical loudspeaker arrays,” in _Proceedings of the 19th International Congress on Acoustics, Madrid_ , no. COM-01-006, September 2007.
  * [5] E. G. Williams, _Fourier acoustics: sound radiation and nearfield acoustical holography_. New York: Academic Press, 1999.
  * [6] A. M. Pasqual, J. R. de Franca Arruda, and P. Herzog, “Application of Acoustic Radiation Modes in the Directivity Control by a Spherical Loudspeaker Array,” _Acta Acustica united with Acustica_ , vol. 96, no. 1, pp. 32–42, 2010.
  * [7] M. Pollow and G. K. Behler, “Variable directivity for platonic sound sources based on spherical harmonics optimization,” _Acta Acoustics united with Acoustica_ , vol. 95, pp. 1082–1092, 2009.
  * [8] J. Meyer and G. W. Elko, “A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield,” _Proceedings ICASSP 2002_ , vol. II, pp. 1781–1784, 2002.
  * [9] B. Rafaely, “Analysis and design of spherical microphone arrays,” _IEEE Trans. Speech Audio Proc._ , vol. 13, no. 1, pp. 135–143, January 2005.
  * [10] B. Rafaely, Y. Peled, M. Agmon, D. Khaykin, and E. Fisher, “Spherical microphone array beamforming,” in _Speech Processing in Modern Communications: challenges and perspectives_ , I. Cohen, J. Benesty, and S. Gannot, Eds. Berlin: Springer-Verlag, 2010, ch. 11, pp. 281–305.
  * [11] F. Zotter and R. Höldrich, “Modeling a spherical loudspeaker system as a multipole source,” in _Proceedings of the 33rd German Annual Conference on Acoustics, Stuttgart_ , March 2007.
  * [12] G. Arfken and H. J. Weber, _Mathematical methods for physicists_ , 5th ed. San Diego: Academic Press, 2001.
  * [13] L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, _Fundamentals of Acoustics_ , 4th ed. New York: John Wiley & Sons, 1999.
  * [14] H. L. Van-Trees, _Optimum Array Processing (Detection, Estimation, and Modulation Theory, Part IV)_ , 1st ed. Wiley-Interscience, 2002.
  * [15] B. Rafaely, “Phase-mode versus delay-and-sum spherical microphone array processing,” _IEEE Sig. Proc. Let._ , vol. 12, no. 10, pp. 713–716, October 2005.

Figure 1: Balloon plot of the directivity function, designed using the maximum
WNG method with $N=2$, for an operating frequency of $400\,$Hz. Left:
simulated, right: measured. Figure 2: Same as in Fig. 1, but showing a cross-
section along $(\pi/2,\phi)$.

Figure 3: Balloon plot of the directivity function, designed using the maximum
directivity method with $N=2$, for an operating frequency of $1000\,$Hz. Left:
simulated, right: measured. Figure 4: Same as in Fig. 3, but showing a cross-
section along $(\pi/2,\phi)$.