Networks Navigability: Theory and Applications

Networks Navigability: Theory and Applications

Denis Helic & Christoph Trattner

KMI, TU Graz

August 31, 2011

Denis Helic & Christoph Trattner (KMI, TU Graz)
Networks Navigability: Theory and Applications August 31, 2011 1 / 75

Internet of Things

http://www.youtube.com/watch?v=sfEbMV295Kk


Internet of Things

We are heading towards a completely interconnected society
Where people, devices, sensors are all connected to each other
producing billions of billions of data each day...


Internet of Things

One big challenge in this context is how we can ﬁnd relevant
information in such a networked world of data
Hence, in this presentation:
Latest research results on the navigability of such networks will be
shown


Internet of Things

In particular I will show:
what are structural clues that make such networks
navigable/searchable?
In addition to this, I will present a framework that is able to measure
network navigability.
and I will present two algorithms to generate eﬃcient navigational
tools for that networks.


Networks

What are networks?
Basically a network is a system that can be modeled with graphs.
Graphs are mathematical structures consisting of vertices and edges
connecting the vertices
When we observe large graphs that exist in nature, societies, or
systems we refer to them as networks


Networks

What are popular examples of such networks?
Social networks. Nodes are people and links are acquaintances,
friendship, and so on.
Communication networks. Internet: nodes are computers and links
are cables connecting computers
Biological networks. Metabolism: nodes are substances and links are
metabolic reactions
Information networks. Web: nodes are Web pages and links are
hyperlinks connecting pages


Networks
6 How to search in a small world

Pajek

Figure 2: HP Labs’ email communication (light grey lines) mapped onto the organizational
Figure: Social network of lines). Note that communication tends to “cling” toof formal organizational
hierarchy (black HP Labs constructed out the e-mail communication.
chart.
From: How to search a social network, Adamic, 2005.
with one another. The h-distance, used to navigate the network, is computed as
follows: individuals have h-distance one to their manager and to everyone they share
a manager with. Distances are then recursively assigned, so that each individual
has h-distance 2 to their ﬁrst neighbor’s neighbors, and h-distance 3 to their second

Networks

Figure: Network of pages and hyperlinks on a Website. From: Networks, Mark
Newman, 2011.


Structure and Function of Networks

One of the most important research questions in the study of
networks: what is the relation between structure and function of
networks
For example, the Internet – how should the link structure of the
Internet look like that supports eﬃcient routing?
Or how should the link structure of the Web look like to be eﬃcient
navigable?
In this presentation we will focus on network navigability!


Network Navigability

Deﬁnition
Put simple, a network is navigable if and only if there is a short path
between all or almost all pairs of nodes in the network.

Formally:
1 There exist a giant component
2 The eﬀective diameter is low – bounded by log (n), where n is the
number of nodes in the network


Knowledge Management Institute

Navigability: Examples
Example 1:
Example 1:

Not navigable: No giant component
Figure: Network is not navigable because there is no giant component, i.e. the
network is not connected.
Example 2:

Not navigable: giant component, BUT
eff.diam: 7 > log2(8)

Example 1:

Not navigable: No giant component
Example 2:
Example 2:

Not navigable: giant component, BUT
Figure: Now, there is a giant component, i.e. the network is connected. However
the network is not navigable because eﬀ .diam = > log26 > log2 (8).
eff.diam: 7 6, and (8)

Denis Helic 2010
7


Knowledge Management Institute

Navigability: Examples
Example 3:

Figure: The network is navigable because there is AND component and
Navigable: Giant component a giant
eﬀ .diam = 2. Eﬀective diamater is boundedlog2(10)
eff.diam: 2 < by log2 (10).

Is this efficiently navigable?
There are short paths between all nodes, but can an
agent or algorithm find them with local knowledge
only?

Global Network Navigability

We discussed so far global network navigability
Suppose that the network is navigable and we have global knowledge
of network
Then it is easy to design efficient procedures to find an arbitrary
target node from an arbitrary start node
For example, breadth-first search is such an algorithm that has linear
time complexity O(n + m), where m is the number of links
Such procedures are called centralized search


Local Network Navigability

Let us now discuss local network navigability
Suppose that the network is navigable but we have only local
knowledge of network
That means when we arrive at a particular node we know only
outgoing links from that node and nothing beyond that
For instance on Facebook we only know our friends or the friends of
of our friends.
These procedure are typically called decentralized search



But, how efficient are people in such social search?
As shown by Millgram’s experiment, people are very efficient in social
search.
As shown, people are able to find each other in less than seven hops
(friends), ∝ log (n)
Hence, people have an extremely efficient decentralized search
procedure



How we are able to find other people efficiently?
Or in other words, what are the properties of social networks, or
networks in general that make efficient decentralized search possible?
Are there some structural clues in the network which allows us to
design sub-linear algorithms?
And if yes, what are these structural clues?


