1 Introduction
As of June 2021, more than 172 million cases have occurred, with more than 3.7 million deaths, across the world (Dong, Du and Gardner, 2020). In spite of emergence of COVID19 vaccines, most countries still suffer from COVID19 and we are still far from overcoming it. Tremendous efforts to understand and overcome this fatal virus have led to the rich amount of biomedical literature about COVID19. As of June 2021, searching with the term “COVID19” in the PubMed biomedical literature database (https://pubmed.ncbi.nlm.nih.gov) resulted in more than 140,000 publications. These literature covers a wide range of topics, including general description, mechanism, transmission, diagnosis, treatment, prevention, case report, and forecasting, among others, as profiled and categorized in LitCovid, a biomedical literature database dedicated to COVID19 (Chen, Allot and Lu, 2020). In order to facilitate understanding of relevant mechanisms and come up with effective treatment and preventive strategies, it is critical to follow up and digest these publications that are being published in a fast phase. However, given the rich volume of COVID19 literature and its rapid publication phase, it is practically impossible for biomedical experts to trace all of these literature manually in real time. Statistical and computational approaches, especially text mining, can be a powerful solution for the researchers to address this challenge. Since literature is unstructured text data, a document is usually first summarized with the corpus, representing word counts. The tfidf approach is most commonly used to summarize the document with the words’ frequency (Chowdhury, 2010). In spite of its popularly, this approach is still naive and limited in the sense that each single word is treated independently and interactions among them are totally ignored. However, such latent relationships can provide invaluable information that leads to effective modeling of literature and ultimately deeper understanding of the literature. Therefore, it is of great interest to cluster words effectively and understand meaning of these clusters. In the text mining area, topic modeling is the most wellknown approach for this purpose. It essentially extracts topics based on the words’ distribution in each document and various algorithms have been proposed for topic modeling. Blei, Ng and Jordan (2003)
made an important step in this direction and proposed a generative probabilistic model for word set, called the Latent Dirichlet Allocation (LDA). LDA assumes each document is structured in the context of topics while words are allocated to these topics. The topics are regarded as latent variables and characterized by words with probabilities assigned to each topic. To estimate latent topics, LDA uses Bayesian statistical methods such as ExpectationMaximization (EM) algorithm and variational inference to construct the posterior distributions of output: (1) topic distributions and (2) topicword distributions. First, the topic distribution models how likely each topic is relevant to a given document. Second, the topicword distribution represents the probability how likely each given word is associated with a particular topic. Further topic modeling based on LDA is to model literature text data; such as authordocument models
(McCallum, CorradaEmmanuel and Wang, 2005) and abstractreference models (Erosheva, Fienberg and Lafferty, 2004). On the perspective of biological or bimedical literature text mining, Liu et al. (2016) applied topic modeling to biological literature and showed that topic modeling can be a practical solution for the bioinformatics research.Since COVID19 is a hot topic and its research is active and ongoing, some articles are released without full context but with only abstract. Abstracts of the COVID19 literature are categorized as short text. Unfortunately, with short texts, conventional topic models including LDA often suffer from poor performance due to the sparsity problem, which causes inferior topic inferences. There have been some attempts to handle this problem by using additional assumptions for short text data. For instance, Zhao et al. (2011) and Lakkaraju, Bhattacharya and Bhattacharyya (2012) trained a topic model on tweet data as a mixture of unigrams (Nigam et al., 2000), where a document is considered as a word set drawn independently from a single topic. Likewise, Gruber, Weiss and RosenZvi (2007) assumed that the words within the same sentence share the same topic. Although these constraints may help alleviate the data sparsity problem caused by short text data, this improvement was achieved by using more information to capture multiple topics from each document. Moreover, these assumptions tend to result in peaked posteriors of topics in a document, making the model susceptible to overfitting (Blei, Ng and Jordan, 2003). Yan et al. (2013) made important progress for modeling of short text data, socalled Biterm Topic Model (BTM). Unlike the LDA, BTM replaced words with biterms, where a biterm is defined as a set of two words occurring in the same document. This approach attempted to make up for the lack of words in a short text by pairing two words, thereby creating more words in the document. This allows considering that if two words are mentioned together, they are more likely to belong to the same topic. Some studies apply BTM to short text data such as microblog (Li et al., 2016), largescale short texts, and tweets for clustering and classification (Chen and Kao, 2017).
