1. Network Structure of Folksonomies
Vito D. P. Servedio
Dipartimento di Fisica, Università di Roma "La Sapienza“
Centro Studi e Ricerche "Enrico Fermi"
TAGora: Semiotic Dynamics of Online Social Communities
EU-IST

2. In collaboration with:
Andrea Baldassarri, Ciro Cattuto,
Vittorio Loreto
Miranda Grahl, Andreas Hotho, Christoph Schmitz,
Gerd Stumme

3. Properties of folksonomy hypergraphs Network of tag co-occurrences
AGENDA
Properties of folksonomy hypergraphs
Network of tag co-occurrences
Clustering of resources
V D P Servedio ~ECCS07~

4. a folksonomy example: del.icio.us screenshot
resource
user
tags
V D P Servedio ~ECCS07~

5. Post = ({tags}, user, resource)
data structure: basic units of information
Post = ({tags}, user, resource)
TAS = tag assignment (tag, user, resource)
({bookmarking, sharing, collaborative, folksonomy}, andreab,
(bookmarking, andreab,
(sharing, andreab,
(collaborative, andreab,
(folksonomy, andreab,
V D P Servedio ~ECCS07~

6. folksonomy hypergraph structure
Can be viewed as a 3-modes network
User 4
User 3
User 2
User 1
Tag 1
Res 1
Res 2
Res 3
Tag 2
hyperlink
Tag 3
V D P Servedio ~ECCS07~

7. TAGora Project (STREP FP6)
data collection
TAGora Project (STREP FP6)
Semiotic Dynamics in Online Social Communities
del.icio.us
Work co-ordinated by Uni of Kassel
Collected data from Nov
Over 667K users
~19 million resources
Nearly 2.5 million tags
~ 140 million tag assignments
50GB of data
del.icio.us
Consortium:
University of Roma “La Sapienza”
SONY CSL Paris
University of Kassel
University of Koblenz-Landau
University of Southampton
flickr
Work co-ordinated by Uni of Koblenz
Collected data 21st May 2007.
~ 300K users
~25 million photos
1.5 million tags
over 110 million tag assignments
bibsonomy
Complete dataset (june 2007)
~1385 users
37651 tags
Over 149K resources

8. artificial networks: permuted and binomial
In the following slides we shall use some artificial networks defined as:
PERMUTED: take the original folksonomy and shuffle all nodes in the same class.
example
Resource1 User1 Tag1
Resource1 User1 Tag2
Resource1 User1 Tag3
Resource1 User2 Tag1
Resource1 User2 Tag2
Resource2 User3 Tag4
permuted example
Resource1 User3 Tag2
Resource2 User2 Tag3
Resource1 User1 Tag1
Resource1 User1 Tag2
Resource1 User2 Tag1
Resource1 User1 Tag4
We end up with a hypergraph with same degree of the original one
BINOMIAL: same number of hyperedges;
endpoints chosen uniformly at random among T, U, R
V D P Servedio ~ECCS07~

9. average path length (extimated)
moving on hyperedges
T1 U1 R1
T2 U1 R1
T2 U2 R2
T3 U2 R3
time
V D P Servedio ~ECCS07~

10. cliquishness
A high resource cliquishness indicates that many of the users related
to that resource assign overlapping sets of tags to it r2 r t1 t2 u1 u2 t3
|Tr|=3
|Ur|=2
|tur|=3
|tur| = # of hyperlinks connected to r
|Tr | = # of adjacent tags
|Ur | = # of adjacent users
V D P Servedio ~ECCS07~

11. connectedness / transitivity
|tur| = # of hyperlinks connected to r
|tur| = number of tag-user pairs from tur that also
occur with some other resource other than r r2 r t1 t2 u1 u2 t3
|tur|=3
|tur|=1
V D P Servedio ~ECCS07~

12. Properties of folksonomy hypergraphs Network of tag co-occurrences
AGENDA
Properties of folksonomy hypergraphs
Network of tag co-occurrences
Clustering of resources
V D P Servedio ~ECCS07~

13. networks of tag co-occurrence
Tags acquire a stronger semantic context when they co-occur each other
e.g.:
{Roma, holidays, Italy} vs {Roma, football, we_won} vs {Roma, love, girls} etc.
Tag co-occurrences in posts
Weighted graph of tags
Weight = number of common posts
Strength of a tag
Sum of its edge weights
Can we study “sematics“ of tags?
({japan,tokyo} more frequent than {physics,sex})
--check with Google!—
Compare statistics with shuffled graphs
V D P Servedio ~ECCS07~