Efficiently navigable
A network is efficiently navigable iff:
If there is an algorithm that can find a short path with
only local knowledge, and the delivery time of the
algorithm is bounded polynomially by logk(n).
Example:

B D

A C

Efficiently navigable, if the algorithm knows it needs to
Figure: A is start node and D is target node.
go through A B C
J. Kleinberg. The small-world phenomenon: An algorithmic perspective. Proc. 32nd ACM Symposium on Theory of Computing, 2000. Also appears as Cornell Computer Science
Technical Report 99-1776 (October 1999)
Denis Helic 2010
9


Local A networkNavigability navigable iff:
Network is efficiently
Step 1:

B D

A C

Figure: Efficiently navigable, if the algorithm knows it needs to
There are two possible paths from A. Obviously, the optimal path leads to
B. What is the structuralA
go through property that can guide us in selecting B?
B C
Denis Helic 2010
10


Step 1:

B D

A C

Figure: Efficiently navigable, if the algorithm knows it needs to
There are two possible paths from A. Obviously, the optimal path leads to
B. What is the structuralA
go through property that can guide us in selecting B?
B C
Denis Helic 2010
Nodes degree 10


Step 2:

B D

A C

Figure: Efficiently navigable,paths from B. Obviously, the it needs to leads
There are seven possible if the algorithm knows optimal path
to C. What is through A property that can guide us in selecting C?
go the structural B C
Denis Helic 2010
11


Step 2:

B D

A C

Figure: Efficiently navigable,paths from B. Obviously, the it needs to leads
There are seven possible if the algorithm knows optimal path
to C. What is through A property that can guide us in selecting C?
go the structural B C
Denis Helic 2010
Nodes clustering 11



Summarizing, local network navigability requires:
1 Existence of network hubs that are connected to many nodes
2 Existence of network clusters where nodes are highly interlinked



Formally:
1 Power-low degree distribution with exponent γ
2 High clustering coeﬃcient C


γ=2.2
γ=2.6 α=1.5 free nor clustered

success pro
γ=2.3
γ=2.4
γ=2.7 α=2.0
γ=2.8 α=3.0
γ=2.5
γ=2.9
α=1.1
0.2
α=5.0
γ=3.0
0 IV. AIR TRAV
3 4 5 2 2.2 2.4 2.6 2.8 3
10
network size (N)
10 10
degree exponent (γ) A
3
non-navigable region

degree exponent (γ)
We illustrate th
2.5 structure of netwo Web of trust

Metabolic an example of pa
Internet to travel from Tok
α=5.0
2
Airports the public air tran
navigable region
work are airports,
3 4 50 0.1 0.2 0.3 0.4 0.5 0.6 0.7
10 10 10 is at least one flig
network size (N) clustering coefficient (C)
ing to the greedy
Success probability of greedy routing. Left the underlying me
Figure: Navigable networks in γ, C space. the next-hop airpo
ccess probability ps as a function of network size N
ent values of γ with weak (top) and strong (bottom) nation. Under th
g. The top-right plot shows ps as a function of γ Bethel, then to An
r networks of fixed size N ≈ 105 . In the bottom- to Paris, then to V
t, parameter α is mapped to Navigability: Theorycoefficient
Networks clustering
Denis Helic & Christoph Trattner (KMI, TU Graz) and Applications August 31, 2011 24 / 75

Local If there is an algorithm that can find a short path with
Revisiting Step 2:

B D

A E C

Figure: There are seven possible paths from B. Obviously, the optimal path leads
Denis Helic 2010

to C. What is an additional hint that can guide us in selecting C over E? 12


Local If there is an algorithm that can find a short path with
Revisiting Step 2:

B D

A E C

Figure: There are seven possible paths from B. Obviously, the optimal path leads
Denis Helic 2010

to C. What is an additional hint that can guide us in selecting C over E? 12

Nodes similarity



Nodes similarity is external to the network
It is derived from some additional information that we have about
network nodes
In Millgram’s experiment people selected the next person according to
their occupation or geography