1.1 Interaction Map of Topic Relationships
It is important to note that it is hard to find the data that contain independent topics towards one subject in the real world. Still, instead, multiple topics are often intercorrelated. Therefore, to tackle this practical issue, there have been attempts to model interactions among topics by modeling the correlated structure within the topic model or combining the topic model with statistical models. For instance, Blei and Lafferty (2007)
regarded the topic of correlation as a structure of heterogeneity. To capture the heterogeneity of topics, they suggest Correlated Topic Model(CTM), which models topic proportions to exhibit correlation through the logistic normal distribution within LDA. They validated their performance by applying CTM to the articles from Science. On the other hand,
Rusch et al. (2013)combined LDA with model trees to interpret the topic relationships from Afghanistan war logs. It classified the topics into tree structures which helped to understand the different circumstances in the Afghanistan war. One of statistical methods for handling correlated structure is network analysis. Specifically, network modeling estimate the relationships of interactions among nodes based on their dependency structure. It can provide global and local representation of nodes at the same time. In this context,
Mei et al. (2008) tried to identify topical communities by combining a topic model with a social network. Specifically, it estimated topic relationships given the known network structure and tried to separate out topics based on connectivity among them. However, in this approach, the network information needs to be given to construct and visualize the topic network, which is not a trivial task in practice. Our study aims to overcome these limitations and estimate the topics’ relationship and visualize their dependency structure simultaneously, by considering interaction among topics using network models. In addition, we also aim to overcome a static topic network by dynamically representing fundamental associations among topics through tracking the change in relationships. There are four steps to estimate the interaction relationship among topics. In the first step, text mining is conducted to extract nouns and corpus is constructed for modeling literature data. In the second step, we use BTM (Yan et al., 2013) to estimate topics and their associated words. In the third step, latent topic positions are estimated based on the distance that measures similarity between a topic and a word. In the last step, we visualize relationships among topics by tracking the transition of latent positions of topics. This approach represents interactions among topics on the latent positions and this facilitates understanding of distinct properties of the topics. Specifically, the more topic A shares words with topic B, the more likely topic A is located closer to topic B, which nicely depicts the topic relationships identified by BTM.This article is composed of three parts. First, we will briefly summarize the contributions of this paper. Second, we will introduce our methods and how we combine two different statistical approaches: (1) the topic modeling, specifically the BTM, an alternative topic modeling to LDA for the purpose of tackling the short text problem and (2) the latent space item response model (Jeon et al., 2021), which estimates associations between items based on the latent distance between item and response. Finally, we will apply our approach to the COVID19 literature to evaluate and demonstrate the usefulness of our approach.
2 Contribution
There are three key contributions of this work. First of all, our paper estimates and visualizes the topic relationships by mapping unobserved interactions among topics onto the interaction map based on the latent distance between topics and words, where the interactions among topics are quantified by their interactions with words. This embedded derivation of topic relationships will reduce the burden of data analysts because it does not require prior knowledge about relationships between topics, e.g., a connectivity matrix. Instead, our approach utilizes the topicword matrix for calculating the latent positions of each topic, where each cell corresponds to the probability of a word’s priority linkage to a topic. Since our approach uses continuous values ranging from 0 to 1 for the modeling purpose, it can quantify closeness between topics by reflecting degrees of linking of words to topics and, hence, using latent positions for topics, we could represent relationships among topics more precisely. Secondly, we visualize the topic relationship as a trajectory plot to detect the change of interactions of topics over different set of words. This feature has two important properties; (1) it could measure the main location of the topic, which is steadily positioned in a similar place in spite of differing the network structure; and (2) we could infer popular topics mentioned across articles and recently emerging topics by scanning the latent position of each topic. Specifically, if a particular topic shares most of the words associated with it with other topics, it is more likely to be located in the center on the latent interaction map. In contrast, if a specific topic consists mostly of words unique to that topic (e.g., a rare topic or an independent topic containing its own referring words), it is more likely to be located away from the center on the interaction map. For example, in the context of COVID19, it is more likely that common subjects like ‘outbreak’ and ‘diagnosis’ are located in the center while more specific subjects like ‘Cytokine Storm’ are located more outside on the interaction map. Finally, this approach helps organize an tremendous amount of literature and mine underlying relationships among topics based on the literature. The topic network that visualizes the relationship of topics gives researchers more intuition to set out their studies. For instance, if some researchers want to investigate a specific topic, say Topic A, our framework can assist them by providing information answering the three following questions: (1) Which set of words are associated with Topic A? Researchers can obtain this information from the BTM results. In addition, since we extract meaningful words that distinctively represent each topic’s meaning, our approach could further support this investigation with a more refined word set. (2) Are there any other topics related to Topic A for extending and elaborating research? Researchers can answer this question by intuitive interrogating the final visualization. (3) Is Topic A is a common or specific topic? Since we could trace change of latent topic positions as a function of words set, our method provides relevant insights through topic locations on the interaction map. Specifically, researchers can consider Topic A to be common if it is located in the center, and to be specific if it is located away from the center.
3 COVID19 Biomedical Literature
We applied our workflow to the COVID19 literature to investigate the latent semantic structure of COVID19 literature. In our implementation, we first downloaded the COVID19 articles published between December 1st, 2019 and August 3rd, 2020 from the PubMed database (https://pubmed.ncbi.nlm.nih.gov) . Specifically, we collected articles of which titles contain “coronavirus2”, “covid19” or “SARSCoV2” and this resulted in total 35,585 articles. After eliminating articles without abstracts (i.e., only titles or abstract keywords), our final text data contained the total 15,015 documents. To construct the corpus, we used abstract keywords that concisely capture messages delivered by the paper. To achieve the richer corpus, we also used the word2vec (Mikolov et al., 2013a) to train against relationships between nouns from the abstract and the abstract keywords. Specifically, word2vec extracted nouns from abstracts, which were embedded near to the abstract keywords, and added those selected words to the corpus. To train the words’ network, Mikolov et al. (2013b)
suggested the negativesampling approach, which fits the network of words by training the near words and unrelated words, and this approach was reported to be efficient in vectorizing the words’ relationships.
