Literary Cluster Analysis

I: Introduction

My PhD research will involve arguing that there has been a resurgence of modernist aesthetics in the novels of a number of contemporary authors. These authors are Anne Enright, Will Self, Eimear McBride and Sara Baume. All these writers have at various public events and in the course of many interviews, given very different accounts of their specific relation to modernism, and even if the definition of modernism wasn’t totally overdetermined, we could spend the rest of our lives defining the ways in which their writing engages, or does not engage, with the modernist canon. Indeed, if I have my way, this is what I will spend a substantial portion of my life doing.

It is not in the spirit of reaching a methodology of greater objectivity that I propose we analyse these texts through digital methods; having begun my education in statistical and quantitative methodologies in September of last year, I can tell you that these really afford us no *better* a view of any text then just reading them would, but fortunately I intend to do that too.

This cluster dendrogram was generated in R, and owes its existence to Matthew Jockers’ book Text Analysis with R for Students of Literature, from which I developed a substantial portion of the code that creates the output above.

What the code is attentive to, is the words that these authors use the most. When analysing literature qualitatively, we tend to have a magpie sensibility, zoning in on words which produce more effects or stand out in contrast to the literary matter which surrounds it. As such, the ways in which a writer would use the words ‘the’, ‘an’, ‘a’, or ‘this’, tends to pass us by, but they may be far more indicative of a writer’s style, or at least in the way that a computer would be attentive to; sentences that are ‘pretty’ are generally statistically insignificant.

II: Methodology

Every corpus that you can see in the above image was scanned into R, and then run through a code which counted the number of times every word was used in the text. The resulting figure is called the word’s frequency, and was then reduced down to its relative frequency, by dividing the figure by total number of words, and multiplying the result by 100. Every word with a relative frequency above a certain threshold was put into a matrix, and a function was used to cluster each matrix together based on the similarity of the figures they contained, according to a Euclidean metric I don’t fully understand.

The final matrix was 21 X 57, and compared these 21 corpora on the basis of their relative usage of the words ‘a’, ‘all’, ‘an’, ‘and’, ‘are’, ‘as’, ‘at’, ‘be’, ‘but’, ‘by’, ‘for’, ‘from’, ‘had’, ‘have’, ‘he’, ‘her’, ‘him’, ‘his’, ‘I’, ‘if’, ‘in’, ‘is’, ‘it’, ‘like’, ‘me’, ‘my’, ‘no’, ‘not’, ‘now’, ‘of’, ‘on’, ‘one’, ‘or’, ‘out’, ‘said’, ‘she’, ‘so’, ‘that’, ‘the’, ‘them’, ‘then’, ‘there’, ‘they’, ‘this’, ‘to’, ‘up’, ‘was’, ‘we’, ‘were’, ‘what’, ‘when’, ‘which’, ‘with’, ‘would’, and ‘you’.

Anyway, now we can read the dendrogram.

III: Interpretation

Speaking about the dendrogram in broad terms can be difficult for precisely the reason that I indicative above; quantitative/qualitative methodologies for text analysis are totally opposed to one another, but what is obvious is that Eimear McBride and Gertrude Stein are extreme outliers, and comparable only to each other. This is one way unsurprising, because of the brutish, repetitive styles and is in other ways very surprising, because McBride is on record as dismissing her work, for being ‘too navel-gaze-y.’

Jorge Luis Borges and Marcel Proust have branched off in their own direction, as has Sara Baume, which I’m not quite sure what to make of. Franz Kafka, Ernest Hemingway and William Faulkner have formed their own nexus. More comprehensible is the Anne Enright, Katherine Mansfield, D.H. Lawrence, Elizabeth Bowen, F. Scott FitzGerald and Virginia Woolf cluster; one could make, admittedly sweeping judgements about how this could be said to be modernism’s extreme centre, in which the radical experimentalism of its more revanchiste wing was fused rather harmoniously with nineteenth-century social realism, which produced a kind of indirect discourse, at which I think each of these authors excel.