All of this information, i.e. degrees, clustering, similarity can be
understood as a kind of our background knowledge about the network
We use this background knowledge to guide us in our search for a
target node
When we have more than one link to follow we consult the
background knowledge and ask which of the links will lead us with
highest probability to a given target node


Greedy Decentralized Search

On the next abstraction level we can say that background knowledge
deﬁnes a notion of distance between nodes
In other words, background knowledge is a metric space where each
node has unique coordinates and we can calculate the distance
between nodes
Or in other words, we can abstract background knowledge as a
black-box executing a simple function:
getDistance(node, target node)



Let us now take an algorithmic perspective on decentralized search
We start at an arbitrary node and need to ﬁnd as fast as possible a
target node having only local knowledge of the network
In addition, we have background knowledge represented through
getDistance(node, target node) function
At each search step we have to make a decision which of the available
links to follow



In order to maximize the probability of ﬁnding the target node we
always select a node which has the smallest distance to the target
node
It has been shown that the greedy algorithm is very eﬃcient, i.e. the
number of steps to reach an arbitrary target node is ∝ log (n)
Kleinberg proved it theoretically, Watts by simulation
Watts was able to reproduce Millgram’s experiment with proper
selection of parameters: Identity and Search in Social Networks, 2002


Background Knowledge

Now, how does our background knowledge of people typically look
like?
It is a metric space, e.g. 1-D spaces, 2-D vector spaces, 3-D Euclidean
spaces, hyperbolic spaces, ... or does it look like completely diﬀerent?
Actually, it was observed by Kleinberg and also by Watts that a
hierarchy of nodes is also a very good approximation of how people
think
Hence, we will also use hierarchical background knowledge


Hierarchy as a Metric Space

2 3

2
3 3
23 24 21

4 4 4 4 1
1 15 22 25 3

5 5 5 5 1 1
11 12 13 14 31 32 33

Figure: Node distances in a hierarchy.

Distance: d(i, j) = h(i) + h(j) − 2h(lca(i, j)) − 1


Example of a Greedy Navigation

3
2

2
3 3
23 24 21
2 3
4 4 4 4 1
1 15 22 25 3
4
1
5 5 5 5 1 1
11 12 13 14 31 32 33

11 2 21 3 31

12

1 1 22 2 3 4

13 23 25 32 33

14 15 24

Figure: Greedy search.


Calculating Network Navigability

Now in order to measure network navigability, we developed a
theoretical framework to estimate network navigability by simulations
As input we take a network, e.g. information network like Wikipedia,
or Delicious
and a suitable hierarchy that models background knowledge
For example, Wikipedia categories or Delicious folksonomy
and simulate decentralized search on 106 start and target node pairs


Network Navigability Simulation Framework

The metrics we measure by our framework are
success rate s
and stretch τ
For both metrics we calculate distributions over global shortest path

Deﬁnition
Stretch: τ = h , where h is the number of simulator steps and l is the
l
global shortest path.


Evaluating hierarchies

The framework lets you e.g. estimate the quality of a hierarchy to
serve as background knowledge
A hierarchy with better navigational properties will have better
success rate and stretch in comparison with other hierarchies
For example, Wikipedia categories versus Delicious tags
For example, diﬀerent folksonomies for navigating social tagging
systems, see Helic et al.: Pragmatic Evaluation of Folksonomies, 2011


Evaluating Navigational Tools

But we can use framework to estimate the eﬀects of changes in the
network on its navigational properties
For example, how navigable is Wikipedia now?
How navigable will be Wikipedia if we include Delicious tags?
How navigable will be Wikipedia if we include breadcrumbs?
We take Wikipedia as the starting network and create new links in the
network to emulate Delicious tags, breadcrumbs, etc.


Evaluating folksonomies

A folksonomy is a hierarchy that is automatically generated from a
tagging system
Today there are several folksonomy algorithms, see e.g. Heymann
2008, or Benz 2010
In addition, you can produce folksonomies by using standard
hierarchical clustering methods such as K-Means or Aﬃnity
Propagation



In Helic et al.: Pragmatic Evaluation of Folksonomies, WWW2011 we
took 5 tagging datasets and 5 diﬀerent folksonomy algorithms
We produced 5x5 folksonomies and simulated (100.000 samples)
greedy decentralized search on the datasets
We measured the success rate and stretch to see if some folksonomies
perform better than the other ones.