Goldberg and Levy (2014) expanded the negativesampling strategy to model the words and the contexts through the joint modeling of words and contexts, which makes the problem nonconvex. Before implementing the negative sampling, we need to assign the window size that defines how many neighbors of words to consider. For example, let’s assume that we want to select four neighboring words of ‘princess’. According to the word embedding network, there are only a few words located close in the latent Euclidean space, e.g., ‘horse’, ‘money’, ‘king’, ‘queen’, ‘princess’, ‘prince’, ‘palace’, ‘flowers’, and ‘…’. Since we want to select four neighboring words, we set window size as 2 so that two words from each side centering ‘princess’ can be considered. Therefore, we define ‘king’, ‘queen’, ‘prince’, and ‘palace’ as near words for the word ‘princess’. On the other hand, we can sample 20 negative words that are not included in these near word sets. By repeating this process, it trains the words’ network that reflects the context. In this way, we could obtain the word embedding network with 256 dimensions. Using the trained word2vec network, we selected ten words from the abstract nouns that were near to each abstract keyword. Table 1 shows the summary of corpus construction results with 9,643 words from 15,015 documents. We further filtered out noise words including single alphabet, numbers, and other words that are not meaningful, e.g., ‘p.001’, ‘p.05’, ‘n1427’, ‘l.’, and ‘ie’. Finally, to obtain more meaningful topics, we removed common words like ‘data’, ‘analysis’, ‘fact’, and ‘disease’. The full list of filtered words can be found in supplementary.Documents  Keywords in Corpus  
COVID19  15,015  9,643 
4 Method
We developed a novel framework for estimating topic relationships through interaction map, which positions topics on an Euclidean latent space. This framework consists of the following four steps, as illustrated in Figure 1
. In the first step, we implement text mining with natural language processing and construct the word corpus by expanding a set of words using the
word2vec model (Griffiths and Steyvers, 2004). In the second step, based on this word corpus, we extract the topicword distribution, where each topic is characterized with the corresponding topicspecific distribution of words estimated using the BTM. Using this topicword distribution, we can extract meaningful words that affect topic characteristics. In the third step, the topic relationships are estimated using the latent space item response model (Jeon et al., 2021), which provides latent topic positions. Finally, in the fourth step, we can map the interactive relationships among topics with topicspecific traces.4.1 Estimating Latent Topics using Biterm Topic Model
The text data from biomedical papers will be input for BTM. We extract information from the text using a morphology analysis, one type of natural language processing techniques. Specifically, it splits each word with suffix to identify the base element unit of a term. Among the basic units of words, we first extract nouns in their most basic forms. This set of nouns is called a corpus. We further expand the corpus by adding relevant words using word2vec, which vectorizes distances among words in the Euclidean latent space according to their similarity in meaning. We extract neighboring words based on these distances and enlarge the word set by collecting these words. Following this, it is necessary to understand the overall semantic structures of a given text. It summarizes the latent structures, called topics, by identifying topics and estimating their corresponding clusters of words. That is, we can estimate topics and their distributions of words using topic modeling. The abstract is an excellent source to understand the overall text. Since most abstracts are limited to 200 words, they could be regarded as short texts. Therefore, we use the BTM for literature mining. To implement BTM, we first need a word corpus. Then, we extract biterms from each paper, which is input for the BTM.
The BTM is based on the following assumption describing how biterms and topics are jointly related:

Two words are assumed to belong to some hidden clustered set of words.

It is assumed that there are hidden topics, each of which contains similar meaning of words.

It is assumed that those hidden clustered set of words are hidden topics.
Based on these assumptions, as shown in Figure 2, the likelihood of BTM consists of both topicword distribution and topic distribution. Therefore, we need two sets of parameters to estimate the topic distribution and the topicword distribution . The whole likelihood of BTM is constructed as follows. First, the prior distribution for words () is set to Dirichlet distribution with hyperparameter while the prior distribution for topics is set to Dirichlet distribution with hyperparameter . Next, we represent the topic with the latent variable , which follows Multinomial distribution with parameter . Likewise, each word follows Multinomial distribution with paramereter so that each word can be generated from a specific topic. Therefore, there are three parameters to estimate, including , , and . The likelihood construction process can be summarized as follows:

[leftmargin=*,labelindent=14pt,label=Step 0.]

Draw a whole topic distribution from .

For each biterm b from biterm set B, calculate to which among latent topics those two words belong:

Draw a topicword distribution of topic from .

