Analyses of Literary Texts by Using Statistical Inference Methods Mehmet Can Yavuz Computer Science and Engineering Department, Sabancı University, Tuzla Management Information Systems Department, Kadir Has University, Cibali Physics Department, Boğaziçi University, Bebek İstanbul, Türkiye mehmetyavuz@sabanciuniv.edu Abstract Criticism (Moretti, 2013) and subsequent Artifi- cial Literature, it would have certainly considered If a road map had to be drawn for Com- Elizabethan drama. In particular, Shakespearean putational Criticism and subsequent Arti- texts are the most outstanding examples of dra- ficial Literature, it would have certainly matic fiction. Demonstration of these structures considered Shakespearean plays. Demon- through text analysis can be seen as both a naive stration of these structures through text effort and a scientific view of the characteristics analysis can be seen as both a naive effort of the texts. In this study, the textual analysis of and a scientific view of the characteristics Shakespeare plays was carried out for this pur- of the texts. In this study, the textual anal- pose. ysis of Shakespeare plays was carried out To begin with, “the First Folio” is the printed for this purpose. material in which all Shakespeare’s works are Methodologically, we consecutively use brought together for the first time, (Synder, 2001). Latent Dirichlet Allocation (LDA) and The edition of 1623 was directed by two actors Singular Value Decomposition (SVD) in from the group called King’s Men. King’s Men order to extract topics and then reduce is the ensemble that Shakespeare is also a mem- topic distribution over documents into ber of. Half of the 36-play collection had never two-dimensional space. The first question been published anywhere before. The Folio was asks if there is a genre called Romance be- also printed in Quarto form. These prints took tween Comedy and Tragedy plays. The their names from the way the books were folded. second question is, if each character’s It is known that the First Folio has 800 prints, speech is taken as a text, whether the dra- 233 of them have reached today. In the First Fo- matic relationship between them can be re- lio, Shakespearean plays are typically divided into vealed. three groups: Comedies, Tragedies, and Histories. Consequently, we find relationships be- Romance is the genre that hybridizes Comedy and tween genres, also verified by literary the- Tragedy, developed at the beginning of the 17th ory and the main characters follow the an- Century. At the end of his career, he wrote four tagonisms within the play as the length romances: Pericles, Cymbeline, The Winter’s Tale of speech increases. Although the results and The Tempest. “The First Folio” groups Cym- of the classification of the side charac- beline with Tragedies; and The Winter’s Tale and ters in the plays are not always what one The Tempest together with Comedies. The rea- would have expected based on the reading son for this may be that The Winter’s Tale and of the plays, there are observations on dra- The Tempest began as tragedies and then turned matic fiction, which is also verified by lit- to comedies, and Cymbeline started as a comedy erary theory. Tragedies and revenge dra- and ended as a tragedy. mas have different character groupings. Shakespeare’s two tragedies Macbeth and Othello 1 Introduction are two very good examples of a true tragedy and a revenge tragedy. Tragedies are designed as the If a road map had to be drawn for Computational struggle of the main characters and the oppos- Copyright c 2019 for this paper by its authors. Use ing characters who create obstacles for the main permitted under Creative Commons License Attribution 4.0 character. The protagonist is generally the main International (CC BY 4.0). character that the audience sympathizes with. Al- tion theoretical approaches are also successfully though not sympathetic, Macbeth is a protagonist applied, (Rosso, 2009). In literature, structural el- and the opposing characters are antagonists: Dun- ements are quantified, such as the dramatis per- can and Banquo. Similarly, there is also antag- sonae as well as scene structures; and applications onism in revenge drama and the main theme is are developed to further increase analysis (Den- revenge. The antagonist or protagonist seeks re- nerlein, 2015; Krautter, 2018; Schmidt, 2019; venge for an imaginary or real injury. Iago the an- Trilcke, 2015; Wilhelm, 2013; Xanthos, 2016). tagonist gets his revenge provoking Othello, the In order to analyze a literary text, we would like protagonist, against his wife. to use unsupervised topic modeling. Although Computerized analysis of literary texts, in other there are linear-algebraic models such as Non- words computational criticism is a new and Negative Matrix Factorization (Lee, 1999), prob- promising field, (Ramsay, 2011). Pioneering abilistic models are more reliable and capable of works aim to answer critical questions by using representing true distributions of topics. Proba- Natural Language Processing (NLP) methods. It bilistic Latent Semantic Analysis (Hoffman, 1999) is of interest to create fictional texts with the help and Latent Dirichlet Allocation (Blei, 2003) are of computer in the developing artificial literature the two major unsupervised topic modeling algo- along with these studies. In this study, we make rithms. Although both allow us to classify texts a computational analysis of Shakespearean texts. according to topic distribution, Latent Dirichlet There are basically two questions we’re trying to Allocation as a generative model has a proven answer. The first is if the genres in Shakespeare’s