These revanchistes are well represented in the dendrogram’s right wing, with Flann O’Brien, James Joyce, Samuel Beckett and Djuna Barnes having clustered together, though I am not quite sure what to make of Ford Madox Ford/Joseph Conrad’s showing at all, being unfamiliar with the work.

IV: Conclusion

The basic rule in interpreting dendrograms is that the closer the ‘leaves’ reach the bottom, the more similar they can be said to be. Therefore, Anne Enright and Will Self are the contemporary modernists most closely aligned to the forebears, if indeed forebears they can be said to be. It would be harder, from a quantitative perspective, to align Sara Baume with this trend in a straightforward manner, and McBride only seems to correlate with Stein because of how inalienably strange their respective prose styles are.

The primary point to take away here, if there is one, is that more investigations are required. The analysis is hardly unproblematic. For one, the corpus sizes vary enormously. Borges’ corpus is around 46 thousand words, whereas Proust reaches somewhere around 1.2 million. In one way, the results are encouraging, Borges and Barnes, two authors with only one texts in their corpus, aren’t prevented from being compared to novelists with serious word counts, but in another way, it is pretty well impossible to derive literary measurements from texts without taking their length into account. The next stage of the analysis will probably involve breaking the corpora up into units of 50 thousand words, so that the results for individual novels can be compared.

Modelling Humanities Data: Deleuze, Descartes and Data

While dealing with the distinctions between data, knowledge and information in class, a pyramidal hierarchy was proposed, which can be seen on the left. This diagram discloses the process of making data (which have been defined as ‘facts’ which exist in the world), into information, and thereafter knowledge. These shifts from one state to another are not as neat as the diagram might suggest; it is just one interpretation giving shape to a highly dynamic and unsettled process; any movement from one of these levels to another is fraught. It is ‘a bargaining system,’ as every dataset has its limitations and aporias, not to speak of the process of interpretation or subsequent dissemination. This temporal dimension to data, its translation from a brute state is too often neglected within certain fields of study, fields in which data is more often understood as unambiguous, naturally hierarchicalised, and not open to contextualisation or debate.

This blog post aims to consider these issues within the context of a dataset obtained from The Central Statistics Office. The dataset contains information relating to the relative risk of falling into poverty based on one’s level of education between the years 2004 and 2015 inclusive. The data was analysed through use of the statistical analysis interface SPSS.

The purpose of the CSO is to compile and disseminate information relating to economic and social conditions within the state in order to give direction to the government in the formulation of policy. Therefore it was decided that the most pertinent information to be derived from the dataset would be the correlations between level of education and the likelihood of falling into poverty. The results appear below.

Correlation Between Risk of Poverty and Level of Education Achieved

Correlation Between Consistent Poverty (%) and Level of Education Received

Correlation Between Deprivation Rate (%) and Level of Education Received

Poverty Risk Based on Education Level

Deprivation Rate Based on Education Level

Consistent Poverty Rate based on Education Level

It can be seen that there is a very strong negative correlation between one’s level of education and one’s risk of exposure to poverty; the higher one ascends through the education system, the less likely it is one will fall into economic liminality. This is borne out both in the bar charts and the correlation tables, the latter of which yield p-values of .000, underlining the certainty of the finding. It should be noted that both graphing the data, and detecting correlations through use of the Spearman’s rho are elementary statistical procedures, but as the trend revealed here is consistent with more elaborate modelling of the relationship,[1] the parsimonious analysis carried out here is all that is required.

It should not be assumed that just because these graphs are informative that it is impossible to garner information from data in any other way. Even in its primary state, as it appears on the website, one could obtain information from a dataset through qualitative means. It is unlikely that this information will be as coherent as that which that can be gleaned from even the most basic graph, but it is important to emphasise the fact that the border that separates data from information is fluid.

It is unlikely to be a novel finding that those who have a third level education have higher incomes than those who do not; there is a robust body of research detailing the many benefits of attending university. [2] Therefore, can it be said that the visualisation of the dataset above has contributed to knowledge? One would answer this question relative to one’s initial research question, and how the information complicates or advances it. If the causal relationship between exposure to poverty and level of education has been confirmed, and a government agency makes the recommendation that further investment in educational support programmes are necessary, it is somewhere in this process that the boundary separating information from knowledge has been crossed.