Draw probabilities for two words from the topicword distribution corresponding to the selected topic:
After the above steps, the joint likelihood of all biterm set B is calculated as:
(1) 
The conditional posterior for a latent topic , , is given as:
(2) 
where is the number of times that the biterm is assigned to topic , refers to the topic without biterm , and is the number of times of the word assigned to the topic . Because a direct application of the Gibbs sampling for sometimes can result in lack of convergence due to dependency between variables, we use the collapsed Gibbs sampling to constrain unnecessary parameters by integrating out (Liu, 1994). In particular, because the prior distributions are Dirichlet distributions, and can be integrated out. After some iterations, we can construct distribution of and with estimated statistics and , given as follows:
(3) 
After then, we can obtain the topicword distribution and the topic distribution . Each topic contains words and their corresponding probabilities so it is meaningful to compare each topic based on their word distributions. The simplest way to distinguish topics is to compare word memberships between topics. Since the output of each topicword distribution includes all words, we might not be able to determine characteristics of topics if we use all the words that topics share. Therefore, we select only meaningful words from each topic to estimate the relationships among topics based on their representative words. According to Figure 2, through the BTM, we can construct the matrix with dimension , where denotes the number of words, refers the number of topics, and each cell represents probabilities to belong to each topic. To determine a criterion to choose words, we calculate coefficient variation and maximum probability from each row of matrix
. Each value represents the variation of word probabilities among different topics and the degree of word’s linkage to a particular topic. Since BTM results in topicword distribution where each word’s probability is measured within each topic, we need to adjust their variation rather than simply calculating a variance. Therefore, we divide the standard deviation by the mean of word’s probabilities from each topic. There are two reasons for choosing a coefficient variation and maximum probability from each row of matrix
as a criterion to select words. First, it is expected that important words have large variation in probabilities among topics because if a word has low variation across topics, it is likely that word does not represent any topic specifically. Therefore, meaningful words can be selected based on their variations and using coefficient variation can further scale the words’ dispersion among topics. Second, in order to be a meaningful word, it should also have high probability in at least one topic. For example, if a word has high variation but only low possibilities across topics, this word still cannot differentiate topics. Therefore, we can effectively characterize the topic by selecting a word with high probability in at least one topics and those with large variation.4.2 Estimating Topic Relationships and Visualizing the Trace of Interaction Map Using Latent Space Item Response Model
We estimate interactions among topics and visualize their relationships by mapping on the interaction map. Hoff, Raftery and Handcock (2002) proposed the latent space model, which expresses a relationship between actors of a network in an unobserved “social space”, socalled latent space. Inspired by Hoff, Raftery and Handcock (2002), Jeon et al. (2021) proposed the latent space item response model (LSIRM) that viewed item response as a bipartite network and estimated the interaction between respondents and items using the latent space. LSIRM models two parts: an attribute part and an interaction part (Figure 3 , and , respectively). In the attribute part, LSIRM estimates how much respondents respond to certain items and how many items are answered by some respondents. In the interaction part, LSIRM estimates the interaction between items and respondents, along with the latent position of each item and respondent on the interaction map. Given our goal to estimate the interactions among topics and visualize their latent positions on the interaction map based on their associated words, we use LSIRM with as a bipartite network, where an item indicates a topic and respondents refers to words. However, the original LSIRM proposed by Jeon et al. (2021) cannot be directly applicable here because it was designed for binary item response dataset, where each cell in the item response data is binary valued (0 or 1). On the contrary, here our input data has continuous probabilities indicating how likely each word belongs to each topic. Therefore, in order to apply LSIRM to our input data , we need to expand the Jeon et al. (2021) model to a Gaussian version, which is described in detail below.
The modified Gaussian version of LSIRM can be written as
(4) 
where indicates the probability of word belongs to topic , for and
. Because the original LSIRM use logit link function to handle the binary data, here we use the linearity assumption between
and the attribute part with the interaction part. We add an error term to satisfy the normality equation. We use the notation , and represents the Euclidean distance between latent positions of word and topic . Here, the shorter distance between and implies the higher probability that word links to in topic. Therefore, latent positions of topics can be estimated based on the distances with words. Given the model described above, we use Bayesian inference to estimate parameters in the Gaussian version of LSIRM. We specify prior distributions for the parameters as follows:
where is a vector of zeros and is the identify matrix. We fixed as constant value. The posterior distribution of LSIRM is
and we use Markov Chain Montel Carlo (MCMC) to estimate the parameters of LSIRM. In this way, we can obtain latent positions of
and on the interaction map . Since we are interested in constructing the topic network, we utilize and make it as matrices of .After proceeding with the LSIRM model with various sets of matrices , we could obtain matrices of , composed of coordinates of each topic. In order to further improve interpretation of relationships among topics, we trace how their latent positions change as a function of word sets. Specifically, we compare topics’ latent positions from each matrix with the following steps. First, we implement a Procrustes matching two times: (1) within the MCMC samples generated from LSIRM, to tackle the invariance property (socalled withinmatrix matching); and (2) for the estimated matrices, to locate topics on the same quadrant (socalled betweenmatrix matching). Second, we take average of the distances of topics’ latent positions from the origin, to measure the degree of dependency structure. Specifically, the longer distance of latent positions implies the stronger dependency of the network. To locate matrix onto the same quadrant, we choose the baseline matrix, which maximizes the dependency structure among topics. It helps nicely show the change of topics’ latent positions because those rotated positions from each matrix are based on the most stretched out network from the origin. Note that the baseline matrix is . Finally, we rotate the axes to improve the interpretability of the relationship among topics using oblique factor rotation (Jennrich, 2002). After implementing these (which correspond to (c) and (d) in Figure 3), we visualize relationships among topics by tracing the coordinates of each topic. As fitting the LSIRM model, we collect MCMC samples for each topic’s latent positions. Note that there exists multiple possible realizations for latent positions because the distances between pairs of respondents and items, which are included in a likelihood function, are invariant under rotation, translation, and reflection (Hoff, Raftery and Handcock, 2002; Shortreed, Handcock and Hoff, 2006). In order to tackle this invariance property for determining latent positions, we implement withinmatrix Procrustes matching (Borg and Groenen, 2005) as postprocessing of MCMC samples. After implementing the withinmatrix matching for the matrix , we additionally execute the betweenmatrix Procrustes matching based on the baseline matrix to compare the transition of the topic’s latent positions for the different input matrices . We assign to the matrix that maximizes dependency. Finally, we can obtain the repositioned matrices , which still maintain the dependency structure among topics but located in the same quadrant. With the oblique rotation, the interpretability of axes can be further improved and topics can be categorized based on these axes. For this purpose, we apply the oblim rotation (Jennrich, 2002) to the estimated topic position matrix , using the R package GPAroation (Bernaards and Jennrich, 2005). We denote the rotated topic position metric by . To interpret the trajectory plot showing traces of topics’ latent positions, we extract the rotation information matrix () resulting from an oblique rotation as the baseline matrix . Then, we multiply each matrix () by the rotation matrix () to plot the topics’ latent positions.
