Topic segmentation via community detection in complex networks

Many real systems have been modelled in terms of network concepts, and written texts are a particular example of information networks. In recent years, the use of network methods to analyze language has allowed the discovery of several interesting findings, including the proposition of novel models to explain the emergence of fundamental universal patterns. While syntactical networks, one of the most prevalent networked models of written texts, display both scale-free and small-world properties, such representation fails in capturing other textual features, such as the organization in topics or subjects. In this context, we propose a novel network representation whose main purpose is to capture the semantical relationships of words in a simple way. To do so, we link all words co-occurring in the same semantic context, which is defined in a threefold way. We show that the proposed representations favours the emergence of communities of semantically related words, and this feature may be used to identify relevant topics. The proposed methodology to detect topics was applied to segment selected Wikipedia articles. We have found that, in general, our methods outperform traditional bag-of-words representations, which suggests that a high-level textual representation may be useful to study semantical features of texts.

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I Introduction

With the ever-increasing amount of information available online, the classification of texts has established itself as one of the most relevant applications supporting the development of efficient and informative search engines Manning and Schütze (1999). As the correct categorization of texts is of chief importance for the success of any search engine, this task has been extensively studied, with significant success in some scenarios Aggarwal and Zhai (2012); Herrera and Pury (2008)

. However, the comprehension of texts in a human-like fashion remains a challenge, as it is the case of semantical analyses performed in disambiguating systems and sentiment analysis 

Golder and Macy (2011); Navigli (2009). While humans are able to identify the content and semantics conveyed in written texts in a artlessly manner, automatic classification methods fail in several aspects mainly because the lack of a general representation of world knowledge. Currently, the automatic categorization of texts stands as one of the most studied applications in information sciences. In recent years, multidisciplinary concepts have been applied to assist the classification, including those based on physical approaches Herrera and Pury (2008); Hernández et al. (2015); Amancio et al. (2012a); Liu and Xu (2011); Delanoe and Galam (2014).

An important subarea of the research performed in text classification is the detection of subtopics in documents Reynar (1999); Lancichinetti et al. (2015)

. This task is not only useful to analyze the set of subjects approached in the document, but also to assist computational applications, such as automatic text summarization 

Gong et al. (2010) and text recommendation Adomavicius et al. (2005). Several approaches have been proposed to tackle the subtopic identification problem. The most common feature employed to cluster together related sentences/paragraphs is the frequency of shared words Clifton et al. (2004); Blei et al. (2003)

. While most of the works on this area considers only the presence/absence of specific words in sentences/paragraphs, only a few studies have considered the organization of words to classify documents 

Amancio (2015a). Specifically, in this paper, we approach the text segmentation problem using the organization of words as a relevant feature for the task. The non-trivial relationships between concepts are modelled via novel networked representations.

Complex networks have been used to analyze a myriad of real systems Costa et al. (2011), including several features of the human language Cong and Liu (2014). A well-known model for text representation is the so-called word adjacency (co-occurrence) model, where two words are linked if they appear as neighbors in the text. Though seemingly simple, this model is able to capture authors’ styles Amancio et al. (2011); Amancio (2015b); Mehri et al. (2012), textual complexity Liu and Xu (2011); Amancio et al. (2012b) and many other textual aspects Cong and Liu (2014); Masucci et al. (2011); Masucci and Rodgers (2009). A similar model, referred to as syntactical network, takes into account the syntactical representation of texts by connecting words syntactically related. Syntactical networks shared topological properties of other real world networks, including both scale-free and small-word behaviors. These networks have been useful for example to capture language-dependent features Cancho et al. (2004). Unlike traditional models, in this paper, we extend traditional text representations to capture semantical features so that words are connected if they are related semantically. Here, we take the view that a given subtopic is characterized by a set of words which are internally connected, with a few external relationships with words belonging to other subjects. As we shall show, this view can be straightforwardly translated into the concept of community structure, where each semantical structure can be regarded as a different network community Fortunato (2010). The proposed framework was evaluated in a set of Wikipedia articles, which are tagged according to their subjects. Interestingly, the network approach turned to be more accurate than traditional method in several studied datasets, suggesting that the structure of subjects can be used to improve the task. Taken together, our proposed methods could be useful to analyse written texts in a multilevel networked fashion, as revealed by the topological properties obtained from traditional word adjacency models and networks of networks in higher hierarchies via community analysis.

This manuscripts is organized as follows. In Section II, we present the proposed network representation to tackle the subtopic identification task. In Section III we present the dataset employed for the task. The results obtained are then shown in Section IV. Finally, in Section V, we conclude this paper by presenting perspectives for further research on related areas.

