# Comparing Writing Styles using
Word Embedding and Dynamic Time Warping

Abhinav Tushar<EMAIL_ADDRESS>Abhinav Dahiya
<EMAIL_ADDRESS>Department of Electrical Engineering
Indian Institute of Technology, Roorkee
(Both authors contributed equally)

###### Abstract

The development of plot or story in novels is reflected in the content and the
words used. The flow of sentiments, which is one aspect of writing style, can
be quantified by analyzing the flow of words. This study explores literary
works as signals in word embedding space and tries to compare writing styles
of popular classic novels using dynamic time warping.

##  I Introduction

Writing style of a novel is based on many factors including the personal style
of the author and the type of the novel itself. For example, thriller novels
by the same author tend to be similar in the way the story develops. Apart
from the specific factual details, literary works tend to have a definite flow
of emotions that define the overall subjective feel of the work as a whole.

This flow can be quantified and compared by analyzing the text using natural
language processing techniques. This study uses word embedding models to
generate time series for novels and then compare the resulting series using
dynamic time warping to find similarities. Considering time series analysis
rather than a pure statistical one can capture the flow of the works and thus
the similarities generated will provide a metric for comparing the novels
based on the progression.

The following section explains the word embedding models and dynamic time
warping. Section III describes the approach followed. Results on few classic
literary works are described in Section IV. Conclusions are drawn in Section
V.

##  II Background

###  II.1 Word Embedding

Word embedding refers to techniques which allow representing words to vectors
of real numbers in a continuous space. The vector representation can be
learned using many techniques and relies on using the information based on the
context, a word is present in.

We use a model proposed by Mikolov et al. (2013a, b) that uses Continuous Bag-
of-Words and Skip-Gram model to learn these continuous representations. This
approach uses the following two models.

####  II.1.1 Continuous Bag-of-Words model

Figure 1: Continuous Bag-of-Words model

This model (figure II.1.1) samples a context of size defined by $c$ from text
around a word and tries to learn a projection to vector space that correctly
predicts the middle word. Assuming words represented as one hot vectors
$w(i)$, where $i$ denotes the position of the word in text, the model takes
$w(t-c),w(t-(c-1)),\cdots,w(t-1),w(t+1),\cdots,w(t+(c-1)),w(t+c)$ and predicts
the middle word $w(t)$.

####  II.1.2 Skip-Gram model

Figure 2: Skip-Gram model

The skip-gram model (figure II.1.2) does the opposite of previous model. It
tries to predict the context, given the middle word. Using the previous
notation, this model takes $w(t)$ as input and outputs
$w(t-c),w(t-(c-1)),\cdots,w(t-1),w(t+1),\cdots,w(t+(c-1)),w(t+c)$.

The projection layers are of desired vector dimension. The weights from one
hot encoding of words to this layer provide, after training, the final
transformation matrix for continuous word representation.

Once trained, words in the vector space are arranged according to semantic
connections. This allows the vectors to have properties as shown below.

$W(king)-W(queen)\approx W(boy)-W(girl)$

$W$ is the function from vocabulary to the vector space.

###  II.2 Dynamic Time Warping

Dynamic Time Warping (DTW) is a technique to measure similarity between two
time series. DTW handles the difference in speed and time between signals and
has been used in applications like speech recognition and signature matching
where the difference of signal speed should not affect the final result. It is
based on optimal matching and the algorithm outputs a value corresponding to
the separation of the two time series. One considerable advantage of DTW is
that the two series need not to be of same length, which is the case here, as
two different books will have different word count and consequently different
length.

The objective of this algorithm is to calculate a distance measure for a given
pair of temporal series, that can represent the similarity / dissimilarity
between those two series. This is done by determining a path $W$ which
minimizes the cumulative euclidean distance between elements of the two
series. Let the two temporal series, which need to be compared, are

$A=a_{1},a_{2},a_{3},...,a_{m}\\\ $ $B=b_{1},b_{2},b_{3},...,b_{n}$

First, all the euclidean distances are calculated between each possible set of
elements from the two series, which results in total of $m\times n$ values.
Let the matrix depicting these distances be

$D=\begin{pmatrix}d_{1,1}&d_{1,2}&\cdots&d_{1,n}\\\
d_{2,1}&d_{2,2}&\cdots&d_{2,n}\\\ \vdots&\vdots&\ddots&\vdots\\\
d_{m,1}&d_{m,2}&\cdots&d_{m,n}\end{pmatrix}$

where the element $d_{i,j}$ represents the euclidean distance between $a_{i}$
and $b_{j}$. Now, using dynamic programming, the optimal path $W$ is
determined from point $(1,1)$ to $(m,n)$ along which the cumulative sum of the
euclidean distances (i.e. the sum of $d_{i,j}$) is minimum. This path is
continuous, which means that the indices of two consecutive elements of $W$ do
not differ by more than one in either series. The path is determined using the
following recursive function:

$\gamma(i,j)=d(i,j)+\min(\gamma(i-1,j-1),\gamma(i-1,j),\gamma(i,j-1))$

where $\gamma(i,j)$ represents the cumulative sum up to elements $a_{i}$, and
$b_{j}$. Figure II.2 shows an example using two sinusoidal series. The optimal
path and the series are shown.