5 Results
To implement BTM, we set the number of topic as 20. For the hyperparameters, we assigned = 3 and = 0.01. Since our main goal is to visualize the topic relationships, we empirically searched and determined the hyperparameters. The posterior distribution of topicword was estimated using the Gibbs sampler, where we generated samples with 50,000 iterations after the 20,000 burnin iterations, and then implemented thinning for every iteration. Table 2 shows the structure of topicword distribution indicating degree of relatedness of words to a specific topic. In each topicword distribution obtained from BTM, words with high probabilities characterize the topic. Figure 3(a) shows histograms of logtransformed probabilities for each of Topics 1  4 (histograms for the other topics can be found in Supplementary) and it indicates bimodal topicword distribution. Specifically, the mode on the left corresponds to the words that had low possibilities of belonging to a specific topic, whereas the mode in the center corresponds to the words that had high probabilities enough to characterize meaning of the topic. Therefore, to reduce noises, it might be desirable to estimate topic relationships using only the words corresponding to the mode in the center, rather than using all the words. Based on these histograms, the minimum cutoff value that defined the tail of a normal distribution was ranged between 11 and 12. We calculated the number of words whose logscaled probabilities were above 11 to 12 to specify the minimum number of words for estimating the topic network, and we found that more than 1,000 words are needed to properly represent topics. Based on this rationale, we decided to use at least 1,000 words to estimate positions of topics on the latent space based on positions of words. In order to extract meaningful words that can discriminate characteristics of topics, we chose words with probabilities varying from topic to topic and with relatively high maximum probabilities. Figure 3(b) shows a plot of the relationship between max probability and coefficient variation. Based on this rationale, we selected words using both max probability and coefficient variation. In this study, rather than using a fixed number of words, we investigated relationships among topics identified with different numbers of words, which were determined using the two criteria described above. Specifically, we obtained multiple matrices corresponding to the top 60% to 40% of words determined based on the two criteria. The numbers of words corresponding to the 60th and 40th percentiles were 2,648 and 1,095, respectively. At the end of the day, we used 21 sets of matrices, , as the LSIRM input data, where their dimensions were ranged from to .
Words  Topic1  Topic2  …  Topic 20 

nutrient  8.4E08  9.8E08  …  9.1E08 
relationship  1.0E03  1.5E03  …  2.7E03 
inflammation  1.4E04  5.8E04  …  6.3E04 
…  …  …  …  … 
After then, we obtained the 21 sets of matrices and we considered 20 items for all the matrix sets. To estimate topics’ latent positions , MCMC was implemented. The MCMC was run 55,000 iterations and the first 5,000 iterations were discarded as a burnedin process. Then, from the remaining 50,000 iterations, we collected 10,000 samples using thinning of 5. To visualize relationships among topics, we used twodimensional Euclidean space. Additionally, we set 0.28 for jumping rule, 1 for jumping rule, and 0.06 for and jumping rules. Here, we fixed prior and let follow N(0,1). We set . LSIRM takes each matrix as input and provides the matrix as output after the ProcrustesMatching within the model. Since we calculate topics’ distance on the 2dimensional Euclidean space, is of dimension . We visualized interactions among topics using the baseline matrix chosen so that we can compare topics’ latent positions without having identifiability issues from the invariance property. From , we calculated the distance between origin and each topic’s coordinates. The closer distance of a topic position from the origin indicates the weaker dependency with other topics. Figure 4(a) showed that dependency structure among topics starts to be built up from . Based on this rationale, we chose as the baseline matrix . With this baseline matrix , we implemented the Procrustes matching to align the direction of the topic’s latent positions from each matrix . Using this process, we could obtain the matrix matched to the baseline matrix . We named the identified topics based on top ranking words using the matrix. This is because the baseline matrix has the most substantial dependency structure comparing other matrix containing the words that characterize topics nicely. Table 3 shows the name of each topic determined based on their associated words. The top 30 words for each topic identified using can be found in Supplementary.
