Category Archives: social phenomena

How our storytelling nature means we deeply misunderstand the mechanics of fame (and much else…)

Should the Mona Lisa be our most famous painting?

Was Harry Potter destined to (repeatedly) sweep the globe?

What would happen to everyone and everything famous if we ran the experiment that is our world over again?

Find out why fame is truly unpredictable, how it lives and dies entirely in our social stories, and why “… there is no such thing as fate, only the story of fate” in a current Nautilus Magazine piece by the Computational Story Lab’s co-team leader Peter Dodds:

“Homo Narrativus and the Trouble with Fame: We think that fame is deserved. We are wrong.”  

Nautilus is a new, design-driven publication on science published both online (free) and in print (unfree).  The Nautilus team is creating a beautiful showcase for scientific knowledge, and we encourage you to explore everything they have on offer.

nautilus-crowd

Leave a comment

Filed under networks, prediction, psychology, social phenomena

How does movement influence your daily happiness?

Imagine commuting an hour to work, one way, grinding through miles of traffic to get from your suburban home to a desk job in the big city. Excited yet?

Ok, now imagine that you lead a life of leisure traveling the world. You fly coast-to-coast to see a concert, soak in some culture, and drink fine wine. Does this lifestyle seem more appealing?

Lets try to quantify the influence of these travel patterns on individual happiness. We do this using geolocated tweets, which we have previously used to reveal the happiness of cities, and to quantify patterns of movement.

Each point corresponds to a geo-located tweet from 2011. (A) USA (B) Washington, D.C. (C) Los Angeles (D) Earth

Each point corresponds to a geo-located tweet from 2011.
(A) USA (B) Washington, D.C. (C) Los Angeles (D) Earth

First, we find the average location of each individual’s tweets. We call this their expected location. Then we draw circles emanating from this spot, like rings on a dart board. Some messages are written close to home, others from very far away.

Then we collect all of the words written at each distance, roughly 500,000 tweets per ring. Averaging the happiness of words found at each distance, remarkably we find that happiness increases logarithmically with distance from expected location. Tweets authored far from home contain a smaller number of negative words.

Tweets are grouped into ten equally populated bins by the distance from their author's average location, and the average happiness of words written at each distance is plotted. Expressed happiness grows logarithmically with distance from home.

Tweets are grouped into ten equally populated bins by the distance from their author’s average location, and the average happiness of words written at each distance is plotted. Expressed happiness grows logarithmically with distance from home.

Home is where the hate is? What? No.

Below we look at the difference between the happiest and saddest distances from home. Words appearing on the right increase the happiness of the 2500km distance relative to the 1km distance. For example, tweets authored far from an individual’s expected location are more likely to contain the positive words `beach’, `new’, `great’, `park’, `restaurant’, `dinner’, `resort’, `coffee’, `lunch’, `cafe’, and `food’, and less likely to contain the negative words `no’, `don’t’, `not’, `hate’, `can’t’, `damn’, and `never’ than tweets posted close to home. Words going against the trend appear on the left, decreasing the happiness of the 2500km distance group relative to the 1km group.

Word shift graph comparing the lowest average word happiness distance group to the words authored farthest from home.

Word shift graph comparing the lowest average word happiness distance group to the words authored farthest from home.

Tweets written close to home are more likely to contain the positive words `me’, `lol’, `love’, `like’, `haha’, `my’, `you’, and `good’. Moving clockwise, the three insets show that the two text sizes are comparable, the biggest contributor to the happiness difference is the decrease in negative words authored by individuals very far from their average location, and the 50 words listed make up roughly 50% of the total difference between the two bags of words. For you visual learning folks, here is a short video explaining how these word shifts work.

Take home story: people tweeting far from home talk about food more, and they swear less than people tweeting close to home. These people are probably enjoying awesome vacations, and tweeting about it!

In summary, if you are a fellow with a daily commute that makes you feel a little bit sad, you are not alone! Try swearing less. Or ride your bike.

If you are lucky enough to travel often, then keep smiling…maybe send the rest of us some pictures to cheer us up!

For more details on our analysis, check our paper “Happiness and the Patterns of Life: A Study of Geolocated Tweets” recently published in Nature Scientific Reports.