Ii Complex network approach

The approach we propose here for segmenting texts according to subjects relies upon a networked representation of texts. In this section, we also detail the method employed for identifying network communities, for the proposed methodology requires a prior segmentation of text networks.

Representing texts as networks

A well-known representation of texts as networks is the word-adjacency model, where each different word is a node and links are established between adjacent words Cancho and Solé (2001); Amancio et al. (2008). This model, which can be seen as a simplification of the so-called syntactical networks Cancho et al. (2004), has been used with success to identify styles in applications related to authorship attribution, language identification and authenticity verification Amancio (2015c); Montemurro and Zanette (2013); Amancio et al. (2013)

. The application of this model in clustering analysis is not widespread because traditional word adjacency networks are not organized in communities, if one considers large pieces of texts. In this paper, we advocate that there is a strong relationship between communities structures and subjects. For this reason, we modify the traditional word adjacency model to obtain an improved representation of words interactions in written texts. More specifically, here we present a threefold extension which considers different strategies of linking non-adjacent words.

Prior to the creation of the model itself, some pre-processing are applied. First, we remove stopwords, i.e. the very frequent words conveying no semantic meaning are removed (e.g. to, have and is). Note that, such words may play a pivotal role in style identification, however in this study they are not relevant because such words are subject independent. The pre-processing step is also responsible for removing other non-relevant tokens, such as punctuation marks. Because we are interesting in representing concepts as network nodes, it is natural to consider that variant forms of the same word becomes a unique node of the network. To do so, we lemmatize the words so that nouns and verbs are mapped into their singular and infinitive forms Miller (1995). To assist this process, we label each word according to their respective parts of speech in order to solve possible ambiguities. This part of speech labeling is done with the high-accurate maximum entropy model defined in Ratnaparkhi et al. (1996); Malecha and Smith (2010). Finally, we consider only nouns and verbs, which are the main classes of words conveying semantical meanings Hindle (1990); Béchet et al. (2014). In all proposed models, each remaining word (lemmatized nouns and verbs) becomes a node. Three variations concerning the establishment of links between such words are proposed:

  • Extended co-occurence (EC) model: in this model, the edges are established between two words if they are separated by or less intermediary words in the pre-processed text. For example, if and the pre-processed text comprises the sentence “ ”, then the following set of edges is created: . Note that, if , the traditional co-occcurrence (word adjacency) model is recovered, because only adjacent words are connected.

  • Paragraph-based (PB) model: in this model, we link in a clique the words belonging to the same paragraph. We disregard, however, edges linking words separated by more than intermediary words in the pre-processing text. This method relies on the premise that paragraphs represents the fundamental sub-structure in which a text is organized, whose words are semantically related Véronis (2004).

  • Adapted paragraph-based (APB) model: the PB model does not take into account the fact that words may co-occur in the same paragraph just by chance, as it is the case of very frequent words. To consider only significant links in the PB model, we test the statistical significance of co-occurrences with regard to random, shuffled texts Martinez-Romo et al. (2011). Given two words and , an edge is created only if the frequency of co-occurrences () (i.e. the number of paragraphs in which and co-occurs) is much higher than the same value expected in a null model. The significance of the frequency can be computed using the quantity

    , which quantifies the probability of two words to appear in the same paragraph considering the null model. To compute the probability

    , let and be the number of distinct partitions in which and occur, respectively. The distribution of probability for , the number of co-occurrences between and , can be computed as

    The above expression for can be rewritten in a more convenient way, using the notation

    (1)

    which is adopted for . In this case, the likelihood can be written as

    (2)

    If in a given text the number of co-occurrences of two words is , the -value associated to can be computed as

    (3)

    where is computed according to equation 2. Now, using equation 3, the most significant edges can be selected.

Figure 1 illustrates the topology obtained for the three proposed models representing a text with four paragraphs from Wikipedia 111en.wikipedia.org/wiki/Car. Note that the structure of communities depends on the method chosen to create the netswork. Especially, a lower modularity has been found for the APB model in this example and for this reason the organization in communities is not so clear. As we shall show, the identification of communities of extreme importance for identifying accurately the subjects.

Figure 1: Example of networks obtained from the following models: (a) EC, (b) PB and (c) APB. The colours represent in this case the community to which each node belongs. To obtain the partitions, we used the fast greedy algorithm Clauset et al. (2004). Note that the organization of nodes in communities varies from model to model. While in (a) and (b) the organization in communities is clear, in (c) the modular organization is much more weak.