Topic  Name 

1  Lung Scan Imaging 
2  Virus Binding 
3  Diet 
4  General Health Care 
5  Patient Subgroup 
6  Cytokines Storm 
7  Immune System 
8  Literature Review 
9  Symptoms 
10  Cardiovascular 
11  Family Impact 
12  Social Impact 
13  Outbreak Environment 
14  Diagnosis 
15  Sociodemographics 
16  Unknown (Hard to characterize) 
17  Treatment 
18  Medical Healthcare 
19  Worldwide View 
20  Molecular Biology 
The first topic is about lung cancer imaging and includes words such as ‘chest’, ‘tomography’, and ‘scan’. The second topic discusses binding mechanism of COVID19, which includes words like ‘dock(ing)’, ‘bind(ing)’, and ‘spike’. The third topic is related to dietary behaviors in the context of COVID19 and includes words like ‘vitamin’, ‘nutrient’, ‘carbon’, and ‘diet(ary)’. The fourth topic discusses various issues related to general health care such as ‘healthcare’, ‘surgery’, ‘telemedicine’, ‘staff’, and ‘equipment’. The fifth topic is related to population subgroups with potentially lower and higher risks, e.g., ‘male’, ‘older’, and ‘comobidity’. The sixth topic is related to the cytokine storm, which occurs due to overactivation of immune system and can result in severe damage across multiple organs of COVID19 patients (Ragab et al., 2020). This topic includes words like ‘cytokine’, ‘storm’, ‘inflammation’, and ‘IL6’ The seventh topic discusses the immune system more in general context, e.g., various immune cell subsets such as ‘lymphocyte’, ‘neutrophil’, and ‘CD8 T cell’. The eighth topic is relevant to the literature review, e.g., ‘database’, ‘review’, ‘literature’, ‘MEDLINE’, ‘metaanalysis’, ‘PubMed’, and ‘Scopus’. The ninth topic describes various types of COVID19 symptoms such as ‘anosmia’ and ‘hyposmia’, i.e., loss of ‘smell’ and ‘taste’. The tenth topic includes various words related to the cardiovascular system, including ‘cardiovascular’, ‘myocardiac’, ‘thrombosis’, ‘stroke’, and ‘coagulation’. The eleventh topic discusses various impact on family such as ‘mental’, ‘children’, and ‘school’. The twelfth topic discusses more general social impact, including ‘sector’ and ‘vulnerable’. The thirteenth topic describes the environment where the COVID19 outbreak occurred, e.g., ‘Wuhan’, ‘Hubei’, ‘Korea’, ‘province’, ‘temperature’, and ‘pollution’. The fourteenth topic is related to the diagnosis of COVID19 such as ‘swab’, ‘IgG’, ‘PCR’, ‘IgM’, ‘immunoassay’, and ‘ELISA’. The fifteenth and sixteenth topics are somewhat vague to characterize but the former seems to be relevant to sociodemographics. The seventeenth topic is about the treatment of COVID19 and includes words like ‘Hydroxychloroquine’, ‘Azithromycin’, and ‘Tocilizumab’. The eighteenth topic discusses more specific medical healthcare such as ‘mask’, ’equipment’, ‘PPE’, ‘surgical’, ‘supply’, ‘glove’, and ‘shield’. The nineteenth topic generally describes what happens worldwide (e.g., ‘worldwide’ and ‘globe’). Finally, the twentieth topic is specific to molecular biology related to COVID19, which includes words such as ‘genome’, ‘epitope’, ‘amino acid’, ‘phylogenetics’, and ‘nucleotide’.
To improve interpretation of the identified latent space (e.g., finding the meaning of topics’ transition based on the Xaxis or Yaxis), we rotated the original latent space so that the axes better encompass topics. We applied oblim rotation to the estimated topic position matrix using the R package GPArotation (Bernaards and Jennrich, 2005), and obtained matrix with the rotation matrix . In the same way, we rotated the other estimated topic position matrix resulting in for . Figure 4(b) shows representing the topics’ latent positions. In this figure, the topics in the center include ‘Outbreak Environment’, ‘Diagnosis’, ‘Worldwide View’, and ‘Immune System’. In contrast, ‘Molecular Biology’ corresponds to the case of weak dependency with other topics. There are two possibilities that lead to low dependency. First, it is possible that there were a small number of words that can distinguish their topics’ characteristics from the other topics. Second, it is also possible that most of the words were common words shared with other topics. To eliminate visualization bias due to selection of the number of words, we tracked the topics’ latent positions by using different input matrices . We interrogated what kind of topics have been extensively studied in the biomedical literature on COVID19. In addition, we also studied how those topics were related to each other, based on their closeness in the sense of latent positions. We also partially clustered the topics based on their relationships using the quadrants. This allows us to check which studies about COVID19 are relevant to each other and could be integrated. Figure 6 displays the trajectory plot and it shows how topics were positioned on the latent space and how these topics make transition. More specifically, the direction of arrows refers to how topics’ coordinates changed as a function of numbers of words, where each arrow moves from to as the number of words decreases.
