Graph mining techniques applied to blogs

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Graph mining techniques applied to blogs
Mary McGlohon Seminar on Social Media Analysis-
Oct 2 2007
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Last week Lots of methods for graph mining and
link analysis.
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Last week Lots of methods for graph mining and
link analysis. This week A few examples of
these methods applied to blogs.
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Paper 1

• Jure Leskovec, Mary McGlohon, Christos Faloutsos,
  Natalie Glance, and Matthew Hurst. Patterns of
  Cascading Behavior in Large Blog Graphs, SDM
  2007.
• What temporal and topological features do we
  observe in a large network of blogs?

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Representing blogs as graphs
slashdot
boingboing
MichelleMalkin
Dlisted

• Blogosphere network

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Representing blogs as graphs
slashdot
boingboing
MichelleMalkin
Dlisted

• Blogosphere network

slashdot
boingboing
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MichelleMalkin
Dlisted
Blog network
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Representing blogs as graphs
slashdot
boingboing
MichelleMalkin
Dlisted

• Blogosphere network

slashdot
boingboing
1
MichelleMalkin
Dlisted
Blog network Post network
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Extracting subgraphs Cascades

• We gather cascades using the following procedure
• Find all initiators (out-degree 0).

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Extracting subgraphs Cascades

• We gather cascades using the following procedure
• Find all initiators (out-degree 0).
• Follow in-links.

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Extracting subgraphs Cascades

• We gather cascades using the following procedure
• Find all initiators (out-degree 0).
• Follow in-links.
• Produces directed acyclic graph.

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Paper 1,2 Dataset (Nielsen Buzzmetrics)

• Gathered from August-September 2005
• Used set of 44,362 blogs, traced cascades
• 2.4 million posts, 5 million out-links, 245,404
  blog-to-blog links

Number of posts
Time 1 day
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Temporal Observations

• Does blog traffic behave periodically?
• Posts have weekend effect, less traffic on
  Saturday/Sunday.

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Temporal Observations

• How does post popularity change over time?

Popularity on day 1
Popularity on day 40
Number in-links (log)
Monday post dropoff- days after post
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Temporal Observations

• How does post popularity change over time?

How does post popularity change over time? Post
popularity dropoff follows a power law identical
to that found in communication response times in
Vazquez2006.
Number in-links (log)
Number of in-links
Monday post dropoff- days after post
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Days after post
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Temporal Observations

• How does post popularity change over time?

How does post popularity change over time? Post
popularity dropoff follows a power law identical
to that found in communication response times in
Vazquez2006.
The probability that a post written at time tp
acquires a link at time tp ? is p(tp?) ?
?1.5
Number of in-links
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Days after post
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Topological Observations

• What graph properties does the blog network
  exhibit?

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Topological Observations

• What graph properties does the blog network
  exhibit?
• 44,356 nodes, 122,153 edges
• Half of blogs belong to largest connected
  component.

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Topological Observations

• What power laws does the blog network exhibit?

Count (log scale)
Count (log scale)
Number of blog in-links (log scale)
Number of blog out-links (log scale)
Both in- and out-degree follows a power law
distribution, in-link PL exponent -1.7,
out-degree PL exponent near -3. This suggests
strong rich-get-richer phenomena.
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Topological Observations
What graph properties does the post network
exhibit?
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Topological Observations
What graph properties does the post network
exhibit?

• Very sparsely connected 98 of posts are
  isolated.
• Inlinks/outlinks also follow power laws.

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Topological Observations
How do we measure how information flows through
the network?

• Common cascade shapes are extracted using
  algorithms in Leskovec2006.

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Topological Observations
How do we measure how information flows through
the network?

• Number of edges increases linearally with
  cascade size, while effective diameter increases
  logarithmically, suggesting tree-like structures.

Number of edges
Effective diameter
Cascade size ( nodes)
Cascade size
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More on cascades

• Cascade sizes, including sizes of particular
  shapes (stars, chains) also follow power laws.
• This paper also presents a model for influence
  propagation that generates cascades based on SIS
  model of epidemiology. The topic of influence
  propagation has been reserved for a later date. ?

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Paper 2

• Mary McGlohon, Jure Leskovec, Christos
  Faloutsos, Matthew Hurst, and Natalie Glance.
  Finding patterns in blog shapes and blog
  evolution, SDM 2007.
• Do different kinds of blogs exhibit different
  properties?
• What tools can we use to describe the behavior of
  a blog over time?

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• Suppose we wanted to characterize a blog based on
  the properties of its posts.
• Obtain a set of post features based on its role
  in a cascade.
• Use PCA for dimensionality reduction.