1 Comment

Filed under geohappiness, psychology, social phenomena

Now Published: The Geography of Happiness

Today we’re pleased to announce that our article “The Geography of Happiness: Connecting Twitter sentiment and expression, demographics, and objective characteristics of place” has been officially published by PLoS ONE.  We wanted to tell you about one key piece we’ve added to the paper and an unusual new Twitter account we’ve created.

After our three blog posts (which coincided with the release of the preprint), we received plenty of media attention, as well as some fantastic feedback from readers (thanks!). One very important question kept coming up: “How well does happiness agree with other measures of well-being?”, or more simply: “Why should we believe you?”

Well, we’re glad you asked.  For the final paper, we’ve added a US state-level comparison between our happiness measure and five other kinds of well-being indices:

  • the Behavioral Risk Factor Surveillance Survey (BRFSS)  for which people were asked to rate their life satisfaction on a scale of 1 to 4 (the BRFSS was explored in this Science paper on well-being from a few years back);
  • Gallup’s health survey-based well-being index;
  • the Peace Index, which aggregates various crime data;
  • the America’s Health Ranking, which aggregates health data; and
  • gun violence, specifically the number of shootings per 100,000 people.

In the figure below, we show a series of scatter plots comparing all pairs of well-being metrics  (happiness runs along the top row).  Each dot represents a US state, and the colors represent strength of correlation or agreement between measures, with blue meaning strong agreement, and red representing no (statistically significant) agreement. (We include the exact Spearman correlation coefficienr and p-value in each scatter plot.)

happinessScatterMatrix1

Scatter matrix showing comparison between different well-being metrics for all US states. The top row shows comparisons with happiness. Colors indicate the strength of correlation between pairs of metrics; shades of blue indicate increasingly significant correlation.

Looking at the top row, we can immediately see that happiness agrees with all measures except for the BRFSS. However, the BRFSS itself doesn’t agree with any other measure except for the Gallup well-being index.  The most striking departure was the BRFSS ranking Louisiana as the happiest state whereas our happiness measure placed it last.  There are a number of possible explanations for these disagreements: one is that the BRFSS data was taken between 2005 and 2008, while all other data is from 2011 only; another is that unlike the other measures, happiness is self-reported in the BRFSS. How would you answer if asked how happy you are? Do you expect that your answer is representative of the population you live in at large? There are certainly many different ways to define “happiness”, as a number of different readers have pointed out.

Of course, this is not to criticize the BRFSS (it remains a significant data source, and Oswald & Wu did fine work analyzing it in their Science paper), but merely to suggest that our word happiness score is measuring something different but perhaps complementary to traditional survey-based techniques. There certainly appears to be plenty of value to observing people “in the wild” via social network data, e.g. with the real-time instrument hedonometer.org.

Finally, to celebrate the publication of our article we created a Twitter feed, @geographyofhapp, dedicated to tweeting the happiest and saddest city every day, and we invite you to follow.  We’re hoping that this is the first research article with its own Twitter account, but perhaps not hoping that it represents the future of scientific publishing…

Leave a comment

Filed under geohappiness, mathematics, psychology, social phenomena

Now online: the Dow Jones Index of Happiness

Total excitement people: our website hedonometer.org has gone live.  We’re measuring Twitter’s happiness in real time.  Please check it out!

If you’re still here, here’s the blurb from the site’s about page:

Happiness: It’s what most people say they want. So how do we know how happy people are? You can’t improve or understand what you can’t measure. In a blow to happiness, we’re very good at measuring economic indices and this means we tend to focus on them. With hedonometer.org we’ve created an instrument that measures the happiness of large populations in real time.

Our hedonometer is based on people’s online expressions, capitalizing on data-rich social media, and we’re measuring how people present themselves to the outside world. For our first version of hedonometer.org, we’re using Twitter as a source but in principle we can expand to any data source in any language. We’ll also be adding an API soon.

So this is just a start – we invite you to explore the Twitter time series, let us know what you think, and follow the daily updates through the hedonometer twitter feed: .

1 Comment

Filed under networks, psychology, social phenomena

A data-driven study of the patterns of life for 180,000 people

Here at the Computational Story Lab, some of us commute by foot, some by car, and a few deliver themselves by bike, even in the middle of our cold, snowful Vermont winter.  Occasionally, we transport ourselves over very long distances in magic flying tubes with wings to attend conferences, to see family, or for travel.  So what do our movement patterns look like over time?  Are there distinct kinds of movement patterns as we look across populations, or are they variations on a single theme?