superiority over competitors. Principal Compo- theater texts can be classified by computer. Sec- nent Analysis (Jolliffe, 2002), Linear Discriminant ondly, if the sentences in which the characters Analysis (Brown, 2000) or Non-Negative Matrix speak are taken as texts, can antagonisms be re- Factorization (NMF) techniques are all dimension vealed? I tried to find answers to both with the reduction algorithms, along side Singular Value same unsupervised learning technique. Decomposition (Golub, 1970). The last algorithm In recent years, NLP methods have been devel- we use is K-Means Clustering algorithm, a well oping rapidly and text analysis methods are get- known clustering algorithm that minimize vari- ting more advanced. Topic Modeling articles are ance within clusters (Llyod, 1982). among the top cited articles. An unsupervised topic modelling algorithm is used in this study. 2 Theory It is able to generate latent topics in which each document is a mixture. Having the latent topic In this study, we will use text analysis to inves- distribution, by using dimension reduction algo- tigate genres and antagonisms in Shakespearean rithm, each document is mapped onto two dimen- plays. By using Latent Dirichlet Allocation sional coordinates without losing intrinsic charac- (LDA), document distributions over topics are teristics. generated. Firstly, optimum number of topics will be obtained for LDA with grid search optimization 1.1 Related Works and then dimension reduction algorithm, truncated Singular Value Decomposition (tSVD) will map Digital Humanities field lets researchers discuss these documents into a two-dimensional plane and quantitative methods in literary and cultural stud- graphed. ies (Clement et al., 2008; Crane, 2006). ”Dramet- In the following sections, generating topics with rics” is a field that deals with quantitative analysis LDA algorithm and dimension reduction by tSVD of the literary genre of drama (Romanska, 2015). algorithm are explained. The aim of using tSVD Digital Shakespeare studies also have gotten at- algorithm is to express each text with two floating tention since the 2000, (Hirsch, 2017; Mueller, numbers while preserving the latent topic proper- 2008). The studies includes issues from digital ties. Thus, classification can be made depending archives to authorship analysis, (Vickers, 2011; on the distances between each text in the new two- Evert, 2017). Besides, machine learning based dimensional feature space. At the last step, we use text analyses are also carried out for genre clas- a clustering with Euclidean distance. Theoretical sifications, (Ardunuy, 2004; Hope, 2010; Schoch, section is kept brief and explanatory due fact that 2016; Underwood, 2013; Yu, 2008). Informa- the main focus is on experimental results. 2.1 Latent Dirichlet Allocation (Blei, 2003) 2.2 SVD (Golub, 1970) LDA is a generative statistical model that explains If data has a large number of features, reduce it why certain parts of the data are similar based on into a subset of features that are the most relevant an observation set. LDA assumes that observa- to the prediction problem. SVD breaks any A ma- tions are generated by latent variables, or latent trix into a multiplication of three matrices so that, topics. Thus, each document is a mixture of top- ics and each topic is a distribution over words and A = U SV 0 which (1) 0 0 each word is drawn from the mixture. The obser- U U = I and V V = I (2) vations are frequency statistics of each document, so called the document-term matrix. The method S is a diagonal matrix that consists of r singu- is called the bag-of-words approach and intends to lar values. r is the rank of A. Truncated SVD is reflects how important a word is in a document. a reduced rank approximation. All singular val- Thus, topics are identified on the basis of term co- ues are equated to zero except for the largest k, occurrence, the topics-term matrix, and each doc- and largest singular values are the first k columns ument is assumed to be characterized by a particu- of U and V. The dimensions of truncated SVD lar set of topics, the document-topics matrix. Top- are [uxk] ⇤ [kxk] ⇤ [kxv] Since A matrix is ap- ics, mixtures and other variables are all hidden and proximated by k dimensions, there is a dimension need to be predicted from the observation data, the reduction between matrix multiplications. A de- document-term matrix. In Figure 1, plate notation scriptive subset of the data is called T, which is a of LDA is represented. In the plate notation, there dense summary of the matrix A, are NxD different variables that represent obser- T = U Sk (3) vations. There are K total topics and D total docu- ments. Sk denotes k largest singular values, which is the All at once, ↵ and ⌘ are parameters of the prior number of reduced features. Each feature can be distributions over ✓ and respectively. ✓d the dis- expressed by a percentage of variance, the reason tribution of topics for document d (real vector of behind this is choosing only the most significant length K). k is the distribution of words for topic ones. k (real vector of length V). zd,n is the topic for the nth word in the dth document. wd,n the nth 2.3 K-means Clustering (Llyod, 1982) word of the dth document. Only gray shaded cir- The K-Means clustering algorithm separates n cles are the observed variables. The rest of the group of equal variance samples from data by min- white circles would be inferred by using Variation imizing the sum-of-squares within clusters. The Inference. The topic for each word, the distribu- number of clusters needs to be pre-determined. tion over topics for each document, and the distri- bution