The above diagram actualises the temporal nature of data to a greater extent than the pyramid, but in doing so it perpetuates a linearisation of the process, a line along which René Descartes’ notion of thought could be said to align. Descartes understood thought as a positive function which tends towards the good and toward truth. This ‘good sense’, allows us to ‘judge correctly and to distinguish the true from the false’.[3] Gilles Deleuze believes Descartes instantiates a model of thought which is oppressive, and which perceives thinking relative to external needs and values rather than in its actuality: ‘It cannot be regarded as fact that thinking is the natural exercise of a faculty, and that this faculty is possessed of a good nature and a good will.’[4]

In Deleuze’s conception, thought takes on a sensual disposition, reversing the Cartesian notion of mental inquiry beginning from a state of disinterestedness in order to arrive at a moment at which one recognises ‘rightness’. Deleuze argues that there is no such breakthrough moment or established methodology to thought, and argues for regarding it as more invasive, or unwelcome, a point of encounter when ‘something in the world forces us to think.’[5]

Rather than taking the neat, schematic movement from capturing data to modelling to interpreting for granted, Deleuze is engaged by these moments of crisis, points just before or just after the field of our understanding is qualitatively transformed into something different:

How else can one write but of those things which one doesn’t know, or know badly?…We write only at the frontiers of our knowledge, at the border which separates our knowledge from our ignorance and transforms one into the other.[6]

Deleuze’s comments have direct bearing upon our understanding of data, and how they should be understood within the context of the wider questions we ask of them. Deleuze argues that, ‘problems must be considered not as ‘givens’ (data) but as ideal ‘objecticities’ possessing their own sufficiency and implying acts of constitution and investment in their respective symbolic fields.’[7] While it is possible that Deleuze would risk overstating the case, were we to apply his theories to this dataset, it is nonetheless crucial to recall that data, and the methodologies we use to unpack and present them participate in wider economies of significance, ones with indeterminate horizons.


[1] Department for Business, Education and Skills, ‘BIS Research Paper №146: The Benefits of Higher Education and Participation for Individuals and Society: Key Findings and Reports’, (Department for Business, Education and Skills: 2013)

[2] OECD, Education Indicators in Focus, (OECD: 2012)

[3] Descartes, René, Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences (Gutenberg: 2008),

[4] Deleuze, Gilles, Difference and Repetition (Bloomsbury Academic: 2016), p.175

[5] Ibid.

[6] Ibid, p. xviii

[7] Ibid, p.207


Deleuze, Gilles, Difference and Repetition (Bloomsbury Academic: 2016), p.175

Department for Business, Education and Skills, ‘BIS Research Paper №146: The Benefits of Higher Education and Participation for Individuals and Society: Key Findings and Reports’, (Department for Business, Education and Skills: 2013)

Descartes, René, Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences (Gutenberg: 2008),

OECD, Education Indicators in Focus, (OECD: 2012)

The question that this blog post sets itself is: What differences and similarities can be detected in modernist and contemporary authors on the basis of three stylistic variables; hapax, unique and ambiguity, and how are these stylistic variables related to one another?

I: The Data

The data to be analysed in this project were derived from an analysis of twenty-one corpora of avant-garde literary prose through use of the open-source programming language R. The complete works of the authors James Joyce, Virginia Woolf, Gertrude Stein, Sara Baume, Anne Enright, Will Self, F. Scott FitzGerald, Eimear McBride, Ernest Hemingway, Jorge Luis Borges, Joseph Conrad, Ford Madox Ford, Franz Kafka, Katherine Mansfield, Marcel Proust, Elizabeth Bowen, Samuel Beckett, Flann O’Brien, Djuna Barnes, William Faulkner & D.H. Lawrence were used.