According to Figure 6, we observed two meaningful distinct groups: One group independent of other topics and the other with strong dependency with other topics. First, the topics ‘Outbreak Environment’, ‘Diagnosis’, and ‘Worldwide’ (Topics 13, 14, and 19, respectively) were located in the center of the plot. This indicates that no matter how many words were used to estimate the topics’ latent positions, those topics remained as general topics and have shares many words with other topics. This makes nice sense given the fact that many articles have mentioned the outbreak of COVID19, the diagnosis of COIVD19, and how the world treats or considers this notorious pandemics. For example, among the 137K publications mentioning “COVID19” in the PubMed database, more than 76,000 and 35,000 publications also mentioned “outbreak” and “diagnosis”, respectively. Second, the topics ‘Social Impact’, ‘Family Impact’, ‘Cardiovascular’, and ‘Cytokine Storm’ (Topics 12, 11, 10, and 6, respectively) were located away from the center in the plot, which implies their dependency structures with other topics. These topics usually stay on the boundary of the plot regardless of the number of words because they consist mainly of unique words. Finally, the topics like ‘Sociodemographics’, ‘General Health Care’, and ‘Virus Binding’ (Topics 15, 4, and 2, respectively) start from the origin, stay away from the origin for a while, and then return to the origin. This implies that it could not maintain the nature of the topic when less words are considered, and it is likely that those topics are either ongoing research or burgeoning topic that is not studied enough yet. Moreover, we interpreted the topics’ meaning based on their latent positions. We now make interpretation using subsets of topics divided by the axes. Since we implemented the oblique rotation that maximizes each axis’ distinct meaning, we can render meaning to an axis. Figure 6 indicates that there are five topic clusters. First, the center cluster denoted as (A) in Figure 6 are about the outbreak of COVID19: The world view of COVID19, diagnosis of cover 19, and the environment of outbreak COVID19. These topics are positioned in the center because they share the common words with the other topics, i.e., most literature mention the outbreak of COVID19. Second, the topics located on the left side of the plot (cluster (B) in Figure 6) are related to the impact of COVID19 at the society level. For instance, the impact of COVID19 on health care centers, including hospitals, are visible phenomena of COVID19. These subjects pertain to ‘Social Impact (12)’, ‘Medical Healthcare (18)’, ‘Family Impact (11),’ ‘Sociodemographics (15)’, and ‘General Health Care (4)’. Third, the next cluster, called (C), is relevant to the strategies to study COVID19. For instance, this cluster includes the literature review of COVID19, patients’ lung scan image, symptoms, and treatment. Fourth, the topics corresponding to the cluster (D) are related to what happens inside our body in response to COVID19, e.g., cytokine storm, immune system responding to the COVID19 infection, and cardiovascular impacts of COVID19. Finally, the cluster (E) is related to molecular changes upon the COVID19 infection, e.g., binding mechanism of SARSCoV2. We note that, aforementioned, we can also interpret each axis and x axis can be interpreted as spectrum from macro (more negative) to micro perspectives (more positive). In summary, we identified five main groups of the COVID19 literature: The outbreak of COVID19, lifestyle after COVID19 attack, COVID19 study strategies, impacts of COVID19 effect on the body, and molecular changes by COVID19 infection counterclockwise. Here we can derive another insight from the locations of clusters. Specifically, from the cluster (A) to the cluster (E), we can observe transition from macro perspectives to micro perspectives clockwise. Specifically, this flow starts with the center cluster (A) related to the occurrence of COVID19, followed by studies of the social impact of COVID19 (cluster (B)) and then patientlevel investigation (cluster (C); lunch scanning and symptoms). This flow ends with the clusters (D) and (E), which are related to microlevel events, e.g., how SARSCoV2 binding occurs and how the immune system responds to upon the COVID19 infection.
6 Discussion
In this manuscript, we proposed a novel analysis framework to estimate and visualize relationships among topics based on the text mining results. It allows enhancing our understanding of COVID19 knowledge reported in the biomedical literature, by evaluating topics’ networks through their latent positions estimated based on topic sharing patterns. The proposed approach overcame limitations of existing approaches, especially discrete and static visualization of relationship among topics. First, because we position topics on a latent space, relationships among topics can be intuitively investigated and also easy to interpret. Second, our method allows deeper understanding of the network among topics and capturing their dynamics with a continuous representation by tracking the change of topics’ relationships. To the authors’ best knowledge, this is the first attempt to integrate the biterm model and the latent space item response model within a unified framework. The application of our method to COVID19 literature indicated that there are five main subjects in the COVID19 biomedical literature. The proposed framework can still be further improved in several ways, especially by allowing wordlevel inference, i.e., extraction of meaningful words that characterize each topic. Although distance between each topic and relevant words is taken into account in our model when estimating topics’ latent positions, simultaneous representation and visualization of words are still not embedded in the current framework. We believe that adopting a variable selection procedure to determine key words can potentially address this issue and this will be an interesting future research avenue.
Acknowledgements
This work was supported by the National Institutes of Health [grant numbers R01GM122078, R21CA209848, U01DA045300 awarded to DC], Yonsei University Research Fund [grant number 2019220210 awarded to IHJ] and the National Research Foundation of Korea [grant number NRF 2020R1A2C1A01009881; Basic Science Research Program awarded to IHJ]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
References
 Bernaards and Jennrich (2005) [author] Bernaards, Coen AC. A. Jennrich, Robert IR. I. (2005). Gradient projection algorithms and software for arbitrary rotation criteria in factor analysis. Educational and Psychological Measurement 65 676–696.
 Blei and Lafferty (2007) [author] Blei, David MD. M. Lafferty, John DJ. D. (2007). A correlated topic model of science. The annals of applied statistics 1 17–35.

Blei, Ng and Jordan (2003)
[author] Blei, David MD. M., Ng, Andrew YA. Y. Jordan, Michael IM. I. (2003). Latent dirichlet allocation. Journal of machine Learning research 3 993–1022.
 Borg and Groenen (2005) [author] Borg, IngwerI. Groenen, Patrick JFP. J. (2005). Modern multidimensional scaling: Theory and applications. Springer Science & Business Media.
 Chen, Allot and Lu (2020) [author] Chen, Q.Q., Allot, A.A. Lu, Z.Z. (2020). Keep up with the latest coronavirus research. Nature 579 193. 10.1038/d41586020006941
 Chen and Kao (2017) [author] Chen, GuanBinG.B. Kao, HungYuH.Y. (2017). Word cooccurrence augmented topic model in short text. Intelligent Data Analysis 21 S55–S70.
 Chowdhury (2010) [author] Chowdhury, Gobinda GG. G. (2010). Introduction to modern information retrieval. Facet publishing.
 Dong, Du and Gardner (2020) [author] Dong, EnshengE., Du, HongruH. Gardner, LaurenL. (2020). An interactive webbased dashboard to track COVID19 in real time. The Lancet infectious diseases 20 533–534.