Inspired by an analysis of mobile phone data by Marta Gonzalez at MIT, James Bagrow at Northwestern, and colleagues, we used 37 million geotagged tweets to characterize the movement patterns of 180,000 people during their 2011 travels. We used the standard deviation in their position, a.k.a. radius of gyration, as a reflection of their movement. As an example, below we plot a dot for each geotagged tweet we found posted in the San Francisco Bay area, colored by the author’s radius of gyration.

The Bay Area is shown with a dot for each tweet, colored by the radius of gyration of its author.

The Bay Area is shown with a dot for each tweet, colored by the radius of gyration of its author. The color scale is logarithmic, so we can compare people with very different habits.

You can see from the picture that there are many people with a radius near 100km tweeting from downtown San Francisco. This pattern could reflect a concentration of tourists visiting the area, or individuals who live downtown and travel for work or pleasure. Images for New York City, Chicago, and Los Angeles are also quite beautiful.

In the image below, we rotated every individual’s movement pattern so that the origin represents their average location, and the horizontal line heading to the left represents their principle axis (most likely the path from home to work). We also stretched or shrunk the vertical and horizontal axes for each individual, so that everyone could fit on the same picture. Basically, we have a heatmap of collective movement, with each individual in their own intrinsic reference frame.  The immediate good news for these kinds of data-driven studies is that we see a very similar form to those found for mobile phone data sets.  Apart from being a different social signal, Geotagged Tweets also have much better spatial resolution than mobile phone calls which are referenced by the nearest cellphone tower.

Movement pattern exhibited by 180,000 individuals in 2011, as inferred from 37 million geolocated tweets. Colormap shows the probability density in log10. Note that despite the resemblance, this image is neither a nested rainbow horseshoe crab, nor the Mandelbrot set.

Movement pattern exhibited by 180,000 individuals in 2011, as inferred from 37 million geolocated tweets. Colormap shows the probability density in log10. Note that despite the resemblance, this image is neither a nested rainbow horseshoe crab, nor the Mandelbrot set.

Several features of the map reveal interesting patterns. First, the teardrop shape of the contours demonstrates that people travel predominantly along their principle axis, with deviations becoming shorter and less frequent as they move farther away. Second, the appearance of two spatially distinct yellow regions suggests that people spend the vast majority of their time near two locations. We refer to these locations as the work and home locales, where the home locale is centered on the dark red region right of the origin, and the work locale is centered just left of the origin.

Finally, we see a clear horizontal asymmetry indicating the increasingly isotropic variation in movement surrounding the home locale, as compared to the work locale. We suspect this to be a reflection of the tendency to be more familiar with the surroundings of one’s home, and to explore these surroundings in a more social context. The up-down symmetry demonstrates the remarkable consistency of the movement patterns revealed by the data.

We see a clear separation between the most likely and second most likely position.

We see a clear separation between the most likely and second most likely position.

Looking just at the messages posted along the work-home corridor, the distribution is skewed left, with movement from home in a heading opposite work seen to be highly unlikely.

The isotropy ratio shows the change in the probability density's shape as a function of radius.

The isotropy ratio shows the change in the probability density’s shape as a function of radius.

Above we see that individuals who move around a lot have a much larger variation in their positions along their principle axis, exhibiting a less circular pattern of life than people who stay close to home. Remarkably, the isotropy ratio decays logarithmically with radius.

Finally, we grabbed messages from the most prolific tweople, those 300 champions who had posted more than 10,000 geotagged messages in 2011. We received 10% of these messages through our gardenhose feed from Twitter. Below, we plot the times during the week that they post from their most frequently visited location. These folks most likely have the geotag switch on for all messages, and exhibit a very regular routine.

A robust diurnal cycle is observed in the hourly time of day at which statuses are updated, with those from the mode location (black curve) occurring more often than other locations (red curve) in the morning and evening.

A robust diurnal cycle is observed in the hourly time of day at which statuses are updated, with those from the mode location (black curve) occurring more often than other locations (red curve) in the morning and evening.

Peaks in activity are seen in the morning (8-10am) and evening (10pm-midnight), separated by lulls in the afternoon (2-4pm) and overnight (2-4am) hours.  As we and our friend Captain Obvious would expect, people tend to tweet more from their home locale than any other locale (red curve) in the morning and evening.