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Post features

• There are several terms we use to describe
  cascades
• In-link, out-link
• Green node has one out-link
• Yellow node has one in-link.
• Depth downwards/upwards
• Pink node has an upward depth of 1,
• downward depth of 2.
• Conversation mass upwards/downwards
• Pink node has upward CM 1,
• downward CM 3

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Dimensionality reduction

• Post features may be correlated, so some
  information may be unnecessary.
• Principal Component Analysis is a method of
  dimensionality reduction.

Hypothetically, for each blog...
Depth upwards
Conversation mass upwards
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Dimesionality reduction

• Post features may be correlated, so some
  information may be unnecessary.
• Principal Component Analysis is a method of
  dimensionality reduction.

Hypothetically, for each blog...
Depth upwards
Conversation mass upwards
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Dimensionality reduction

• Post features may be correlated, so some
  information may be unnecessary.
• Principal Component Analysis is a method of
  dimensionality reduction.

Hypothetically, for each blog...
Depth upwards
Conversation mass upwards
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Setting up the matrix
log( in-links) log(out-links) log(CM up)
log(CM down) log(depth up)
log(depth down)
Run PCA
2,400,000 posts
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PostFeatures Results

• Observation Posts within a blog tend to retain
  similar network characteristics.

• PC1 CM upward
• PC2 CM downward

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PostFeatures Results

• Observation Posts within a blog tend to retain
  similar network characteristics.

• PC1 CM upward
• PC2 CM downward

MichelleMalkin
Dlisted
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• Suppose we want to cluster blogs based on
  content. What features do we use?
• Get set of features based on cascade shapes.
• Run PCA to reduce dimensionality.

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PCA on a sparse matrix

• This time, each blog is one row.
• Use log(count1)
• Project onto 2 PC

9,000 cascade types

44,000 blogs
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CascadeType Results

• Observation Content of blogs and cascade
  behavior are often related.

• Distinct clusters for conservative and
  humorous blogs (hand-labeling).

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CascadeType Results

• Observation Content of blogs and cascade
  behavior are often related.

• Distinct clusters for conservative and
  humorous blogs (hand-labeling).

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• What about time series data? How can we deal
  with that?
• Problem time series data is nonuniform and
  difficult to analyze.

in-links over time
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BlogTimeFractal Definitions

• Fortunately, we find that behavior is often
  self-similar.
• The 80-20 law describes self-similarity.
• For any sequence, we divide it into two
  equal-length subsequences. 80 of traffic is in
  one, 20 in the other.
• Repeat recursively.

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Self-similarity

• The bias factor for the 80-20 law is b0.8.

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80
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Self-similarity

• The bias factor for the 80-20 law is b0.8.

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Q How do we estimate b?
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Self-similarity

• The bias factor for the 80-20 law is b0.8.

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Q How do we estimate b?
A Entropy plots!
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BlogTimeFractal

• An entropy plot plots entropy vs. resolution.
• From time series data, begin with resolution R
  T/2.
• Record entropy HR

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BlogTimeFractal

• An entropy plot plots entropy vs. resolution.
• From time series data, begin with resolution R
  T/2.
• Record entropy HR
• Recursively take finer resolutions.

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BlogTimeFractal

• An entropy plot plots entropy vs. resolution.
• From time series data, begin with resolution r
  T/2.
• Record entropy Hr
• Recursively take finer resolutions.

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BlogTimeFractal Definitions

• Entropy measures the non-uniformity of histogram
  at a given resolution.
• We define entropy of our sequence at given R
• where p(t) is percentage of posts from a blog on
  interval t, R is resolution and 2R is number of
  intervals.

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BlogTimeFractal

• For a b-model (and self similar cases), entropy
  plot is linear. The slope s will tell us the
  bias factor.
• Lemma For traffic generated by a b-model, the
  bias factor b obeys the equation
• s - b log2 b (1-b) log2 (1-b)

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Entropy Plots

• Linear plot ? Self-similarity

Entropy
Resolution
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Entropy Plots

• Linear plot ? Self-similarity
• Uniform slope s1. bias.5
• Point mass s0. bias1

Entropy
Resolution
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Entropy Plots

• Linear plot ? Self-similarity
• Uniform slope s1. bias.5
• Point mass s0. bias1

Michelle Malkin in-links, s 0.85 By Lemma 1, b
0.72
Entropy
Resolution
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BlogTimeFractal Results

• Observation Most time series of interest are
  self-similar.
• Observation Bias factor is approximately 0.7--
  that is, more bursty than uniform (70/30 law).

Entropy plots MichelleMalkin
in-links, b.72 conversation mass, b.76 number
of posts, b.70
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Papers 1,2 conclusions

• There are several power laws observed in a
  network of blogs.
• We can extract cascades to help describe how
  information propagates through a network.
• We can use cascade properties to describe
  behavior of some blogs.
• We can also use self-similarity to describe
  behavior of blogs over time.