of words per topic are all latent variables in 3 Experiments2 this model. By this formulation, similarities can We included two evaluations in our experiments. be introduced between documents. The first is whether or not the genre of Romance The model contains both continuous and discrete can be distinguished computationally by com- variables. ✓d and k are vectors of probabilities. puter. In order to carry out this experiment, each zd,n is an integer in {1, ...K} that indicates the tragedy, comedy and romance is treated as a dif- topic of the nth word in the dth document. wd,n is ferent document; and is processed by LDA. After- an integer in {1, ...V }which indexes over all pos- wards, for the document-topic distribution matrix, sible words. the number of topics is reduced to two by means of dimension reduction algorithm, tSVD. Similarly, in the second evaluation, the lines of each charac- ter were treated as a text and the document-subject matrix was reduced to two after processing it with LDA. Two different type of tragedies are consid- ered: Macbeth and Othello. Thus, three different Figure 1: Plate notation representing the LDA 2 In Python, Scikit-learn library used for LDA, tSVD and model. GridSearch functions. experiments and optimization were conducted for 4 Discussion these two evaluations. 4.1 Tragedy-Comedy-Romance In Figure 3, documents consisting of Tragedy- 3.1 Dataset and Preprocess Comedy-Romance plays are represented. The Two preprocesses were performed for each set of document-topic distribution matrix is reduced to documents. Primary, stop-words were removed two dimensions, and graphed. More than half of from the dictionary. These stop-words were cre- variances is explained by these two components. ated for both the usual English and Elisabethan Even in three dimensions, the clustering does not English. The number of stop words is 1144. The change. The plays that are shown in red are Come- characteristic of these words is that they often ap- dies, the blues are Tragedies and the greens are pear in every text. The secondary process is the Romances according to the First Folio. expression of texts with word frequencies and the In the upper left corner, the majority of the Come- creation of the document-term matrix. Thus, each dies are clustered, and likewise in the lower right text could be expressed in a dictionary size fixed- corner Tragedies are clustered. In the middle of length vector. Concatenations of these vectors cre- these two clusters, three plays, ”All’s Well That ates the document-term matrix. Ends Well”, ”Measure for Measure” and ”Troilus and Cressida” are placed known as problem plays. Some critics also includes ”Timon of Athens” 3.2 Optimization which is a neighbor of other problem plays, (Sny- der, 2001). Thus, in the middle of the two clus- In order to find the right topic number, we need an ters, there is a gray zone in which problem plays optimization. Since the subjects/topics are latent are placed. An interesting fact is, although “All’s variables, there is no right number of topics. Grid- Well That Ends Well“ and “Measure for Measure” search optimization over topic numbers is carried are grouped as Comedies in the First Folio, they out, and the highest log-likelihood is the optimal are much closer to tragedies. An unexplained fact settings. In all three experiments, the values be- is that Coriolanus and Othello are also placed in tween 6 and 12 were tried three times and drawn this gray zone. Another question in this grouping in Figure 2. Thus for example, for Macbeth, 3 ex- is ”Romeo and Juliet”. As a tragedy that has com- periments were conducted for a certain topic num- edy elements is placed thematically very close to ber. The LDA function that we called for the ex- the Comedies cluster. periment was repeated up to 10 times before giv- Another important distinction is that these three ing results. Thus, for example, the LDA algorithm Romances are clustered within the Tragedies. Ac- was repeated up to 30 times in total for a certain cording to this analysis, the genre of Romance is topic number. not different from tragedy. As an observation, as the number of topics de- creases, log-likelihood increases. However, we prefer not to try less than 6 latent topics because, in literature, the number of themes/topics for Shake- spearean plays is generally at least 6, (”William Shakespeare”, 2015). Figure 2: Optimization. Likelihood w.r.t. Top- ics Numbers. Tragedies-Comedies, Macbeth, Oth- ello, respectively. Figure 3: Genre classification of Tragedies, Comedies and Romance 4.2 Macbeth 4.3 Othello After the analysis, the characters of Macbeth The characters of the Othello play are shown in the clearly demonstrate Antagonist/Protagonist rela- Figure 5 in accordance with the analysis. I give tions as graphed in Figure 4. There are two basic Othello as an example of revenge tragedies. Un- clusters in the tragedy of Macbeth. The first is the like a true tragedy, Macbeth, the Othello play does protagonists, led by Macbeth and Lady Macbeth. not have antagonist/protagonist clusters in the Fig- The second is the antagonists, who are the mur- ure 5. Iago is a single character who sets traps dered king and Macduff who suspects foul play. to get revenge on Othello. Throughout the play, In the plot, protagonists are shown in blue and an- Iago misleads Othello for reasons and purposes tagonists in red. Lady Macbeth stands at the bot- that only he and the reader know. Othello kills his tom left corner, since Lady Macbeth doesn’t have beloved wife in a crisis of jealousy. much to talk except to Macbeth. Macbeth’s him- There are three different colored clusters shown. self is closer