We can also use this to plot word distribution, where the x-axis can be the document sample size and the y-axis can be the number of unique words. The curve will respond the same way. This type of curve that plots word frequency can be used to estimate the total vocabulary of a writer from a given sample Efron and Thisted, An Accumulative Word Type Usage Curve for the largest word types is calculated so that we can examine the Richness of the Shakespeare and Marlowe corpus from their plotted curves using the example in Efron and Thisted Initially, we create a word type frequency list of the Shakespeare corpus and order the data from the smallest number of unique words types to the largest.

We aggregate the data for the first word groups. We do the same to the smaller Marlowe data and plot the results of both playwrights. The number of word groups largest appears on the x-axis, while the number of accumulated unique word types appear on the y-axis. We then visually compare the asymptotes of both playwrights using a different Word Accumulative Curve from the one mentioned in the previous paragraph.

In this one, each of the works of Shakespeare are ordered from the largest work size number of individual tokens to the smallest. Then the number of unique words in each work new types introduced is calculated. This data is then aggregated, and we have a data point for each file that introduces new unique words types. This process is applied to the works of Marlowe. We plot both playwrights.

The values of lexical richness change for different measures used because of text length, and it is necessary to correct for this Tweedie and Baayen, We do this with ratios Singhal et al. The data is clustered using three complementary techniques.

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The first attempts to separate the playwrights, the second separates known works from contested works—publications believed to be of different authorship — and, the third separate the three playwright's known works with the contested ones removed. SPSS is used to conduct testing. The Hierarchical Cluster Analysis technique uses Ward's Method with Squared Euclidean distance measurement, and nearest neighbor using both Squared Euclidean distance and Cosine options.

The data is forced into three clusters for each playwright, Shakespeare, Marlowe, and Cary to observer where the chunks cluster. EFA aims to reduce the variables in the data into a smaller set of factors that explain the pattern of the relationships between the variables Burns and Burns, By setting the threshold to 0. Once this is achieved, we use the identified components, also known as factors, for each of the significant variables that make up the components factors to plot the 57 chunks and observe how the known and contested works visually cluster.

We test the data initially by using the Kaiser-Meyer-Olkin KMO to measure of sampling adequacy to ensure the value is greater than 0. We also ensure that Bartlett's Test of Sphericity has a significance value less than 0. We apply Kaiser's criterion rule by producing as scree plot which highlights all of the eigenvalues and suggests retaining only factors that are above the eigenvalue of 1.

We remove the contested works from the data and categorize all of the individual known authors' chunks, numbering them 1—3 and train the model. Using the resultant coefficients from the three Canonical Discriminant Functions, we plot the functions and compare the clusters. Finally, we test the effectiveness of the algorithm. Rather than use k-fold cross-validation to test the accuracy of the model Rodriguez et al. We elect to use the partial approach because we are not concerned with data disclosure Drechsler et al.

Five Shakespeare works are chosen at random and divided into 62 word chunks. Five partially synthetic samples are constructed using 12 randomly selected chunks. Using the LDA resultant coefficients from the previous test, these new 24,word synthetic works are overlayed against the uncontested works to see how close they cluster to Shakespeare, Marlowe, and Cary. Within this section, we discuss the correlation analysis results, the differences in the word accumulation curves, the hierarchical clustering, and PCA.

We conclude with the stepwise LDA predictive model that is verified using a partial synthetic approach. The results were significant at the 0. In all cases, the relationship between Referential Activity Power and all other variables had an inverse relationship. Overall, the elements were independent of each other. Pearson's correlation testing was conducted on the sensory adjectives that made up the Sensory element: Auditory, Gustatory, Haptic, Olfactory, and Visual. Gustatory, Olfactory, and Haptic had the same correlations and did not have a significant relationship to Auditory.

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Again, the elements were independent of each other. Pearson's correlation coefficient testing was used to determine the independence of the four linguistic variables known as particles that create the Referential Activity Power variables: Articles, Conjunctives, Prepositions, and Pronouns. The analysis showed that Prepositions are substantial as shown by its relationship with Articles In this case, it would seem overall that the elements were less independent of each other. There is a significant difference in the sample sizes of Shakespeare, Marlowe, and Cary.

Therefore, as an alternate test for the Richness calculations, Word Accumulation Curves were plotted for Shakespeare's ,word, Marlowe's ,word, and Cary's 17, word corpus to examine if their use of vocabulary was similar. Marlowe's unique word list reached an asymptote at about the 21st largest word group, a total of 8, unique words, and Cary's unique word list reached an asymptote at about the 15th largest word group with a total of 2, unique words.

