The emotional flows of stories are important to engage the readers. Skillful writers grasp this very well by natural instinct. There are theories about this, called folkloristics. However, is there a way to see the flows in a graph? Linear algebra and natural language processing (NLP) kick in.

Andrew Reagan at the Computational Story Lab, University of Vermont, together with his colleagues and collaborators, did a numerical studies about this. [Reagan et. al., 2016] Their paper is now on the arXiv. He prepared a set of words with scores that quantitatively describe their sentiments, as in sentiment analysis. He then went through the text with a sliding window to measure the sentiments. Then for each book, there is a vector of a time series of these sentiment scores. For example, using this method, the plot of the emotional scores, or the emotional arc, of J. K. Rowling’s Harry Potter and the Deathly Hallows is as shown in the following plot: [Reagan et. al., 2016]

They did the same thing with other English fictions in the Project Gutenberg Corpus, giving a vector of these emotional scores for each fiction. They performed a principal component analysis (PCA) for all these books (represented by a matrix containing all vectors). PCA is a common dimensionality reduction techniques, and also useful for information retrieval (IR) in another name called latent semantic analysis (LSA). Reagan and his colleagues identify six major components of these emotional arcs, as shown below: [Reagan et. al., 2016]

These computational studies on fictions further reinforce our common belief that (good-selling) fictions do have resonating themes to keep the readers.

One fascinating application of deep learning is the training of a model that outputs vectors representing words. A project written in Google, named Word2Vec, is one of the best tools regarding this. The vector representation captures the word contexts and relationships among words. This tool has been changing the landscape of natural language processing (NLP).

Let’s have some demonstration. To use Word2Vec in Python, you need to have the package gensim installed. (Installation instruction: here) And you have to download a trained model (GoogleNews-vectors-negative300.bin.gz), which is 3.6 GB big!! When you get into a Python shell (e.g., IPython), type

from gensim.models.word2vec import Word2Vec


This model enables the user to extract vector representation of length 300 of an English word. So what is so special about this vector representation from the traditional bag-of-words representation? First, the representation is standard. Once trained, we can use it in future training or testing dataset. Second, it captures the context of the word in a way that the algebraic operation of these vectors has meanings.

Here I give 5 examples.

A Juvenile Cat

What is a juvenile cat? We know that a juvenile dog is a puppy. Then we can get it by carry out the algebraic calculation $\text{puppy} - \text{dog} + \text{cat}$ by running

model.most_similar(positive=['puppy', 'cat'], negative=['dog'], topn=5)


This outputs:

[(u'kitten', 0.7634989619255066),
(u'puppies', 0.7110899686813354),
(u'pup', 0.6929495334625244),
(u'kittens', 0.6888389587402344),
(u'cats', 0.6796488761901855)]


which indicates that “kitten” is the answer (correctly!) The numbers are similarities of these words with the vector representation  $\text{puppy} - \text{dog} + \text{cat}$ in descending order. You can verify it by calculating the cosine distance:

from scipy.spatial import distance
print (1-distance.cosine(model['kitten'], model['puppy']+model['cat']-model['dog']))


which outputs 0.763498957413.

This demonstration shows that in the model, $\text{puppy}-\text{dog}$ and $\text{kitten}-\text{cat}$ are of similar semantic relations.

Capital of Taiwan

Where is the capital of Taiwan? We can find it if we know the capital of another country. For example, we know that Beijing is the capital of China. Then we can run the following:

model.most_similar(positive=['Beijing', 'Taiwan'], negative=['China'], topn=5)


which outputs

[(u'Taipei', 0.7866502404212952),
(u'Taiwanese', 0.6805002093315125),
(u'Kaohsiung', 0.6034111976623535),
(u'Chen', 0.5905819535255432),
(u'Seoul', 0.5865181684494019)]


Obviously, the answer is “Taipei.” And interestingly, the model sees Taiwan in the same footing of China!

Taipei (taken from Airasia: http://www.airasia.com/mo/en/destinations/taipei.page)

Past Participle of “eat”

We can extract grammatical information too. We know that the past participle of “go” is “gone”. With this, we can find that of “eat” by running:

model.most_similar(positive=[‘gone’, ‘eat’], negative=[‘go’], topn=5)

which outputs:

[(u'eaten', 0.7462186217308044),
(u'eating', 0.6516293287277222),
(u'ate', 0.6457351446151733),
(u'overeaten', 0.5853317975997925),
(u'eats', 0.5830586552619934)]


Capital of the State of Maryland

However, this model does not always work. If it can find the capital of Taiwan, can it find those for any states in the United States? We know that the capital of California is Sacramento. How about Maryland? Let’s run:

model.most_similar(positive=['Sacramento', 'Maryland'], negative=['California'], topn=5)


[(u'Towson', 0.7032245397567749),
(u'Baltimore', 0.6951349973678589),
(u'Hagerstown', 0.6367553472518921),
(u'Anne_Arundel', 0.5931429266929626),
(u'Oxon_Hill', 0.5879474878311157)]


But the correct answer should be Annapolis!

