Topic structure of the COVID-19 education literature as a document-word hypergraph • hypernets

The text hypergraph pipeline in hypernets represents a corpus as a document-word hypergraph and partitions it with a spectral method. This vignette applies the pipeline to the covid corpus of the sbert package, a Scopus export of 4,170 records on COVID-19 and education published between 2020 and 2024. Each record has an abstract and a publication year. The analysis proceeds in eight steps: text cleaning, hypergraph construction, selection of the number of topics, partitioning, topic description, topic sizes, topic quality, soft membership, and the network of relations between topics.

Text cleaning

clean_text() removes the non-content that a bibliographic export carries in its abstracts. It decodes HTML entities, strips tags, normalises typographic characters, and removes bracketed citation numbers, list markers, URLs, DOIs, trailing copyright notices and bare numbers. It takes a character vector or a data frame with a text column and returns an object of the same length or the same rows. A text whose share of alphabetic characters falls below min_content is replaced by the empty string. The remove argument takes additional patterns; here it names the placeholder that Scopus inserts for a missing abstract.

abstracts <- clean_text(sbert::covid, column = "Abstract",
                        remove = "no abstract available", min_content = 0.5)
abstracts <- unique(abstracts)

The result is a data frame with the same columns as the input. The 323 placeholder rows and four low-content rows now hold empty abstracts, and unique() has collapsed the records that appear twice in the export. Empty abstracts are retained at this stage so that the year column stays aligned with the text.

Hypergraph construction

text_hypergraph() builds a weighted hypergraph from a corpus. With the default construction = "bag" and nodes = "doc", each document is a node and each word is a hyperedge that contains every document using the word. With the default weight = "n", the incidence cell of a document and a word is the count of the word in the document. Tokens are lower-cased alphabetic strings, so numbers do not enter the vocabulary. Documents without any remaining token are dropped with a warning.

stops <- c(stop_words_en(), "covid", "pandemic")
hg <- text_hypergraph(abstracts, column = "Abstract", stop_words = stops,
                      min_count = 5L)
hg

The stop list contains the English function words of stop_words_en() and the two words that name the subject of every abstract; a word present in every document does not separate any two documents. Words used in fewer than five abstracts are excluded by min_count. The incidence matrix has more than a million cells, so the default sparse = NULL stores it as a sparse matrix.

Number of topics

hg_cluster() with what = "eigenvalues" returns the leading eigenvalues of the normalised hypergraph Laplacian (Zhou, Huang and Schölkopf, 2007) and the gap after each. A large gap between consecutive eigenvalues indicates a partition that the structure supports.

hg_cluster(hg, k = 18, seed = 1, what = "eigenvalues")

The gap after the second eigenvalue is the largest, followed by the gaps after the third and fourth. The gaps after the fifth and later eigenvalues are an order of magnitude smaller. The spectrum therefore supports two or four clusters. The partition below uses sixteen clusters, the number of topics in the structural topic model of this literature reported by Saqr et al. (2023), so that the two sets of topics can be compared. Sixteen is a finer partition than the spectrum supports on its own; its justification is the vocabulary each cluster owns, reported in the last section.

Partition

hg_cluster() embeds the documents in the leading eigenvectors of the Laplacian and partitions the embedding with k-means. With the default type = "zhou" the Laplacian is built from hyperedge membership alone: each hyperedge has unit weight and the incidence cells are not read. The function takes the hypergraph, the number of clusters and a seed, and returns a data frame with one row per document and its cluster label.

topics <- hg_cluster(hg, k = 16, seed = 1)
head(topics)

Topic description

hg_keywords() ranks the words of each cluster. It takes the hypergraph and the partition and returns a data frame with one row per cluster and word, containing the score, the word’s share and the number of cluster documents that contain the word. The print method shows one row per cluster with its words joined; the returned table itself is the long form. The default score, type = "mass", is the summed incidence weight that a cluster’s documents place on the word, which under weight = "n" is the word’s count within the cluster.

hg_keywords(hg, topics)

Under the default ranking every cluster lists the same words: learning, students, education, online and teaching. These are the most frequent words of the corpus, and they are the most frequent words of every cluster as well. The share column, the fraction of a word’s corpus count that falls in the cluster, separates the clusters. sort_by = "share" ranks by that column, and min_docs sets a support floor so that a word owned by a cluster only because it occurs in a few of its abstracts does not reach the top. The type argument accepts several scores at once and returns one block of rows per score.

words <- hg_keywords(hg, topics, type = c("frequency", "ctfidf", "centrality"),
                     sort_by = "share", min_docs = 15)
words

The three scores are the raw count of the word in the cluster (frequency), the class-based tf-idf of Grootendorst (2022) (ctfidf), and the PageRank of the word in the cluster’s own word hypergraph, in which the cluster’s abstracts are the hyperedges (centrality; the default measure). Ten words per cluster are returned by default. Ranked by share, the three scores return the same owned vocabulary for each cluster and differ in the order of the words. The sixteen clusters correspond to distinct literatures: parents and childhood, infection prevention, systematic reviews, lockdown policy, narrative essays, messaging tools in Indonesian higher education, industry and recovery, laboratory teaching, teacher agency, questionnaire validation, Spanish methodological studies, technology acceptance models, dental and surgical assessment, disadvantaged households, the spring campus transition, and residency training.