to the red cluster. He has relations The red set consists of the main people of the play. with red clusters as a new King. Macduff, who Blue and green clusters belong to side characters is suspicious and kills Macbeth in the last scene, and antagonisms are computationally ambiguous. is in the center of the red cluster. Lady Macduff The main characters of the red cluster at the bot- is also in this cluster. The murdered King Dun- tom right, Othello, Emilia, Iago and Cassio have can is also at the center of this cluster. However, spoken almost the same subject because of the fre- there is also a misclassification. Siward is in the quency of their dialogue with each other. There- blue cluster. However, Siward and Macbeth have fore, a conflict between them is not visible. But a clash in which Siward is killed. Other than that, Iago is shown in the lower right corner because he the witches who oracles, are in the opposite clus- shows his true intention in his monologues. There- ter of Macbeth. Other characters may not be fully fore, Othello is a negative example for the method- explained due to their small and ambiguous roles. ology we developed. Characters such as the Duke Apart from these two clusters, there is a top left of Venice and the Senator are mentioned in the green cluster. The main character of this cluster top left corner and are in fact extremely outside is Banquo. This character is Macbeth’s brave and the plot. Shown from the green cluster, Bianca is noble companion. But he had no idea about Mac- again outside the plot as Cassio’s lover. beth’s machinations until he is killed. In Othello, there are interesting observations on Tragedy of Macbeth has a very clear separation revenge tragedies. In revenge tragedies of Shake- between clusters. The distance between clusters is speare, a lonely character shows him/herself dif- also meaningful. The reds are between green and ferently and his/her true intentions remain hidden. blues. The greens are actually closer to reds rather Thus, the clear difference from tragedies, is their than Macbeth’s evil cluster. dramatic structure. Figure 4: Characters of the play Macbeth are rep- Figure 5: Characters of the play Othello are repre- resented. sented. 5 Conclusion terms of hiding their true intentions. The dramatic fiction in Shakespeare’s texts is The classification of genres shows us that the shown to a certain extent. The advantage of the method we use provides successful quantitative in- proposed pipeline is using non-linearity over a formation for the differentiation of genres. The linear layer. Instead of directly clustering the length of the texts can be mentioned among the document-term matrix, a powerful representation reasons for this success. Positioning the plays of each document in a feature space is generated between Tragedy and Comedy is much discussed by LDA. After generating document-topic matrix, in the literature theory. The Romance genre hy- a linear layer of dimension reduction, tSVD, that bridizes Tragedy and Comedy elements. Instead extracts principal directions or principal axes in of mapping the Romance genre in between, the al- which the document-topic matrix have the largest gorithm mapped four ”Problem Plays” in a region variance. between Tragedies and Comedies. Another inter- I think that these naive efforts on the way to Artifi- esting finding is that Romance cannot be distin- cial Literature also have a positive effect. The pro- guished from Tragedies. The method used shows duction of a play is possible with the knowledge of that the reason for some literary discussion is at authorship for humans and even for Shakespeare. the same time quantitative. The method classi- By authoring knowledge, we mean, for example, fies Romances within the Tragedies. In the light how to write a play from dramatic perspective. It of theoretical discussions, of course, there may be is firstly introduced by Aristotle to shed light on a genre called Romance, but we have not been able present-day methods. It would be possible to re- to quantify this difference yet. verse engineering them for artificial literature. Go- There are also some results from our experiments ing from a quantitative analysis to plays would be on the two tragedies we have chosen. I inten- possible. Therefore, as we analyze literary pieces, tionally choose a tragedy and a revenge play, al- especially texts in dialogue form can help us verify though Macbeth clearly shows antagonisms. This critical questions and theories. From these analy- is mainly due to the frequency of conversations ses, going back to the literary text generation be- within these clusters. For example, Macbeth and comes possible. Lady Macbeth are always aware of each others true intentions. Dialogues within these clusters Acknowledgments are always compatible with each other. Therefore, This work was supported by grant 12B03P4 of the cluster forms. There is a group subjectivity, Boğaziçi University. also verified computationally. The war scene at the The author would like to thank Muhittin Mungan end of Macbeth can clearly be observable from the for suggesting Master of Science thesis as his clusters. Two clusters to clash are formed through advisor and Meltem Gürle Mungan for her kind out the play, which is quantifiable. On contrary, opinion. The author would also like to thank actor Iago who hides his true intention from everyone, Güneş Yakın, for talks together on Shakespeare. has apparently always agreed with Othello. On the contrary, Iago never shares his intentions with any- one in the play. His intentions are shared through References monologues. 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