Figure 3: Optimal path calculated using DTW for two sinusoidal series

##  III Approach

###  III.1 Novels to Signal

Figure 4: Anchor point similarities for The Sign of the Four. Deeper color
curves represent the filtered signal.

Our approach for converting a novel to signal uses sentence vectors by taking
mean of word vectors in a sentence. A word embedding model is trained using
1000 free e-books gathered from Project Gutenberg111Project Gutenberg
https://www.gutenberg.org. The model is trained using Word2Vec222Python
adaptation here https://radimrehurek.com/gensim/models/word2vec.html.

Training is done using feature (word vector) size of 100 and context window
size of 10 words. Once trained, a novel with $N_{w}$ words results in a 100
dimensional time series of length $N_{w}$.

To reduce the dimension of data word vectors in a sentence are averaged,
resulting in a time series matrix of shape $N_{s}\times 100$, where $N_{s}$ is
the number of sentences in the novel. To reduce the row dimensions, we find
cosine similarity of each row with few anchor points in the word space. This
provides a measure of the movement of the signal in the whole vocabulary
space.

For selecting appropriate anchor points to better cover the space in its
entirety, we perform k-means clustering on the vocabulary of the embedding
model and find 4 cluster centers. These 4 points act as the anchors, resulting
in a final matrix of size $N_{s}\times 4$ for each book.

A plot of distances from these 4 points for The Sign of the Four by Arthur
Conan Doyle is shown in figure 4. Due to the fickle nature of text a large
amount of noise is present. After smoothing with a gaussian filter (window
size = 200, $\sigma$ = 60), the essential rising and falling trend of curve is
preserved. Filtered lines are shown with deeper color in the plot.

###  III.2 Comparing Signals

Once generated, the signals are compared using FastDTW (Salvador and Chan,
2004) which implements a faster version of DTW algorithm. Vanilla DTW requires
$O(n^{2})$ computation, while FastDTW computes in linear time.

We use 24 classic novels collected from Project Gutenberg (listed in table 1)
and generate distance matrix for the items.

S.no. | Book Name | Author
---|---|---
1. | A Study in Scarlet | Arthur Conan Doyle
2. | The Adventures of Sherlock Holmes | Arthur Conan Doyle
3. | The Hound of the Baskervilles | Arthur Conan Doyle
4. | The Return of Sherlock Holmes | Arthur Conan Doyle
5. | The Sign of the Four | Arthur Conan Doyle
6. | A Christmas Carol | Charles Dickens
7. | A Tale of Two Cities | Charles Dickens
8. | Bleak House | Charles Dickens
9. | David Copperfield | Charles Dickens
10. | Great Expectations | Charles Dickens
11. | Hard Times | Charles Dickens
12. | Oliver Twist | Charles Dickens
13. | Emma | Jane Austen
14. | Pride and Prejudice | Jane Austen
15. | Persuasion | Jane Austen
16. | Sense and Sensibility | Jane Austen
17. | A Connecticut Yankee in King Arthur’s Court | Mark Twain
18. | Adventures of Huckleberry Finn | Mark Twain
19. | Life on the Mississippi | Mark Twain
20. | The Adventures of Tom Sawyer | Mark Twain
21. | The Innocents Abroad | Mark Twain
22. | The Mysterious Stranger | Mark Twain
23. | The Prince and the Pauper | Mark Twain
24. | Treasure Island | Robert Louis Stevenson
Table 1: List of novels compared

##  IV Results

Figure 5: Books scattered according to similarity. Look up table 1 for
indices.

A scatter plot of the books using multi dimensional scaling is shown in figure
IV. Although the similarity measure itself is a useful metric for comparison,
the scatter plot also clusters the authors according to the writing styles,
affirming the hypothesis that a comparison of flow in the time series of word
vectors can have subjective projections.

##  V Conclusions and Future Works

This study provides a way to explore literary works as signals in word
embedding space. The clusters of authors formed as the result of analysis
provides encouraging support for this method as a high level text analysis
technique.

A more rigorous study can be done by building on present method to identify
the principle components involved in shaping the overall picture of a book
while at the same time, being agnostic of factual details. The text
representation can be made better using paragraph (or sentence) vectors
instead of word vectors. Anchor points can be improved based on the effects
and the number of points. A frequency based analysis of signals can provide a
better insight.

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