Greedy Search Success Rate: BibSonomy
100
Folksonomy
Random
Aff.Prop.

Success Rate (Percentage)
80 K-Means
Deg/Cooc
Clo/Cos
60

40

20

0
1 2 3 4 5 6 7
Shortest path

Figure: Success Rate of diﬀerent folksonomies in BibSonomy



Greedy Search Success Rate: CiteULike
100
Folksonomy
Random
Aff.Prop.

80 K-Means
Deg/Cooc
Clo/Cos
60

40

20

0
1 2 3 4 5 6 7
Shortest path

Figure: Success Rate of diﬀerent folksonomies in CiteULike



Greedy Search Success Rate: Delicious
100
Folksonomy
Random
Aff.Prop.

80 K-Means
Deg/Cooc
Clo/Cos
60

40

20

0
1 2 3 4 5 6 7
Shortest path

Figure: Success Rate of diﬀerent folksonomies in Delicious



Greedy Search Success Rate: Flickr
100
Folksonomy
Random
Aff.Prop.

80 K-Means
Deg/Cooc
Clo/Cos
60

40

20

0
1 2 3 4 5 6
Shortest path

Figure: Success Rate of diﬀerent folksonomies in Flickr



Greedy Search Success Rate: LastFM
100
Folksonomy
Random
Aff.Prop.

80 K-Means
Deg/Cooc
Clo/Cos
60

40

20

0
1 2 3 4 5
Shortest path

Figure: Success Rate of diﬀerent folksonomies in LastFM



Centrality-based algorithms such as Heymann 2008 or Benz 2010
outperform traditional methods
However, these are all theoretical results
Because, what is if we wanted to embed folksonomies in the user
interface (UI) to support users in their navigation tasks
and the space in user interface is limited?


Embedding folksonomies in UI Google Directory - Computers > Internet > On the Web > Online Communities

Directory Help

Online Communities
Computers > Internet > On the Web > Online Communities Go to Directory Home

Categories

Bulletin Board Directories (9) PowerPets (6)
Systems (132) Events (1) Second Life (119)
By Region (8) Mailing Lists (85) Social Networking
By Subject (204) Message Boards (222)
Chat (745) (154) Software and
Community MySpace (28) Services (27)
Management (36) Neopets (171) The Palace (51)
Community Zetapets (3)
Providers (14)

Related Categories:
Society > Activism > Community Building (26)
Society > Organizations (16987)
Society > People > Personal Homepages (8890)
Society > Relationships > Cyber Relationships (59)
Society > Subcultures > Cyberculture (162)

Web Pages Viewing in Google PageRank order View in alphabetical order
Talk City - http://www.talkcity.com/
Figure: Directory Based Navigation technology, health and other
Participate in discussions about relationships, hobbies, business,
topics. Socialize with friends, or start your own chat group.
Whyville - http://www.whyville.net/
A virtual 3-D world for curious minds where you can own land, build your own house, play
simulation games, win prizes, chat, and help the community grow.
Buzznet - http://www.buzznet.com/
Denis Helic & Christoph Trattner (KMI, TU Graz) create communitiesTheory and Applications
Users can
Networks Navigability: and share blogs and photographs. August 31, 2011 46 / 75

Embedding folksonomies in UI

We have breadcrumbs connecting each node all the way up to the
root node
We have limited number of subcategories (n)
We have limited number of related categories (m)
Now we embed folksonomy as in Benz 2010 and apply diﬀerent
restrictions



- Greedy Navigator (1000000 Runs)
-
l=3.585123, h=5.936013, sg=0.005548, τg=1.655735

Success Rate (s)
3 Stretch (τ)

2.5

2
s, τ

1.5

1

0.5

0
1 2 3 4 5 6 7 8 9
Shortest Path

Figure: Success Rate and stretch in BibSonomy with n = 20 and m = 20



-
l=3.634634, h=6.536937, sg=0.001110, τg=1.798513

9 Success Rate (s)
Stretch (τ)
8
7
6
5
s, τ

4
3
2
1
0
1 2 3 4 5 6 7 8 9
Shortest Path

Figure: Success Rate and stretch in CiteULike with n = 20 and m = 20



-
l=3.518932, h=5.557032, sg=0.000903, τg=1.579181

7 Success Rate (s)
Stretch (τ)
6

5

4
s, τ

3

2

1

0
1 2 3 4 5 6 7 8 9 10 11 12
Shortest Path

Figure: Success Rate and stretch in Delicious with n = 20 and m = 20



-
l=3.467684, h=4.162304, sg=0.000382, τg=1.200312

Success Rate (s)
7 Stretch (τ)