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When we compared the point where both word group curves asymptote, we could see Marlowe used about Cary used about It highlighted that Marlowe and Shakespeare have similar word growth that might take into account the influence of vocabulary size. We cannot make a comparison with Cary with a single work.

There is an age difference between Shakespeare and Marlowe which could account for these differences. People's vocabulary is known to peak late in adulthood before it declines currently peaking around 65 years. See Hartshorne and Germine, , but this could highlight that age differences contribute to and help differentiate people from their Richness scores. In the lower , the different number of words each playwright used is shown and is different, but in the upper , the similarities between Marlowe and Shakespeare's word usage is highlighted.

In both cases, the chunks are well below a size that would approach the asymptote, and we deem that this phenomenon occurs outside of our enforced limit of a 30,word sample. To determine if there are differences in the writing styles of the three playwrights, the data was forced into three clusters using Hierarchical Cluster Analysis, using Ward's Method with Squared Euclidean distance measure, and nearest neighbor using both Squared Euclidean distance and Cosine measure.

It was expected that by forcing three clusters, one for each playwright Shakespeare, Marlowe, and Cary , they would appear in separate clusters. However, the data variations in the contested and non-contested authored works were too distant in Euclidean space, and one of the clusters that formed had all three playwrights in them see Table S1 External Data.

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Another test would need to be performed on a smaller set of the data without the contested, non-authored works, therefore as an alternative, PCA was conducted. Iterative PCA was conducted to optimize the algorithm by the maximum variance explained by eigenvalues was conducted.

Only one factor was extracted and accounted for All the remaining three factors accounted for PCA was extended, and the Referential Activity Power element was substituted with its four variables. Articles, Conjunctives, Prepositions, and Pronouns were tested to determine if the total variance would increase over the initial However, only one factor was extracted, and it accounted for All the remaining six factors accounted for Overall, the total variance explained by the single factor increased by 1.

PCA was again extended, and the Sensory element was substituted with its five variables.

Communalities varied from 0. By applying Kaiser's Rule and scree test, two factors were deemed important.

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Following rotation, factor one was loaded on five items that reflect four of the five sensory elements variables and RA Power accounted for Factor two is loaded on the Richness, personal pronouns, RA Power, and two of the Sensory adjectives Auditory and Visual and accounted for Overall, the total variance explained by the two factors was These results show an increase of 7. Unweighted least squares Factor Analysis results highlighted Pearson's r correlations and indicated the inverse nature of Referential Activity Power along with the isolated Auditory variable.

This was identified through the two leading factors of the PCA grouped by the Hierarchical Clustering results blue ellipses. These methods are robust enough to correlate precisely. The cluster at the bottom contains most of the chunks for all three authors. The second largest cluster on the top left contains works of uncertain or mixed authorship, such as Shakespeare's The Passionate Pilgrim chunks , and 41 , and Marlowe's two-authored The Passionate Shepherd to his Love chunks The exception was Shakespeare's The Phoenix and the Turtle chunks While the differences in The Phoenix and the Turtle have been put down to Shakespeare's genius Bednarz, and there is still some uncertainty over authorship Richards, , it is an accepted Shakespearian work.

The cluster on the top right showed one work each of Shakespeare and Marlowe's that are stylistically quite different from their other works. Venus and Adonis was suggested to be written during Shakespeare's hard times during the plague Stritmatter, , and it is said to lack a sense of form and seen as dull Putney, The results were reinforced by the personal pronoun analysis. When comparing Richness against Referential Activity Power, four very noticeable spikes occur chunks 24, , 41, and , and these were also the works that appear in the top left cluster.

Two lesser spikes occurred in the top right cluster 8 and This relationship between Richness and Referential Activity Power is unusual and discussed further below.

https://liderthyitawa.tk To further reinforce these consistent results, analysis of Richness against Sensory identified a large cluster of Shakespeare and Marlowe's works, but this time with a diffuse set of outliers. Results of the two clusters from the Principal Component Analysis overlayed with the Hierarchical Cluster Analysis results and showing the three clusters that form to separate the known works of the three playwrights from the works that are of contested authorship or in the case of 8, 29, and 30 are stylistically different.

To look at the data in more detail, the contested works were removed from the data, and stepwise LDA conducted.