From network communities to text subjects

The first step for clustering texts according to subjects concerns the computation of network communities, i.e. a region of nodes with several intra-edges (i.e. edges inside the community) and a few inter-edges (i.e. edges leaving the community). Methods for finding network communities have been applied in several applications Arenas et al. (2004); Guimera et al. (2005); Palla et al. (2005), including in text analysis Londhe et al. (2014). The quality of partitions obtained from community structure detection methods can be obtained from the modularity , which is defined as

(4)

where denotes an element of the adjacent matrix (i.e. if and are linked and , otherwise), represents the membership of the -th node, is the node degree, is the total number of edges in the network and is the Kronecker’s delta. Several algorithms use the modularity to assist the identification of partitions in networks. Note that the modularity defined in equation 4 quantifies the difference between the actual number of intra-links (i.e. the links in the same community, ) and the expected number of intra-links (i.e. the number of links in the same community of a random network, ). Here we use a simple yet efficient approach devised in Clauset et al. (2004), where the authors define a greedy optimization strategy for . More specifically, to devise a greedy optimization the authors define the quantities

(5)

which represents the fraction of edges that link nodes in community and , and

(6)

which denotes the fraction of ends of edges that are linked to nodes in community . The authors redefine in equation 4 by replacing to :

(7)

Using the modularity obtained in equation 7, it is possible to detect communities using an agglomerative approach. First, each node is associated to a distinct community. In other words, the partition initially comprises only singleton clusters. Then, nodes are joined to optimize the variation of modularity, . Thus, after the first agglomeration, a multi-graph is defined so that communities are represented as a single node in a new adjacency matrix with elements . More specifically, the operation of joining nodes is optimized by noting that only if communities and are adjacent. The implementation details are provided in Clauset et al. (2004). Note that our approach does not rely on any specific community identification method. We have specifically chosen the fast-greedy method because, in preliminary experiments, it outperformed other similar algorithms, such as the multi-level approach devised in Blondel et al. (2008) (result not shown).

Given a partition of the network established by the community detection method, we devised the following approach for clustering the text in distinct subjects. Let and be the set of communities in the network and the set of paragraphs in the text, respectively. If the obtained number of communities () is equal to the expect number of subjects , then we assign the label to the word that corresponds to node in the text. As a consequence, each paragraph is represented by a set of labels , where is the label associated to the -th word of the -th paragraph (). The number of occurrences of each label in each paragraph is defined as

(8)

Thus the subject associated to the paragraph is

(9)

i.e. the most frequent label is chosen to represent the subject of each paragraph. To illustrate the application of our method, we show in Figure 2 the communities obtained in a text about cars, whose first paragraph approaches the definition and invention of cars, and the remaining paragraphs present their parts.

Figure 2: Example of community obtained with the following models: (a) EC; and (b) PB. As expected, most of the words belong to a unique subject, while a few words lies at the overlapping region. The visualization of communities obtained with the APB model is not as good as the ones obtained with both EC and PB methods.

The expression in equation 9 is suitable to be applied only when . Whenever the number of expected subjects is lower than the number of network communities, we adopt a strategy to reduce the quantity of communities found. To do so, the following algorithm is applied:

Data: , the number of communities and , the number of subjects.
Result: A match between communities and subjects is established.
while   do
       = label of the community with the largest overlapping region;
       erase all nodes from ;
       detect again the community structure of the network formed of the remaining nodes;
       update ;
      
end while

According to the above algorithm, if the most overlapping community is to be estimated, a measure to quantify the degree of overlapping must be defined. In the present work, we defined an overlapping index,

, which is computed for each community. To compute , we first recover all paragraphs whose most frequent label is the one associated to community . These paragraphs are represented by the subset . Next, we count how many words in are associated with the community . The overlapping is then defined as the the amount of words in which are associated to a community . Mathematically, the overlapping is defined as

(10)

To evaluate the performance of the methods, we employed the following methodology. Let be the subject associated to the -th paragraph according to Wikipedia. Here, we represent each different subtopic as a integer number, so that . Let be the label associated to the -th paragraph according to a specific clustering method, as defined in equation 9. To quantify the similarity of two sets and , it is necessary consider all combinations of labels permutations either on or , because the same partition may be defined with distinct labels. For example, if , and , both partitions are the same, even if a straightforward comparison (element by element) yields a zero similarity. To account for distinct labelings in the evaluation, we define the operator , which maps a sequence of labels to all possible combinations. Thus, if , then

Equivalently, the application of the to yields two components:

The accuracy rate, , is then defined as

(11)

where is the operator that compares the similarity between two subsets and and is mathematically defined as:

(12)

Iii Database

The artificial dataset we created to evaluate the methods is formed from paragraphs extracted from Wikipedia articles. The selected articles can be classified in distinct topics and 5 distinct subtopics:

  1. Actors: Jack Nicholson, Johnny Depp, Robert De Niro, Robert Downey Jr. and Tom Hanks.

  2. Cities: Barcelona (Spain), Budapest (Hungary), London (United Kingdom), Prague (Czech Republic) and Rome (Italy).

  3. Soccer players: Diego Maradona (Argentina), Leonel Messi (Argentina), Neymar Jr. (Brazil), Pelé (Brazil) and Robben (Netherlands).

  4. Animals: bird, cat, dog, lion and snake.

  5. Food: bean, cake, ice cream, pasta, and rice.

  6. Music: classical, funk, jazz, rock and pop.

  7. Scientists: Albert Einstein, Gottfried Leibniz, Linus Pauling, Santos Dumont and Alan Turing.

  8. Sports: football, basketball, golf, soccer and swimming.

To construct the artificial texts, we randomly selected paragraphs from the articles using two parameters: , the total number of subtopics addressed in the artificial text; and , the number of paragraphs per subtopic. For each pair we have compiled a total of documents. To create a dataset with distinct granularity of subtopics, the random selection of subtopics was performed in a two-fold way. In the dataset comprising coarse-grained subtopics, hereafter referred to as CGS dataset, each artificial text comprises subtopics of distinct topics. Differently, in the dataset encompassing fine-grained subtopics, hereafter referred to as FGS dataset, the texts are made up of distinct subtopics of the same major topic.

Iv Results

In this section, we analyze the statistical properties of the proposed models in terms of their organization in communities. We also evaluate the performance of our model in the artificial dataset and compare with more simple models that do not rely on any networked information.

Modularity analysis

The models we propose to cluster topics in texts relies on the ability of a network to organize itself in a modular way. For this reason, we study how the modularity of networks depends on the models parameters. The unique parameter that may affect networks modularity in our models is , which amounts to the distance of links in texts (see definition in the description of the EC model in Section II). Note that the distance controls the total number of edges of the network, so a comparison of networks modularity for distinct values of is equivalent to comparing networks with distinct average degrees. Because the average degree plays an important role on the computation of the modularity Fortunato (2010), we defined here a normalized modularity that only takes into account the organization of the network in modules and is not biased towards dense networks. The normalized modularity of a given network with modularity is computed as

(13)

where is the average modularity obtained in equivalent random networks with the same number of nodes and edges of the original network.

In Figure 3, we show the values of , and in the dataset FGS. In the EC model, high values of modularity are found for low-values of . To the best of our knowledge, this is the first time that a modular structure is found in a traditional word adjacency network (i.e. the EC model with ) in a relatively small network. As takes higher values and the network becomes more dense, the modularity decreases. In a similar way, the average modularity obtained in equivalent random networks also decreases when increases. A different behavior arises for the normalized modularity , as shown in Figure 3(a). The modularity initially takes a low value, reaching its maximum when . Note that when , there is no significant gain in modularity . A similar behavior appears in the other two considered models (PB and APB) as the normalized modularity becomes almost constant for . Because in all models the normalized modularity takes high values for , we have chosen this value to construct the networks for the purpose of clustering topics. Even though a higher value of normalized modularity was found for in Figures 3(b)-(c), we have decided not to use larger values of in these models because only a minor improvement in the quality is obtained for .

(a) ref1
(b) ref2
(c) ref2
Figure 3: Example of modularity evolution using the proposed text representations (EC, PB and APB). The results were obtained in both CGS and FGS datasets (see Section III). Note that the normalized modularity does not display a significant increase for .

Performance analysis

To evaluate the performance of the proposed network-based methods, we evaluate the accuracy of the generated partitions in the CGS and FDS datasets presented in Section III. We have created two additional methods based on linguistic attributes to compare the performance of networked and non-networked methods. Both methods are based on a bag-of-words strategy Manning and Schütze (1999)

, where each paragraph is represented by the frequency of appearance of its words. To cluster the paragraphs in distinct subjects, we used two traditional clustering methods: k-means 

Kanungo et al. (2002)

and Expectation Maximization 

Chai et al. (2015). In our results, the bag-of-words strategy based on the k-means and Expectation Mazimization algorithms are referred to as BOW-K and BOW-EM, respectively.