6

5
s, τ

4

3

2

1

0
1 2 3 4 5 6 7 8 9
Shortest Path

Figure: Success Rate and stretch in Flickr with n = 20 and m = 20



-
l=3.197477, h=6.662900, sg=0.001062, τg=2.083799

Success Rate (s)
6 Stretch (τ)

5

4
s, τ

3

2

1

0
1 2 3 4 5 6
Shortest Path

Figure: Success Rate and stretch in LastFM with n = 20 and m = 20



Under this restriction the navigator in Considering practical user interface
restriction folksonomies are useless for supporting navigation. The success
rate drops below 1%.



Thus, folksonomies (unlimited) are useful theoretically but useless
practically
The problem is that top nodes have many children (possibly
thousands) and UI restrictions cut to many children nodes oﬀ
Hence, we need a new algorithm that takes into account these UI
restrictions
Technically, we need to able to determine the branching factor for the
hierarchy
We developed such an algorithm and published in CIKM2011. Helic
et al. Building Directories for Social Tagging Systems
We were able to almost recover theoretical navigability



-
l=3.585123, h=8.691685, sg=1.000000, τg=2.424376
7
Success Rate (s)
Stretch (τ)
6

5

4
s, τ

3

2

1

0
1 2 3 4 5 6 7 8 9
Shortest Path

Figure: Success Rate and stretch in BibSonomy with new folksonomy algorithm



-
l=3.634634, h=9.163688, sg=1.000000, τg=2.521213

7 Success Rate (s)
Stretch (τ)
6

5

4
s, τ

3

2

1

0
1 2 3 4 5 6 7 8 9
Shortest Path

Figure: Success Rate and stretch in CiteULike with new folksonomy algorithm



-
l=3.518932, h=9.720769, sg=1.000000, τg=2.762420

6 Success Rate (s)
Stretch (τ)
5

4
s, τ

3

2

1

0
1 2 3 4 5 6 7 8 9 10 11 12
Shortest Path

Figure: Success Rate and stretch in Delicious with new folksonomy algorithm



-
l=3.467684, h=8.886960, sg=0.996066, τg=2.562794

Success Rate (s)
6 Stretch (τ)

5

4
s, τ

3

2

1

0
1 2 3 4 5 6 7 8 9
Shortest Path

Figure: Success Rate and stretch in Flickr with new folksonomy algorithm



-
l=3.197477, h=9.830726, sg=1.000000, τg=3.074526
6
Success Rate (s)
Stretch (τ)
5

4
s, τ

3

2

1

0
1 2 3 4 5 6
Shortest Path

Figure: Success Rate and stretch in LastFM with new folksonomy algorithm


Why usefulness of folksonomies for navigation is limited?

Even if folksonomies allow the user to navigate to related concepts in
an eﬃcient manner navigation to a particular resource is still a
problem
As shown related work, in tagging systems the tag-resource
distribution follows a power-law function, i.e. there are many tags
that refer to a large number of resources.
In BibSonomy or CiteULike for instance there are tags, which refer to
hundreds or even thousands of resources.
To display such long resource lists, developers typically paginate the
resource lists in a tagging system by a certain factor k



(a) Austria-Forum (b) BibSonomy (c) CiteULike

Figure: Tag distributions.


Creating tag-resource Taxonomies

To support the user not only to navigate to related tags in efficient
manner but also to the resources of a tagging system, we invented
the approach of the so-called tag-resource taxonomies.

Car

Car
Tire Motor

Tire Motor
Mercedes VOLVO VW BMW

VW BMW VW BMW

(a) Folksonomy (b) Tag-Resource Taxonomy

Figure: Folksonomy vs. Tag-Resource Taxonomy. In a Folksonomy tags appear
only once. However, resources can be referred by different tags. In a tag-resource
taxonomy on the other hand resources can occur only once while tags can appear
on multiple and on different levels.