Downtown Annapolis (taken from Wikipedia)

Word2Vec was developed by Tomáš Mikolov. He previously worked for Microsoft Research. However, he switched to Google, and published a few influential works on Word2Vec. [Mikolov, Yih, Zweig 2013] [Mikolov, Sutskever, Chen, Corrado, Dean 2013] [Mikolov, Chen, Corrado, Dean 2013] Their conference paper in 2013 can be found on arXiv. He later published a follow-up work on a package called Doc2Vec that considers phrases. [Le, Mikolov 2014]

Earlier this year, I listened to a talk in DCNLP meetup spoken by Michael Czerny on his award-winning blog entry titled “Modern Methods for Sentiment Analysis.” He applied the vector representations of words by Word2Vec to perform sentiment analysis, assuming that similar sentiments cluster together in the vector space. (He took averages of the vectors in tweets to extract emotions.) [Czerny 2015] I highly recommend you to read his blog entry. On the other hand, Xin Rong wrote an explanation about how Word2Vec works too. [Rong 2014]

There seems to be no progress on the project Word2Vec anymore as Tomáš Mikolov no longer works in Google. However, the Stanford NLP Group recognized that Word2Vec captures the relations between words in their vector representation. They worked on a similar project, called GloVe (Global Vectors), which tackles the problem with matrix factorization. [Pennington, Socher, Manning 2014] Radim Řehůřek did some analysis comparing Word2Vec and GloVe. [Řehůřek 2014] GloVe can be implemented in Python too.

Wall Street is not only a place of facilitating the money flow, but also a playground for scientists.

When I was young, I saw one of my uncles plotting prices for stocks to perform technical analysis. When I was in college, my friends often talked about investing in a few financial futures and options. When I was doing my graduate degree in physics, we studied John Hull’s famous textbook [Hull 2011] on quantitative finance to learn about financial modeling. A few of my classmates went to Wall Street to become quantitative analysts or financial software developers. There are ups and downs in the financial markets. But as long as we are in a capitalist society, finance is a subject we never ignore. However, scientists have not come up with a consensus about the nature of a financial market.

Agent-Based Models

Economists believe that individuals in a market are rational being who always aim at maximizing their profits. They often apply agent-based models, which employs complex system theories or game theory.

Random Processes and Statistical Physics

However, a lot of mathematicians in Wall Street (including quantitative analysts and econophysicists) see the stock prices as undergoing Brownian motion. [Hull 2011, Baaquie 2007] They employ tools in statistical physics and stochastic processes to study the pricings of various financial derivatives. Therefore, the random-process and econophysical approaches have nothing much about stock price prediction (despite the fact that they do need a “return rate” in their model.) Random processes are unpredictable.

However, some sort of predictions carry great values. For example, when there is overhypes or bubbles in the market, we want to know when it will burst. There are models that predict defaults and bubble burst in a market using the log-periodic power law (LPPL). [Wosnitza, Denz 2013] In addition, there has been research showing the leverage effect in stock markets in developed countries such as Germany (c.f. fluctuation-dissipation theorem in statistical physics), and anti-leverage effect in China (Shanghai and Shenzhen). [Qiu, Zhen, Ren, Trimper 2006]

Reconciling Intelligence and Randomness

There are some values to both views. It is hard to believe that stock prices are completely random, as the economic environment and the public opinions must affect the stock prices. People can neither be completely rational nor completely random.

There has been some study in reconciling game theory and random processes, in an attempt to bring economists and mathematicians together. In this theoretical framework, financial systems still sought to attain the maximum entropy (randomness), but the “particles” in the system behaves intelligently. [Venkatasubramanian, Luo, Sethuraman 2015] (See my another blog entry: MathAnalytics (1) – Beautiful Mind, Physical Nature and Economic Inequality) We are not sure how successful this attempt will be at this point.

Sentiment Analysis

As people are talking about big data in recent years, there have been attempts to apply machine learning algorithms in finance. However, scientists tend not to price using machine learning algorithms because these algorithms mostly perform classification. However, there are attempts, with natural language processing (NLP) techniques, to predict the stock prices by detecting the public emotions (or sentiments) in social media such as Twitter. [Bollen, Mao, Zeng 2010] It has been found that measuring the public mood in a few dimensions (including Calm, Alert, Sure, Vital, Kind, and Happy) allows scientists to accurately predict the trend of Dow Jones Industrial Average (DJIA). However, some hackers take advantage on the sentiment analysis on Twitter. In 2013, there was a rumor on Twitter saying the White House being bombed, The computers responded instantly and automatically by performing trading, causing the stock market to fall immediately. But the market restored quickly after it was discovered that the news was fake. (Fig. 1)

Fig. 1: DJIA fell because of a rumor of the White House being bombed, but recovered when discovered the news was fake (taken from http://www.rt.com/news/syrian-electronic-army-ap-twitter-349/)

P.S.: While I was writing this, I saw an interesting statement in the paper about leverage effect. [Qiu, Zhen, Ren, Trimper 2006] The authors said that:

Why do the German and Chinese markets exhibit different return-volatility correlations? Germany is a developed country. To some extent, people show risk aversion, and therefore, may be nervous in trading as the stock price is falling. This induces a higher volatility. When the price is rising, people feel safe and are inactive in trading. Thus, the stock price tends to be stable. This should be the social origin of the leverage effect. However, China just experiences the first stage of capitalism, and people are somewhat excessive speculative in the financial markets. Therefore, people rush for trading as the stock price increases. When the price drops, people stay inactive in trading and wait for rising up of the stock price. That explains the antileverage effect.

Does this paragraph written in 2006 give a hint of what happened in China in 2015 now? (Fig. 2)

Fig. 2: The fall of Chinese stock market in 2015 (taken from http://www.economicpolicyjournal.com/2015/06/breaking-biggest-chinese-stock-market.html)