 Erosheva, Fienberg and Lafferty (2004) [author] Erosheva, ElenaE., Fienberg, StephenS. Lafferty, JohnJ. (2004). Mixedmembership models of scientific publications. Proceedings of the National Academy of Sciences 101 5220–5227.
 Goldberg and Levy (2014) [author] Goldberg, YoavY. Levy, OmerO. (2014). word2vec Explained: deriving Mikolov et al.’s negativesampling wordembedding method. arXiv preprint arXiv:1402.3722.
 Griffiths and Steyvers (2004) [author] Griffiths, T. L.T. L. Steyvers, MM. (2004). Finding scientific topics. Proceedings of the National Academy of Sciences 101 5228–5235.

Gruber, Weiss and
RosenZvi (2007)
[author] Gruber, AmitA., Weiss, YairY. RosenZvi, MichalM. (2007). Hidden topic markov models. In Artificial intelligence and statistics 163–170. PMLR.
 Hoff, Raftery and Handcock (2002) [author] Hoff, Peter DP. D., Raftery, Adrian EA. E. Handcock, Mark SM. S. (2002). Latent space approaches to social network analysis. Journal of the american Statistical association 97 1090–1098.
 Jennrich (2002) [author] Jennrich, Robert IR. I. (2002). A simple general method for oblique rotation. Psychometrika 67 7–19.
 Jeon et al. (2021) [author] Jeon, M.M., Jin, I. H.I. H., Schweinberger, M.M. Baugh, SamS. (2021). Mapping Unobserved Item–Respondent Interactions: A Latent Space Item Response Model with Interaction Map. Psychometrika. https://doi.org/10.1007/s11336021097625
 Lakkaraju, Bhattacharya and Bhattacharyya (2012) [author] Lakkaraju, HimabinduH., Bhattacharya, IndrajitI. Bhattacharyya, ChiranjibC. (2012). Dynamic multirelational Chinese restaurant process for analyzing influences on users in social media. In 2012 IEEE 12th International Conference on Data Mining 389–398. IEEE.

Li et al. (2016)
[author] Li, WeijiangW., Feng, YanmingY., Li, DongjunD. Yu, ZhengtaoZ. (2016). Microblog topic detection method based on BTM topic model and Kmeans clustering algorithm. Automatic Control and Computer Sciences 50 271–277.
 Liu (1994) [author] Liu, Jun SJ. S. (1994). The collapsed Gibbs sampler in Bayesian computations with applications to a gene regulation problem. Journal of the American Statistical Association 89 958–966.
 Liu et al. (2016) [author] Liu, LinL., Tang, LinL., Dong, WenW., Yao, ShaowenS. Zhou, WeiW. (2016). An overview of topic modeling and its current applications in bioinformatics. SpringerPlus 5 1608.
 McCallum, CorradaEmmanuel and Wang (2005) [author] McCallum, AndrewA., CorradaEmmanuel, AndrésA. Wang, XueruiX. (2005). The authorrecipienttopic model for topic and role discovery in social networks: Experiments with enron and academic email. Computer Science Department Faculty Publication Series 44.
 Mei et al. (2008) [author] Mei, QiaozhuQ., Cai, DengD., Zhang, DuoD. Zhai, ChengXiangC. (2008). Topic modeling with network regularization. In Proceedings of the 17th international conference on World Wide Web 101–110.
 Mikolov et al. (2013a) [author] Mikolov, TomasT., Chen, KaiK., Corrado, GregG. Dean, JeffreyJ. (2013a). Efficient estimation of word representations in vector space. arXiv preprint arXiv:1301.3781.
 Mikolov et al. (2013b) [author] Mikolov, TomasT., Sutskever, IlyaI., Chen, KaiK., Corrado, GregG. Dean, JeffreyJ. (2013b). Distributed representations of words and phrases and their compositionality. arXiv preprint arXiv:1310.4546.
 Nigam et al. (2000) [author] Nigam, KamalK., McCallum, Andrew KachitesA. K., Thrun, SebastianS. Mitchell, TomT. (2000). Text classification from labeled and unlabeled documents using EM. Machine learning 39 103–134.
 Ragab et al. (2020) [author] Ragab, DinaD., Salah Eldin, HaithamH., Taeimah, MohamedM., Khattab, RashaR. Salem, RamyR. (2020). The COVID19 cytokine storm; what we know so far. Frontiers in Immunology 11 1446.
 Rusch et al. (2013) [author] Rusch, ThomasT., Hofmarcher, PaulP., Hatzinger, ReinholdR. Hornik, KurtK. (2013). Model trees with topic model preprocessing: An approach for data journalism illustrated with the WikiLeaks Afghanistan war logs. The Annals of Applied Statistics 7 613–639.
 Shortreed, Handcock and Hoff (2006) [author] Shortreed, SusanS., Handcock, Mark SM. S. Hoff, PeterP. (2006). Positional estimation within a latent space model for networks. Methodology 2 24–33.
 Yan et al. (2013) [author] Yan, XiaohuiX., Guo, JiafengJ., Lan, YanyanY. Cheng, XueqiX. (2013). A biterm topic model for short texts. In Proceedings of the 22nd international conference on World Wide Web 1445–1456.
 Zhao et al. (2011) [author] Zhao, Wayne XinW. X., Jiang, JingJ., Weng, JianshuJ., He, JingJ., Lim, EePengE.P., Yan, HongfeiH. Li, XiaomingX. (2011). Comparing twitter and traditional media using topic models. In European conference on information retrieval 338–349. Springer.
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