Bottom line: Despite our seemingly different patterns of life, we are remarkably similar in the way we move around. Our walks are a far cry from random.

Next up: We’ll examine the emotional content of tweets as a function of distance.  Is home where the heart is?

For more details on these results, see our paper Happiness and the Patterns of Life: A Study of Geolocated Tweets.

2 Comments

Filed under networks, physics, prediction, social phenomena

The Twitter Diet

How does food (or talking about food online) relate to how happy you are? This is part 3 of our series on the Geography of Happiness. Previously we’ve looked at how happiness varies across the United States (as measured from word frequencies in geotagged tweets), and then at how different socioeconomic factors relate to variations in happiness. Now we focus in on one particular important health factor that might influence happiness, obesity.

We looked at how happiness varied with obesity across the 190 largest metropolitan statistical areas in the United States, giving us the following scatter plot:

happinessObesity

Each point represents one city; for example the city with both(!) lowest obesity and greatest happiness in this set is Boulder, CO, located at the top left. The red line is a linear trend through the data (a line of best fit). Again, for the mathematically minded onehappybird watchers, we show the Spearman correlation coefficient and its corresponding p-value at the lower left. We do this to convince you that there is, in fact, a statistically significant downward trend in the blob of points in the picture! The big story here is of course that as obesity goes up, happiness goes down.

The natural next question to ask is: are there any words which could be indicators of obesity? What foods are people in obese cities eating, or talking about? To answer this question we correlated word frequencies with obesity, and searched for the most strongly-correlating food-related words. Below are two examples: on the left, “mcdonalds”, and on the right, “cafe”.

cafeMcDonalds

As obesity goes up, so does talk (at least on Twitter) about McDonalds, but talk about cafes follows the opposite trend! Does that mean that in order to lose weight we should spend more time sipping lattes in cafes? I wish.

Looking through the list of words, the top 5 food-related words that increase in frequency as obesity went up were:

  1. mcdonalds
  2. eat
  3. wings
  4. hungry
  5. heartburn

We were surprised by ‘hungry’! On the other hand, the top food-related words which were used more as obesity went down were:

  1. cafe
  2. sushi
  3. brewery
  4. restaurant
  5. bar

Perhaps unsurprisingly, these are words typically used by the high-socioeconomic group described in our previous post on city happiness, suggesting that better health correlates with higher socioeconomic status. You can find the complete list of how all words correlate with happiness here (page best viewed using Google Chrome). One surprising result was the observation that far more food-related words appeared in the low-obesity group than in the high-obesity group; in other words, food was being talked about more in the less-obese cities!

Summarizing: based on word usage, the Twitter diet consists of: breakfast at your favorite cafe, a delicious sushi lunch, dinner out at a fancy restaurant, with a nightcap at the best local bar or brewery. Thank you Twitter, don’t mind if I do.

All jokes aside, this sort of technique has great potential. Imagine being able to predict whether obesity was going to rise or fall in a city, or estimate changes in other demographics, just by analyzing the words people use online. Perhaps New York City Mayor Michael Bloomberg would find some early indicators of the success or failure of his war on soda!

And that’s all for this series of posts on the geography of happiness. More information on all of the results in this series can be found in our recently submitted arxiv paper. Please take a look at it and the accompanying online appendices, where you can look through all of the data yourself. As a special bonus feature, you can check out this video of me talking about this work at our recent TEDxUVM conference.  Thanks for reading!

4 Comments

Filed under mathematics, psychology, social phenomena

What makes a city happy?

Welcome back, onehappybird watchers! Wow, what a crazy week of coverage of our post about how happiness varies by city and state across the United States. Many, many people read, shared, and commented on the post, for which we are grateful. For the detailed explanation of the results, check out the full paper we recently submitted to PLoS ONE.

A number of readers wondered how variations in happiness relate to different underlying social and economic factors. To try to answer this question, we took data from the 2011 census (all helpfully available online on the Census Bureau’s American FactFinder website) and correlated it with our measure of happiness. Surprisingly, happiness generally decreases with the number of tweets per capita in a city (this doesn’t mean that tweeting more will make you less happy, it’s only a correlation):

happinessTweetsPerCapita

Next, we grouped covarying demographic characteristics obtained from the census, and looked at how these clusters varied with happiness. For example, it might not surprise you that cities with a larger percentage of married couples also contain a larger percentage of children – this is what we mean by covarying demographics.  And you might or might not be surprised that more marriage is positively correlated with happiness.  There’s plenty of scatter but the connection is there:

Scatter plot of happiness vs. percentage of population married. Each dot represents one city, the rho and p-values reported are Spearman correlations.