14. weighted network of tag co-occurrence
Two Tags co-occur if they are present in the same post
We can say more:
Two tags t, t’ co-occur with weight w if they are simultaneously
present in w posts.
In terms of adjacency Tensors:
tensor contraction in flat space…
We examine the weighted undirected network defined by W
V D P Servedio ~ECCS07~

15. strength cumulative distribution
Strength of node i:
Strength distribution
SPAM
tag shuffled example
Resource1 User1 Tag2
Resource1 User1 Tag3
Resource1 User1 Tag1
Resource1 User2 Tag4
Resource1 User2 Tag1
Resource2 User3 Tag2
The tag reshuffling procedure makes almost no changes in the P(s):
the strength is related to frequency of tags, not on semantics
V D P Servedio ~ECCS07~

16. Average neighbour strength
Examine strength correlation between neighbors:
Positive correlation: Assortative mixing
e.g. Social networks
Negative correlation: Disassortative mixing
e.g. Technological networks
Look for spam infection
Reveal semantics via shuffled graph
V D P Servedio ~ECCS07~

17. average neighbor strength
Scatter plot
Tags introduced with spamming, cluster together
Shuffling the graph changes the measure
Correlations related to semantics correspond to a region in the graph
spam
spam
spam
V D P Servedio ~ECCS07~

18. Properties of folksonomy hypergraphs Network of tag co-occurrences
AGENDA
Properties of folksonomy hypergraphs
Network of tag co-occurrences
Clustering of resources
V D P Servedio ~ECCS07~

19. clustering and community detection
Folksonomies: complex tripartite networks
(tag, user, resource)
Clustering detection can reveal
sub-set of users (social communities)
sub-set of tags (semantic frames, jargons…)
sub-set of resources (social classification)
Other…
Now we focus on clustering of resources using only tag assignments
V D P Servedio ~ECCS07~

20. resource similarity network
Weighted network How to choose weights? How to take into account tag frequency?
V D P Servedio ~ECCS07~

21. tag clouds for resources
Each resource is characterised by a tag-cloud:
tags are assigned by users, and appear with different frequency.
V D P Servedio ~ECCS07~

22. TF/IDF-like weighting procedure
similarity metrics
TF/IDF-like weighting procedure
Tag frequencies:
Global frequency
Relative frequencies T1 T2 K
STATEMENT:
Resources sharing “rare” tags are
closely related
V D P Servedio ~ECCS07~

23. 200 resources tagged with “design”
case in study
Sample of 400 resources:
200 resources tagged with “design”
200 resources tagged with “politics”
Does the similarity network show two clusters?
Finer structure?
Subclusters?

24. Broad variability of similarity strengths on logarithmic scale.
similarity matrix
Broad variability of similarity strengths on logarithmic scale.
P(w)
A small power (0.1) is used as an effective way to treat with vanishing weights.
W = { w’ } w
TASK:
Find column and row permutations
that uncover a block structure
V D P Servedio ~ECCS07~

25. First non trivial eigenvalues
spectral analysis
A. Capocci, V.D.P. Servedio, G. Caldarelli and F. Colaiori, Physica A 352, 669 (2005).
and many others
First non trivial eigenvalues
Q Eigenvalues
« Laplacian » matrix
V D P Servedio ~ECCS07~

26. cluster identification
Correlation of homologous components reveals cluster structure.
V2 = {v2,1, v2,2, ...,v2,n }, V3 = { v3,1, v3,2, ..., v3,n }, V4 = { v4,1, v4,2, ..., v4,n }
[ v2,i ; v3,i ; v4,i ]
reordered matrix
politics
design 2 4 3 1

27. cooperative classification
Tag clouds of the six identified clusters of resources:
“humor” in politics
news in politics
visual design
web design

28. Conclusions and outlooks
Folksonomies are the way people is building the information and communication systems of our future.
Folksonomies are a laboratory to study human/social/semiotic dynamics.
A Folksonomy is a growing tri-partite network, whose nodes are users, resources and metadata (tags), while (hyper)links are annotation events
(note that this structure is similar to search queries:
user, search string, resource retrieved).
Folksonomies’ statistical structure reveals many complex features, typical of interacting humans.
Projections of folksonomy on different spaces can be useful to study:
spam infection;
semantic of tags;
emerging resource classification.
V D P Servedio ~ECCS07~