plot() on the keyword table draws one panel per cluster and score, with one bar per word.

plot(words, value = "share")

Topic sizes

hg_topic_sizes() counts the documents of each topic and their share of the clustered documents. With weights, a numeric vector named by document, it also reports the weighted size and share; a citation count or a repeat count are typical weights. One row per topic.

sizes <- hg_topic_sizes(hg, topics)
sizes
plot(sizes)

Topic coherence and exclusivity

hg_topic_quality() scores each topic’s top words on two axes, with the definitions the structural topic model uses (Roberts, Stewart & Tingley 2019), so a hypergraph clustering and a probabilistic topic model can be compared on the same numbers. The top words are the most probable words of the topic’s documents.

Coherence is UMass (Mimno et al. 2011): for every pair of top words, the log of how often the rarer word’s documents also contain the other, counted over the whole corpus and summed. It is never positive; closer to zero means the words turn up in the same documents.
Exclusivity is FREX (Bischof & Airoldi 2012): a weighted harmonic mean of how frequent each top word is in the topic and how exclusive it is to the topic, summed over the top words. Higher means the topic owns its words rather than sharing them with the rest of the corpus.

quality <- hg_topic_quality(hg, topics, min_docs = 15)
quality
plot(quality)

A topic high on both axes has a vocabulary that co-occurs and that no other topic uses; a topic low on coherence gathers abstracts that share words but not a subject. coherence = "npmi" gives normalised PMI instead (Bouma 2009; Lau, Newman & Baldwin 2014), and words = scores the top words of a topic model fitted elsewhere with the same measures.

Soft membership

hg_membership() turns the hard partition into a membership of every document in every topic. Documents are placed in the spectral embedding that hg_cluster() cut, each topic’s centre is the mean position of its documents, and a document’s membership in a topic is the fuzzy c-means weight with fuzziness 2, the inverse squared distance to the centre normalised over topics. A document at a centre has membership 1 there; one halfway between two centres has 0.5 in each. One row per document and topic.

membership <- hg_membership(hg, topics)
head(membership, 16)
plot(membership)

The memberships sum to one over the sixteen topics, so the uniform value is 0.0625 and a document’s own-topic membership of 0.15 is 2.3 times that. They are read as ratios between topics: the first document above is 1.3 times closer to topic 1 than to topic 2 and four times closer than to topic 3. For the median document the nearest centre is 17% closer than the second nearest, so most abstracts lie near a boundary between topics; the hard label records the side they fell on. The plot shows, per topic, the distribution of its own documents’ membership in it. A compact topic has its documents well above the uniform value; a diffuse topic sits close to it.

Relations between topics

hg_relations() builds the topic-by-topic co-occurrence network through shared vocabulary. For each pair of topics it sums, over all words, the product of the number of documents in each topic that contain the word, the full-counting aggregation of bibliometric keyword networks. The similarity argument normalises that sum by the measures of van Eck and Waltman (2009); "cosine" divides it by the geometric mean of the two topics’ totals and lies in [0, 1]. The function returns an edge list with source, target and weight, the columns Gephi reads, and with what = "network" a cograph_network.

relations <- hg_relations(hg, topics, similarity = "cosine")
head(relations)

Every pair of topics shares the corpus vocabulary, so all 120 cosine weights lie between 0.58 and 0.90. The plot keeps the upper quartile of the edges (minimum = 0.82), places the topics with a spring layout and scales line width by weight.

network <- hg_relations(hg, topics, similarity = "cosine", what = "network")
cograph::splot(network, layout = "spring", minimum = 0.82,
               edge_width_range = c(0.5, 8))

Summary

The pipeline produced sixteen document clusters from 3,666 abstracts without embeddings or truncation. The spectrum of the hypergraph Laplacian supports two or four clusters; the finer partition was chosen to match a published topic model. Ranking words by the share of their corpus count that falls in a cluster, with a support floor, yields a distinct vocabulary for each cluster, whereas ranking by frequency yields the corpus vocabulary for all of them.

References

Grootendorst, M. (2022). BERTopic: Neural topic modeling with a class-based TF-IDF procedure. arXiv:2203.05794.

Saqr, M., Raspopovic Milic, M., Pancheva, K., Jovic, J., Peltekova, E. V., and Conde, M. Á. (2023). A multimethod synthesis of Covid-19 education research: the tightrope between covidization and meaningfulness. Universal Access in the Information Society.

van Eck, N. J., and Waltman, L. (2009). How to normalize cooccurrence data? An analysis of some well-known similarity measures. Journal of the American Society for Information Science and Technology, 60(8), 1635-1651.

Bezdek, J. C. (1981). Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum.

Bouma, G. (2009). Normalized (pointwise) mutual information in collocation extraction. Proceedings of GSCL, 31-40.

Zhou, D., Huang, J., and Schölkopf, B. (2007). Learning with hypergraphs: clustering, classification, and embedding. Advances in Neural Information Processing Systems 19.