Scatter plot of happiness vs. percentage of population married. Each dot represents one city, the rho and p-values reported are Spearman correlations.

We used an automated algorithm to bin the census data for us into eight groups and then compared the happiness of those groups, leading to the following figure:

demographic_groupings_sort_blog

Each point represents a characteristic from the census (for example, the % married/happiness plot above is now represented by one point in this figure), with the horizontal groupings representing covarying demographic characteristics. A point’s position on the vertical axis shows how that characteristic varies with happiness across all cities. A positive value means that happiness is higher in cities where that characteristic is higher, while a negative value means that happiness is lower in cities where that characteristic is higher. For example, the figure shows that as the percentage of married couples in a city increases, so does the average happiness of that city (no causality is implied).

Only two groupings (the colored dots on the far left and right) showed strong correlation (either positive or negative) with happiness. Looking at which characteristics make up these groups, it appears that the general story here is a socioeconomic one, and one that holds only at the extremes. With our peculiar Twitter-based lens, we see money statistically correlates with happiness, which is not quite as catchy as “money buys happiness” (see the debate over the Easterlin Paradox for more). You can delve into the data yourself – the correlations of all 432 characteristics of cities recorded by the census with happiness can be found here (page best viewed using Google Chrome).

A more interesting question might be how word usage varies with different demographics – to do this we correlated each word with each demographic characteristic across all 373 cities in our dataset, leading to a lot of data to sift through! (And you can too, by following the link in the above paragraph.) As an example, take a look at how the word “cafe” varies with the percentage of population with a college degree:

cafe_bachelors_correlation

Each point in the figure represents one city, and broadly the trend is that the more “college-y” the city is, the more people talk about cafes online. (You can decide for yourself whether that’s surprising or not). The top 10 emotive words whose usage went up as percentage of population with a college degree went up turned out to be:

  1. cafe
  2. pub
  3. software
  4. yoga
  5. grill
  6. development
  7. emails
  8. wine
  9. art
  10. library

And the emotive words which went up as college degrees went down?

  1. me
  2. love
  3. my
  4. like
  5. hate
  6. tired
  7. sleep
  8. stupid
  9. bored
  10. you

We saw similar patterns of word use across many socioeconomic characteristics – emotive words and words about interpersonal relationships (‘me’ and ‘you’) at one end of the spectrum, and words about more complex social or intellectual themes at the other. Interestingly, we find more food-related words in this group as well.

Of course, all of this is open to interpretation. As many commenters last week pointed out, Twitter users (indeed, specifically those users who geotag their tweets using a mobile device) are a small, non-representative sample of the global population. Furthermore, our method is undeniably crude, and by breaking texts up into their constituent words ignores the context in which those words were used. That said, many of these results agree with our intuition (for example, many of the cities with low happiness scores also appeared on a list of America’s “most miserable cities” published late last week by Forbes), while some surprise us. There is certainly a lot to be learned by looking at what the data can tell us, and we encourage you to do so by exploring our website of supplementary data. Again, you can read the full technical details in our research paper here.

We’ll pick up on the theme of food again in our next post, which will focus on one important health factor relating to happiness – obesity.

9 Comments

Filed under mathematics, psychology, social phenomena

Where is the happiest city in the USA?

(Update: this work is now published at PLoS ONE)

Is Disneyland really the happiest place on Earth?* How happy is the city you live in? We have already seen how the hedonometer can be used to find the happiest street corner in New York City, now it’s time to let it loose on the entire United States.

We plotted over 10 million geotagged tweets from 2011 (all our results are in this paper, also on the arxiv), coloring each point by the average happiness of nearby words (detail on how we calculate happiness can be found in this article published in PLoS ONE):

Image

As well as cities and the roads between them, we can make out many regions of higher and lower happiness, even within individual cities. As an example, check out this tweet-generated map of the city of Chicago:

Tweet-generated map of Chicago. Click to enlarge.