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Paper 3

• Eytan Adar, Li Zhang, Lada A. Adamic, and Rajan
  M. Lukose. Implicit Structure and the Dynamics of
  Blogspace. WWW 2004.
• What are the large- and small- scale patterns of
  blog epidemics?

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Large scale Epidemic profiles

• Example The effects of popular websites linking
  to a given blog may cause popularity spikes.

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Large scale Epidemic profiles

• Quantify popularity of a topic into a vector.
• Then, cluster different topics profiles.

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Large scale Epidemic profiles

• Used k-means clustering on topic buzz to identify
  different ways ideas gain and lose popularity.
  Found k4 worked best.

Centroids of clusters identified
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Large scale Epidemic profiles

• Catchall- picked up by different communities,
  no major spike.
• Back page news- delayed spike, broader
  popularity.
• Slashdot- link picked up quickly, dies off
  quickly.
• Front page news- immediate spike, broader
  popularity.

catchall 48
slashdot 14
back page 20
front page 18
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Link gathering

• Links acquired by blogrolls or automated
  trackbacks.
• Posts sometimes give information on source of
  information (via).

May 16 2003, 848a GIANTmicrobes
http//www.giantmicrobes.com/ We make stuffed
animals that look like tiny microbes only a
million times actual size! Now available The
Common Cold, The Flu, Sore Throat, and Stomach
Ache. (via BoingBoing)
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Small scale link mining

• Links acquired by blogrolls or automated
  trackbacks.
• Posts sometimes give information on source of
  information (via).

May 16 2003, 848a GIANTmicrobes
http//www.giantmicrobes.com/ We make stuffed
animals that look like tiny microbes only a
million times actual size! Now available The
Common Cold, The Flu, Sore Throat, and Stomach
Ache. (via BoingBoing)
Epstein- Barr
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Ebola
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Small scale link mining

• Unfortunately, since via information is rare
  (O(.1)), there needs to be a better way to infer
  infection paths.
• Solution link prediction.

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Link prediction

• Predict likelihood of 2 blogs linking to each
  other.
• Blog similarity- common links to other blogs
• Link similarity- common non-blog links
• Textual similarity- text vector similarity
• Timing of posts on certain topics.
• First three are cosine similarity, timing is
  likelihood based on observed distributions of
  link timings.

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Link prediction results

• Used SVMs to predict links.
• Undirected link prediction accuracy 91
• (Directed link prediction, 57)

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More goodies from Paper 3

• And
• Built Zoomgraph, a visualization tool (stay tuned
  next week.)
• Proposed iRank, a ranking based on
  infectiousness of blogs (stay tuned Oct. 23.)
• A more in-depth slide show may be found here
  http//www.blogpulse.com/papers/Adar_blogworkshop2
  _ppt.pdf

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Paper 4

• Noor Ali-Hasan and Lada Adamic. Expressing
  Social Relationships on the Blog through Links
  and Comments. ICWSM 2007
• Do different blog communities exhibit certain
  structural properties?

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Ali-Hasen and Adamic 2007

• Dataset of 3 blogging communities
• Dallas/Ft. Worth
• United Arab Emirates (UAE)
• Kuwait
• Analyzed 3 types of links
• Blogrolls (on a blogs webpage)
• Citations (link in a post)
• Comments (interaction in a posts discussion)

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Citation link
Blogroll link
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Comment link
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Link type analysis
Co-occurrence of link types (Kuwait)

• It is of interest to compare different types of
  links
• Co-occurrences of different link types.

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Link type analysis
Co-occurrence of link types (Kuwait)

• It is of interest to compare different types of
  links
• Co-occurrences of different link types.
• Reciprocity among link types, between communities.

Link reciprocation rates
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Structural properties
Links per blog

• Centralization- to what extent links are not
  uniformly distributed. (low in all communities,
  indicating hubs)

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Structural properties
Links per blog

• Centralization- to what extent links are not
  uniformly distributed. (low in all communities,
  indicating hubs)
• Modularity- to what extent subcommunities have
  formed.

Modularity
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Comparing communities
Kuwait -Fewest links external to community
(53) -Highly centralized -Much reciprocity
UAE -Fewer links external to community -More
centralization -Obvious hub structure
Dallas-Fort Worth -Most links are external to
community (91) -Low centralization -Low
reciprocity
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Paper 4 Conclusions

• Based on a survey, they suggest that these
  different network characteristics indicated
  different mindsets inside the community.
• Kuwait bloggers more often reported blogging in
  order to make new friends.
• DFW more often reported blogging to update
  friends/family on events.

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Conclusions

• Link analysis has discovered patterns in several
  aspects of the blogosphere.
• Observing general network characteristics.
• Describing behavior of specific blogs, or blog
  topics.
• Illustrating how influence propagates.
• Comparing different blogging communities.