Exploring a new way to compare storytelling in classics by comparing changing signals in a word embedding space using dynamic time warping.

If you are a fanatic reader of a particular author, you can immediately identify
whether a given (unknown) text is written by him/her or not. Apart from the
idiosyncrasies and diction, the flow and development of text is particularly
unique to an author. You can actually visualize a curve of rising and falling
emotional cues like *thrill*, *optimism*, *confusion* in their works. Taking these
works as signals can, in principle, allow us to compare the writing styles. This
post tries to do the same using a technique called *dynamic time warping* on
signals based on word vectors gathered from classic literary works.

## 1 Text to Signal

There are many ways to see text as a time series. I will use a pretty basic and intuitive technique with word embeddings.

### 1.1 Word Embeddings

Word embeddings provide projections of *words* from any language to some \(N\)
dimensional mathematical space. In simple terms, it provides a vector for each
word it has seen. The vector is learned in relation to the context in which it
appears. A popular method uses Continuous Bag of Words and Skip-gram and has a
python implementation in gensim (Word2Vec).

An excellent primer on the topic is on the blog of Christopher Olah here. This vector representation does two things for us:

*Gives us something much more amenable to mathematical analysis, numbers.**Arranges the words in vector space according to the semantic meanings.*

A sample of 1000 words from a 100 dimensional word space (t-SNE/ed/ to 2 dimensions) after training on Project Gutenberg's 1000 ebooks is shown below. Although the words look mostly archaic, lookout for nearby words with semantic connections (hover on dots).

### 1.2 Cramming text

After training an embedding model (with 100 dimensions) and computing vectors
for each word in a book, we are left with a matrix of size \(N_w \times 100\), where
\(N_w\) is the number of words. One simple reduction strategy for \(N_w\) is to
simply take sentence vectors by averaging out the words (though, we could have
used Doc2Vec here, but let's go with this). For 100 columns, we can hinge to few
fixed word vectors like *romance*, *mystery* and calculate cosine distances of the
rows from these anchor points. But, since the word space coverage might be
severely affected, a better way is to create anchor points in the number space
directly.

A simple K-means clustering with 4 centers provide us the anchor points and now
the matrices are of size \(N_s \times 4\). Below is the graph for *The Sign of the Four*
by Arthur Conan Doyle.

The smooth lines are generated after using a gaussian filter and they more or less capture the essence of the flow.

## 2 Comparing signals

Once we have set of comparable signals for each book, next step is to do actual comparison. A simple way would be to extract some sort of features from these time series or directly apply techniques to learn from the series. But, let's try something more crude and direct.

In time series analysis, dynamic time warping (DTW) is an algorithm for measuring similarity between two temporal sequences which may vary in time or speed.

In short this is what we want. DTW has simple working principles and is invariant of length and positions of peaks and valleys in signals. The pseudo code on Wikipedia should get you started.

### 2.1 Distances to coordinates

Once we get the distances, we get 2D cartesian coordinates using Multi Dimensional Scaling (MDS). Although we won't talk about this here, MDS is a cool thing to look for in data visualization.

Anyway, here is the scatterplot of 24 classic books.

Jane Austen gets a personal space of her own. Mark Twain looks versatile.

One thing that personally worries me while reading fiction is the easy predictability, not of facts (which doesn't hurt), but of what will happen next in a global emotional context. Reading The Lost Symbol made me feel like I am reading Digital Fortress all again. Hopefully, this won't happen again.