Seventeen of these writers were active between the years 1895 and 1968, a period of time associated with a genre of writing referred to as ‘modernist’ within the field of literary criticism. The remaining four remain alive, and have novels published as early as 1991, and as late as 2016. These novelists are known for their identification as latter-day modernists, and perceive their novels as re-engaging with the modernist aesthetic in a significant way.

I.II Uniqueness

The unique variable is a generally accepted measurement used within digital literary criticism to quantify the ‘richness’ of a particular text’s vocabulary. The formula for uniqueness is obtained by dividing the number of distinct word types in a text by the total number of words. For example, if a novel contained 20000 word types, but 100000 total words, the formula for obtaining this text’s uniqueness would be as follows:

20000/100000 = Uniqueness is equal to 0.2

I.III Ambiguity

Ambiguity is a measure used to calculate the approximate obscurity of a text, or the extent to which it is composed of indefinite pronouns. The indefinite pronouns quantified in this study are as follows, ‘another’, ‘anybody’, ‘anyone’, ‘anything’, ‘each’, ‘either’, ‘enough’, ‘everybody’, ‘everyone’, ‘everything’, ‘little’, ‘much’, ‘neither’, ‘nobody’, ‘no one’, ‘nothing’, ‘one’, ‘other’, ‘somebody’, ‘someone’, ‘something’, ‘both’, ‘few’, ‘everywhere’, ‘somewhere’, ‘nowhere’, ‘anywhere’, ‘many’, ‘others’, ‘all’, ‘any’, ‘more’, ‘most’, ‘none’, ‘some’, ‘such’. The formula for ambiguity is:

number of indefinite pronouns / number of total words

I.IV Hapax

Finally, the hapax variable calculates the density of hapax legomena, words which appear only once in a particular author’s oeuvre. The formula for this variable is:

number of hapax legomena / number of total words

a bar chart giving an overview of the data

II: Data Overview

Even before analysing the data in great depth, the fact that these variables are interrelated with one another stands to a logical analysis. Hapax and unique are best understood as an indication of a text’s heterogeneity, as if a text is hapax-rich, the score for uniqueness will be similarly elevated. Ambiguity, as it is a set of pre-defined words, can be considered a measure of a text’s homogeneity, and if the occurrences of these commonplace words are increasing, hapax and uniqueness will be negatively effected. The aim of this study will be to first determine how these measures vary according to the time frame in which the different texts were written, i.e. across modern and contemporary corpora, which correlations between stylistic variables exist, and which of the three is most subject to the fluctuations of another.

more overviews for each variable

IV.I: The Three Groups Hypothesis

A number of things are clear from these representations of the data. The first finding is that the authors fall into approximately three distinct groups. The first is the base- level of early twentieth-century modernist authors, who are all relatively undifferentiated. These are Ernest Hemingway, Virginia Woolf, William Faulkner, Elizabeth Bowen, Marcel Proust, F. Scott Fitzgerald, D.H. Lawrence, Joseph Conrad and Ford Madox Ford. They are all below the mean for the hapax and unique variables.

boxplot of outliers for the unique hapax variable

The second group reach into more extreme values for unique and hapax. These are Djuna Barnes, Jorge Luis Borges, Franz Kafka, Flann O’Brien, James Joyce, Eimear McBride and Sara Baume. Three of these authors are even outliers for the hapax variable, which can be seen in the box plot.

Joyce’s position as an extreme outlier in this context is probably due to his novel Finnegans Wake (1939), which was written in an amalgam of English, French, Irish, Italian and Norwegian. It’s no surprise then, that Joyce’s value for hapax is so high. The following quotation may be sufficient to give an indication of how eccentric the language of the novel is:

La la la lach! Hillary rillarry gibbous grist to our millery! A pushpull, qq: quiescence, pp: with extravent intervulve coupling. The savest lauf in the world. Paradoxmutose caring, but here in a present booth of Ballaclay, Barthalamou, where their dutchuncler mynhosts and serves them dram well right for a boors’ interior (homereek van hohmryk) that salve that selver is to screen its auntey and has ringround as worldwise eve her sins (pip, pip, pip)

Though Borges’ and Barnes’ prose may not be as far removed from modern English as Finnegans Wake, both of these authors are known for their highly idiosyncratic use of language; Borges for his use of obscure terms derived from archaic sources, and Barnes for reversing normative grammatical and syntactic structures in unique ways.

