Power Laws Popularity And Interestingness

ITEC, Klagenfurt University, Austria

What is a Hype and Where Can I Get One? Mathias Lux [email_address] Department for Information Technology, Klagenfurt University, Austria

What is this about …
Power Laws & Pareto Distributions
Just a Theory?
Conclusions
ITEC, Klagenfurt University, Austria by betta_design http://www.flickr.com/photos/betta_design/2200198472/

The Long Tail
Common for certain distributions
Zipf‘s Law
Power Law
Pareto Distribution
In Web 2 Context
Chris Anderson …
ITEC, Klagenfurt University, Austria maitland 82 - http://www.flickr.com/photos/maitland82/346065497/

Zipf‘s Law
Few events occur often, many occur rarely
P n ~ 1/n a ... Frequency of the n th ranked item, a close to 1.
Prominent examples
Ranking of words in documents
Ranking of cities and their size
Ranking of movies and sold cinema tickets
… and many more

Zipf‘s Law
Plot of the word frequency in Wikipedia
Most popular: the, of, and
from http://en.wikipedia.org/wiki/Zipf's_law

Pareto Distribution
80:20 Rule
Economics
Continous (Zipf is discrete)
Practical issues
Time Management, …

Power Law
Made famous by Albert Barabasi
Scale free networks (web, power supply, …)
In-degree of web sites, etc.
Defines actually a class of distributions
f(x)=a*x^b + e
Pareto and Zipf are part of the group

How to detect a power law?
Simple empirical tests
Draw points on a log-log plot
Is it a „straight line“?

How to detect a power law?
Statistical Means
E.g. KS-Test, Chi-Square Test
Open research issue …
See e.g. Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. arXiv:0706.1062v1 (2007)

A note on plots … ITEC, Klagenfurt University, Austria Taken from phun.org, tnx to enzo nadrag

A note on statistical means …
http://www.phun.org/newspics/funny_friday/2538.jpg tnx to Enzo Nadrag

Zipf, Pareto & Power Law: Conclusions
They emerge when people are involved
They have interesting characteristics
Mean has virtually no information
Area under the curve (cp. amazon’s long tail strategy)
Power laws emerge somehow …
Multiple generative models (preferntial attachement, memory kernels, etc.)
No one knows for sure

Is this just theory?
Basically: YES!
But there are related practical questions
Are you using Flickr?
How many “interesting” photos did you publish?
How many views do your photos have?
Imagine you publish a video on YouTube
What are the chances that your video is a big hit?
How to “help out” the process of getting a big hit?
Can one distinguish between hit or flop?

Is this just theory? (2)
More related practical questions
Do you have a website?
How to “flat out” resource popularity?
How select popular resources (e.g. for caching, adaptation, preprocessing)?

Getting popular …
Starting with the first view (user)
Some other users find the same resource
They point other to it
Blogging, Digging, word of mouth
Multiplicator of information – cp. Metcalfe’s law
Number of views (users) “explodes”

Some graphs … ITEC, Klagenfurt University, Austria
Data from del.icio.us
Shows
bookmarks / day
relative user count

Observations
There is an initial bend in the curve
The mean user # at the bend is rather small
Around 50
There are outliers
Google Video was doomed to be a success

Conclusions
If there is a bend …
Chances are better for a big hit.
Time is still an issue
Slow start, long vs. short hype, etc.
Resources without this bend:
Better Chances that they are shelf warmers
Decision support for portfolio adaptation

The Flickr way
Flickr defined “Interestingness”
Patented
combining views, comments, age, etc.
Interesting photos are presented
Users see new photos
Not all photos (2.000 new / minute, checked Feb. 1 2008, ~ 11.oo UTC)
They have no “big hit”
ITEC, Klagenfurt University, Austria Kudos given to Horst Gutmann and Marian Kogler

The YouTube way
Smaller resource data base than Flickr
Around 45 videos a day (65.000 a day)
But a lot more views (data Feb. 1st, 08)
73.245.607 for „Evolution of Dance“
20 most viewed have > 30M views
Not obvious counter strategy
Might not (yet) be necessary

Digg
Assumption: Diggs also follow a power law
Quite reasonable …
How to avoid the Digg- effect?
Digg has a mirror …

Thanks ...
... for your
attention
You are interested?
Then talk to me …
ITEC, Klagenfurt University, Austria by Gexydaf http://www.flickr.com/photos/gexydaf/2208215419/

Mathias Lux
Affiliation
Klagenfurt University, ITEC
Contact
mathias @ juggle.at
http://www.semanticmetadata.net

Power Laws Popularity And Interestingness

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