In Figure 4, we show the results obtained in the dataset comprising texts whose subtopics belong to distinct major topics (CGS dataset). We classified the dataset in terms of the number of distinct subtopics in each text () and the total number of paragraphs per subtopic () (see Section III). We first note that, in all cases, at least one networked approach outperformed both BOW-K and BOW-EM approaches. In some cases, the improvement in performance is much clear (see Figure 4 (d), (e) and (f)), while in others the difference in performance is lower. When comparing all three networked approaches, the APB strategy, in average, performs better than others when the number of subtopics is . For , both EC and PB strategies outperforms the APB method.

(a) and
(b) and
(c) and
(d) and
(e) and
(f) and
(g) and
(h) and
(i) and
Figure 4: Performance in segmenting subjects in texts with subtopics on the same major topic. The parameters employed to generate the dataset (, the number of subtopics and , the number of paragraphs per subtopic) are shown in the figure. Note that, in most of the cases, the best performance is obtained with the APBM approach.

In Figure 5, we show the performance obtained in the dataset comprising texts with subtopics belonging to the same major topic (FDS dataset). When one compares the networked approaches with BOW-K and BOW-EM, we note again that at least one networked approach outperformed both non-networked strategies. This result confirms that the networked method seems to be useful especially when the subtopics are not very different from each other, which corresponds to the scenario found in most real documents. The relevance of our proposed methods is specially clear when . A systematic comparison of all three networked methods reveals that the average performance depends on specific parameters of the dataset. In most of the cases, however, the best average performance was obtained with the EC method. The APB method also displayed high levels of accuracy, with no significant difference of performance in comparison with EC in most of the studied cases.

(a) and
(b) and
(c) and
(d) and
(e) and
(f) and
(g) and
(h) and
(i) and
Figure 5: Performance obtained in the FDS dataset. The parameters employed to generate the dataset (, the number of subtopics and , the number of paragraphs per subtopic) are shown in the figure. In most of the cases, the best performance was obtained with the EC approach.

All in all, we have shown that networked approaches performs better than traditional techniques that do not rely on a networked representation of texts. Interestingly, a larger gain in performance was obtained in the TSS dataset, where the difference in subtopics is much more subtle. This result suggests that the proposed networked approaches are more suitable to analyze real texts, as one expects that the changes in subjects in a given text is much more subtle than variations of subjects across distinct texts. Another interesting finding concerns the variations of performance in distinct datasets. Our results revealed that there is no unique networked approach able to outperforms strategies in all studied cases. However, we have observed that, in general, both EC and APB methods performs better than the AP approach and, for this reason, they should be tried in real applications.

V Conclusion

In this paper, we have proposed a method to find subtopics in written texts using the structure of communities obtained in word networks. Even though texts are written in a modular and hierarchical manner Alvarez-Lacalle et al. (2006), such a feature is hidden in traditional networked text models, as it is the case of syntactical and word adjacency networks. In order to capture the topic structure of a text, we devised three methods to link words appearing in the same semantical context, whose length is established via parametrization. In preliminary experiments, we have found that the modular organization is optimized when one considers a context comprising 20 words. Above this threshold, the gain in modularity was found to be not significant. We applied our methods in a subset of articles from Wikipedia with two granularity levels. Interestingly, in all considered datasets, at least one of the proposed networked methods outperformed traditional bag-of-word methods. As a proof of principle, we have shown that the information of network connectivity hidden in texts might be used to unveil their semantical organization, which in turn might be useful to improve the applications relying on the accurate characterization of textual semantics.

In future works, we intend to use the proposed characterization to study related problems in text analysis. The high-level representation could be employed in a straightforwardly manner to recognize styles in texts, as one expects that distinct writing styles may approach different subjects in a very particular way. As a consequence, the proposed networked representations could be used for identifying authors in disputed documents. We also intend to extend our methods to make it suitable to analyze very large documents. In this context, an important issue concerns the accurate choice of values for the context length, which plays an important role in the performance. Our methods could also be combined with other traditional networked representation to improve the characterization of related systems. Thus, a general framework could be created to study the properties of written texts in a multi-level way, in order to capture the topological properties of networks formed of simple (e.g. words) and more complex structures (e.g. communities).

Vi acknowledgments

Henrique Ferraz de Arruda thanks Federal Agency for Support and Evaluation of Graduate Education (CAPES-Brazil) for financial support. Diego Raphael Amancio acknowledges São Paulo Research Foundation (FAPESP) (grant no. 2014/20830-0) for financial support. Luciano da Fontoura Costa is grateful to CNPq (grant no. 307333/2013-2), FAPESP (grant no. 11/50761-2), and NAP-PRP-USP for sponsorship.

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