Tweet-generated map of Chicago. Click to enlarge.

Notice the striking contrast between the relatively happy Central/North Side of the city, and the sadder South Side. You can also find a few airports in this map, and if you look very closely you might even be able to pick out happy and sad terminals!

To quantify this variation in happiness a bit better, let’s look at the average happiness of each state:

Image

Southern states tend to produce sadder words than those in northern New England or out west. Hawaii emerges as the happiest state and Louisiana as the saddest, due to relative differences in the frequencies of happy and sad words used in each state. Here at onehappybird, we characterize such differences by “word shifts”, which are basically word clouds for grown-ups. You can find examples of these, as well as the full list of the average happiness of each state, here (page best viewed using Google Chrome).

Zooming in further to the level of cities, we produced a similar list for 373 cities in the lower 48 states (you can find the full list, as well as maps and word shifts for each city, here). With a score of 6.25, we found the happiest city to be Napa, CA, due to a relative abundance of such happy words as “restaurant”, “wine”, and even “cheers”, along with a lack of profanity.

wordshiftNapaRedacted

At the other end of the spectrum, we found the saddest city to be Beaumont, TX, with a score of 5.82. In general, cities in the south tended to be less happy than those in the north, with a major contributing factor being the relative abundance of profanity used in those cities.

We can go even further than this, and group cities by similarities in word usage. Each square in the heatmap below represents the similarity (Spearman correlation for you mathematically minded onehappybird watchers) between word distributions for the largest cities in the US. Red squares mean that the corresponding cities use words in a similar fashion, while blue means that those cities tend to use different types of words with respect to each other. The colors in the tree diagram at the top signify clusters of cities exhibiting similar word usage (below a certain threshold).

As we might expect for two cities that are geographically nearby, New Orleans and Baton Rouge are clumped together at the bottom right of the figure. On the other hand, New York and Seattle get clumped together as well, suggesting that similarities in language depend on more than just geographical proximity.

cityClusters

You can find more information about happiness and cities, as well as details on the methods used to produce these results, in our arxiv research article. In our next post, we’ll look at how these results are related to various underlying socioeconomic characteristics of cities. What makes a city happy or sad? Can we use Big Data to predict future changes in the demographics, health, or happiness of a city? How does happiness relate to the food you eat?

*By the way, to answer the question at the start of this post: According to this analysis Disneyland is not the happiest place on Earth; it isn’t even the happiest place in Southern California! See if you can find it in this tweet-generated map of LA! Or find your city here.

83 Comments

Filed under geohappiness, mathematics, psychology, social phenomena

Who will your friends be next week? The link prediction problem

Sitting in the student center of our university, I am surrounded by hundreds of students enjoying their lunch and socializing. They’re strengthening (and in some cases weakening) their social ties. Given the ability to observe this social network over time, we would see that some relationships flourish, while others disappear altogether.

This situation is not unique to university students. In fact, whether we’re studying the spreading of an infectious disease, or the growth of an organized crime network, the reality is that the relationships in these social networks are dynamic. They change. Being able to describe the current state of a network is important. Our goal is to predict the future state of the network by forecasting who will connect to whom. If we could make these sorts of predictions, then we may be able to better recommend or warn of future probable links, as well as come to understand mechanisms which may be driving the evolution of the network.

This brings us to the link prediction problem. Liben-Nowell and Kleinberg defined it as follows:

The link prediction problem asks, "Given a snapshot of a network at time t, can we predict new links which will occur at time t+1?"

The link prediction problem asks, “Given a snapshot of a network at time t, can we predict new links which will occur at time t+1?”

In our work, we explore how topological similarity indices of a network can be combined with node specific data to develop a link prediction tool. Rather than pre-supposing that all similarity indices are of equal importance, we employ an evolutionary algorithm to evolve coefficients to be used in a linear combination of these similarity indices. Our approach has the advantage of being able to detect which similarity indices are more salient predictors and doesn’t require any knowledge of the type of network one may be working with.

To test our method, we begin by examining one of the largest social networks in existence, namely Twitter. Below, we visualize the network of reciprocal replies for users who interacted within a single week in late 2008.

Given information about interactions in a given week, we seek to predict links in a future week.

Given information about interactions in a given week, we seek to predict links in a future week.