In the worst case a user would have to click max{click(Ttag )} times
to reach a desired resource with the help of a Folksonomy.

c1 |r |
max{click(Ttag )} = + logb/2 (c2 · |r |), b ≥ 2 (1)
k
or
c1 · |r |
max{click(Ttag )} ≈ (2)
k
c1 ·|r |
supposing that logb/2 (c2 · |r |) k



The worst case scenario of a tag-resource taxonomy is signiﬁcantly
better. In the worst case a user would have to click max{click(Tres )}
times to reach a desired target resource.
max{click(Tres )} = max{depth(Tres )} = logk/2 |r | , k ≥ 2 (3)
Then for large values of |r | we have:

c1 · |r |
logk/2 |r | (4)
k


Why usefulness of folksonomies for navigation is
limited?xxx

Austria-Forum BibSonomy CiteULike
max{click(Ttag )} 184 5,278 20,799
max{click(Tres )} 6.1 7.7 8.5
Table: Tag Taxonomy vs. Tag-Resource Taxonomy: Maximum number of clicks
for k = 10.



To calculate the number of tags suﬀering from the so-called
pagination eﬀect, we can user the following equation:
1
α 1 (α)
|tp | = |t| · − (5)
k k

Austria-Forum BibSonomy CiteULike
|tp | (%) 5079 (38%) 7401 (28%) 51748 (32%)
Table: Number of paginated tags for k = 10.



The mean number of clicks is calculated as follows:
Tag-Resource Taxonomy: mean{click(Tres )} = logk (|r |)
|t|
Folksonomy: mean{click(Ttag )} = logk (|t|) + |t| i=1 ri
1
k

k Austria-Forum BibSonomy CiteULike
mean{click(Tres )} 2 14.2 17.8 19.8
mean{click(Ttag )} 2 29.5 22.4 30.7
mean{click(Tres )} 5 6.1 7.6 8.5
mean{click(Ttag )} 5 11.6 9.2 12.3
mean{click(Tres )} 10 4.3 5.3 5.9
mean{click(Ttag )} 10 6.4 5.6 7.3

Table: Tag Taxonomy vs. Tag-Resource Taxonomy: Mean number of clicks for
diﬀerent branching factors k.


Creating tag-resource Taxonomies

1. Computer Degree centrality of the resource-to-resource tag network
2. Take most general resource as root an attach max. b resources as
childs. Child-nodes are selected according their cos-sim values.
3. After that we take the resource taxonomy and apply labels (tags)
to the resource (top-down, in left-order)
3.1 We calculate candidate labels by the method of co-occurance, i.e.
we take the tags of the related resources into account to rank the
actual tags of the currently processed resource.
3.2. If the candidate tag has already been applied to one of the
parent resources of the currently processed resource we take the next
candidate tag from the co-occurance vector and try to apply it.


Evaluating Tag-Resource Taxonomies

In the ﬁrst experiment we measured the average and maximum
number of clicks and the drop rate

Name b n max{click(Tres )} mean{click(Tres )}
Res2 2 19,430 17 12.45
Res5 5 19,430 10 5.93
Res10 10 19,430 8 4.44

Table: max{click(Tres )} and mean{click(Tres )} for diﬀerent branching factors b.



In the second experiment we measured the number of collisions

Name b n CR (%)
Res2 2 19,430 0.1%
Res5 5 19,430 0.2%
Res10 10 19,430 0.2%

Table: Collision Rates (CR) for diﬀerent resource taxonomies with diﬀerent
branching factor b.


In the third experiment we measured the semantic structure of the
tag-resource taxonomy compared to popular folksonomy induction
algorithms such as Heymann, K-Means, Aﬃnity Propagation and
Co-Occurance
As measure for this experiment we used Taxonomic Recall/Prec. and
overlap.
Ground truth: Germanet ontholoy
0.4
Taxonomic F−Measure
0.35 Taxonomic Overlap

0.3
Count (1 = 100%)

0.25

0.2

0.15

0.1

0.05

0
Res2 Res5 Res10 Deg/Cooc Aff. Prop K−Means Heymann



In the fourth and last experiment a user study was conducted to test
weather the approach is also useful for humans or not
As ground truth for the experiment the best so far known folksonomy
generation approach was used
All over we had 9 test users who had to judge 200 tag trails extracted
from both hierarchies

Name b Correct (%) Related (%) Equivalent (%) Not Related (%
Deg/Cooc10 10 33.2 27.3 13 21.9
Res10 10 27.3 36.2 12.3 19.8
Table: Results of the empirical analysis of the tag-resource taxonomy with
branching factor b = 10 compared to a Deg/Cooc folksonomy with branching
factor b = 10.


End of presentation

Thank you very much for your attention!
Christoph Trattner (ctrattner@iicm.edu)


Networks Navigability: Theory and Applications

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