The third and final group may be thought of as an intermediary between these two extremes, and these are Katherine Mansfield, Samuel Beckett, Will Self and Anne Enright. These authors share characteristics of both groups, in that the values for ambiguity remain stable, but their uniqueness and hapax counts are far more pronounced than the first group, but not to the extent that they reach the values of the second group.

boxplot displaying stein as an extreme outlier for ambiguity

Gertrude Stein is the only author who’s stylistic profile doesn’t quite fit into any of the three groups. She is perhaps best thought of as most closely analogous to the first group of early twentieth century modernists, but her extreme value for ambiguity should be sufficient to distinguish her in this regard.

The value for ambiguity remains fairly stable throughout the dataset, the standard deviation is 0.03, but if Stein’s values are removed from the dataset, the standard deviation narrows from 0.03 to 0.01.

Two disclaimers need to be made about this general account from the descriptive statistics and graphs. The first is that there is a fundamental issue with making such a schematic account of these texts. The grouping approach that this project has taken thus far is insufficiently nuanced as it could probably be argued that McBride could just as easily fit into the third group as the second. Therefore, the stylistic variables do not adequately distinguish modern and contemporary corpora from one another.

IV.II Word Count

word count for the most prolific authors

It should not escape our attention that those authors who score lowest for each variable and that the first group of early twentieth-century author are the most prolific. The correlation between word count and the stylistic variables was therefore constructed.

Pearson correlation for word count and stylistic variables

Both the Pearson correlation and Spearman’s rho suggest that word count is highly negatively correlated with hapax and unique (as word count increases, hapax and unique decreases and vice versa), but not with ambiguity.

Spearman’s rho for word count and stylistic variables

The fact that the Spearman’s rho scores significantly higher than the Pearson suggests that the relationship between the two are non-linear. This can be seen in the scatter plot.

scatter plot showing the relationship between word count and uniqueness

In the case of both variables, the correlation is obviously negative, but the data points fall in a non-linear way, suggesting that the Spearman’s rho is the better measure for calculating the relationship. In both cases it would seem that Joyce is the outlier, and most likely to be the author responsible for distorting the correlation.

scatter plot displaying the relationship between word count and hapax density
Pearson correlations for word count and each stylistic variable

SPSS flags the correlation between hapax and unique as being significant, as this is clearly the most noteworthy relationship between the three stylistic variables. The Spearman’s rho exceeded the Spearman correlation by a marginal amount, and it was therefore decided that the relationship was non-linear, which is confirmed by the scatter plot below:

Spearman’s rho correlation for word count and stylistic variables

The stylistic variables of unique and hapax are therefore highlycorrelated.

VI: Conclusion

As was said already, the notion that stylistic variables are correlated stands to reason. However, it was not until the correlation tests were carried out that the extent to which uniqueness and hapax are determined by one another was made clear.

The biggest issue with this study is the issue that is still present within digital comparative analyses in literature generally; our apparent incapacity to compare texts of differing lengths. Attempts have been made elsewhere to account for the huge difference that a text’s length clearly makes to measures of its vocabulary, such as vectorised analyses that take measurements in 1000 word windows, but none have yet been wholly successful in accounting for this difference. This study is therefore one among many which presents its results with some clarifiers, considering how corpora of similar lengths clustered together with one another to the extent that they did. The only author that violated this trend was Joyce, who, despite a lengthy corpus of 265500 words, has the highest values for hapax and uniqueness, which marks his corpus out as idiosyncratic. Joyce’s style is therefore the only of the twenty-one authors that we can say has a writing style that can be meaningfully distinguished from the others on the basis of the stylistic variables, because he so egregiously reverses the trend.

But we hardly needed an analysis of this kind to say Joyce writes differently from most authors, did we.