Our evolved predictors exhibit a thousand fold improvement over random link prediction, and a substantial improvement over individual indices used in isolation. The predictor also suggests possible factors which may be driving the evolution of Twitter reciprocal reply networks during the timespan of this study.

Our predictor reveals which topological and/or user specific indices are most important in link detection for a given a network. For example, index B is most often the top ranking index detected by the predictor. Other indices which were ranked well were indices E and I. This type of output can be helpful in detecting the salient features which may be driving the network's evolution over time.

Our predictor reveals which topological or user specific indices are most important in link detection for a given a network. For example, index B is most often the top ranking index detected by the predictor, while indices E and I are also important. This type of output can be helpful in detecting the salient features which may be driving the network’s evolution over time.

Returning to our original question, we ask: Given a snapshot of a Twitter reciprocal reply network, is it possible to predict the links which will occur in the future?

One approach is to predict a link between all of the people in the network, but clearly this is not the approach we wish to take. For example, in the case of a modestly sized network (say N=30,000 nodes), the number of potential links is roughly half a million! If we’re trying to recommend books to a shopper or potential dates to a person using a dating service, we certainly would not want to suggest half a million people for potential dates. It would be nice if we could recommend 10 books (or dates) and have the majority of those suggested links be successful.

In the language of signal processing, we hope to have a true positive rate (e.g., the % of time you’re actually right about the links that you predict) that is greater than the false positive rate (e.g., the % of time you’ve issued a false alarm). This relationship can be captured by the Receiver Operating Curve (ROC) shown below.

The Receiver Operating Curve (ROC) compares the true positive rate (TPR) and the false positive rate (FPR). The ROC curve shown here depicts a classifier (our link predictor) for which TPR>FPR.

The Receiver Operating Curve (ROC) compares the true positive rate (TPR) and the false positive rate (FPR). The ROC curve shown here depicts a classifier (our link predictor) for which TPR>FPR.

The area under the curve (AUC) provides one way of measuring the relative success of one’s method. An AUC of .50 suggests that the true positive rate is equal to the false positive rate, while an AUC > 0.50 indicates that the true positive rate is greater than the false positive rate. As shown in the picture above, our AUC is well above 0.50, in fact it is approximately 0.72, which is good!

These results are exciting! We’ve put together a research paper in which we describe our analysis and algorithm in more detail (http://arxiv.org/abs/1304.6257). Although we focused on Twitter in this investigation, our methodology is general and may apply to link prediction in many other types of time varying networks, such as disease networks or crime. It could also improve the “friends you may know” feature offered by many social networking services.

Here is a short video summarizing our work on link prediction:

3 Comments

Filed under mathematics, networks, social phenomena

The Daily Unraveling of the Human Mind

Each morning we find ourselves in wide flung arms of drowsy possibilites. Cradled by the warm embrace of our beds, we begin our day, rebooted and rejuvenated. Having not eaten for a full eight hours, we can enjoy a guilt free breakfast, setting a blissful tone for the day.

figtwitter_daily_anewfreq_spesh_thetruth001_noname

Hourly frequency of meal references on twitter.
See figure 1 page 3 of our paper for details.

Last night’s dreams of victory and triumph bolster our delusions of adequacy, preparing us to surmount any of life’s challenges. But the moment we step outside, reality commences its slow and insidious descent. Its weight, compressing our spine, crushing our dreams, alters the course of the day completely.  The soul crushing litany of work, interacting with people, and generally living our lives takes its toll. As our sanity unravels, apathy takes root. The profane becomes our standard of expression. In the throes of despair, we swear just to feel something. We swear increasingly as we realize the inevitability of repeating this all again tomorrow.

F***, that’s a terrifying thought.

This ephemeral pattern is reflected in our tweets, our spontaneous burst of being. Below, we see our happiness peaks during the early hours of the day, and degrades as the hours progress (yellow circles). The proportion of profanity in our tweets, however, follows a reverse cycle. Profanity appears in a smaller percent of tweets at the start of each day, and increases gradually as time wears on.

Daily Unraveling

Daily Unraveling
See figure 10 page 15 of our paper for details.

Remarkably, the relative frequency of these five expressions of frustration (a******,  b****, s***, f***, m***********) are quite similar.

Well done, humans.

To avoid experiencing the daily unraveling, we recommend eating organic, local dark chocolate all day long.

3 Comments

Filed under mathematics, psychology, social phenomena