map
G
if the following equation holds for each
SRS rs
i
For each
G v
v v
k j
i
,
, ,
, ,
,
k i
j i
k i
j i
rs rs
D rs
rs D
v v
d v
v d
1 Where
d is defined to be the number of hops between
i
v
and
j
v
.
D
, on the other hand, is measured using the Levenshtein or edit distance [14] between two
response sets
i
rs
and
j
rs
. The edit distance measures the number of changes required to change one
sequence into another. Intuitively, the alignment equation 1 means that if
the distance between a concept A and a concept B in the mind map is less than the distance between the
concept A and another concept C, then an alignment dictates that the distance between the response set of A
and response set of B should also be less than the distance between the response set of A and the
response set of C. And that this should be true of all pairs of concepts in the mind map.
Deriving an aligned
SRS
from an initial set of response sets is a combinatorial optimization problem
that can be solved using Simulated Annealing [15]. Simulated annealing uses an objective function of cost
or Energy
E
to guide the search for a solution. The Energy
E
for this problem is the number of violations of equation 1; for an ideal solution, the number of
violations should be zero. The simulated annealing algorithm for this problem was implemented in Java
and used the Google API [16] to connect and retrieve response sets from Google.
3. Evaluation
The mind map shown in Figure 1 is a subset of the mind map constructed for an overview of the Java
technology by Sun Microsystems [17]. Objective of the mind map shown in Figure 1 is to provide a broad
overview of java and related technologies. This mind map was used to evaluate the alignment algorithm
described earlier. A response set bound of 10 was used for this experiment; only first ten results from each
query were considered.
Starting from 38 initial violations of equation 1, the simulated annealing algorithm converged to a
minimum Energy of 2 meaning 2 violations of equation 1 after 50,000 iterations. Since the mind
map had a total of 24 concepts, with response set bound of 10, the initial set of response sets resulted in
2410 = 240 page references. Simulated annealing reduced this set to 121 page references that are actually
“aligned” to the mind map. So the total number of pages was narrowed by about half 121240 = 50.4.
The average number of pages per concept was reduced from 10 to 5.04 SD = 1.62. The maximum reduction
was to 2 pages and the minimum to 8 pages.
Figure 1. A mind map for an overview of java and related technologies
There was a correlation r = 0.462; p0.02 using Pearson’s correlation between the distance from the
root and the number of pages left after filtering for each concept. For example, for the root node see Java
in Figure 1, the number of pages were narrowed from 10 to 2. While, for a node like “Web browser”, the
number of relevant pages were reduced from 10 to 7 only. This is consistent with equation 1, because the
closer a node is to the root, the more constraints it needs to satisfy.
Table 1 shows the original ten pages retrieved for the root concept “java.” Table 1 also shows the page
rank from Google, number of sites linking in to the page and the traffic rank from www.alexa.com for
each page.
The alignment algorithm reduced these ten pages to just two pages
www.java.com and
http:www.apl.jhu.edu~halljava . The page
http:www.apl.jhu.edu~halljava had the lowest page
rank, the lowest traffic ranking and a low number of sites linking in. However, this page was selected by
the algorithm. A quick review of the contents of the page, however, shows that this page is exactly what
the mind map was designed for; the page contains an overview and links to all aspects of java technology
ranging from FAQ’s and tutorials, documentation, forums, resources and developer links. The other page
chosen was
www.java.com which includes a download
of the java virtual machine from Sun Microsystems.
Proceedings of the Sixth International Conference on Advanced Learning Technologies ICALT06 0-7695-2632-206 20.00 © 2006
IEEE
Together, these two pages provide both the technology for running Java and a broad overview as intended in
the mind map. It would seem that
http:java.sun.com should have
been the logical choice for a broad overview of java technology. However, the information provided on
this site is analogous to the one in
http:www.apl.jhu.edu~halljava
. Indeed, in another run of the algorithm, the reduced set of pages for
“java” included http:sun.java.com
and http:sun.java.comgetjava
for java virtual machine download.
Table 1. Original response set for Java k=10 Page Page
Rank Sites
Linking Traffic
Rank http:java.sun.com
9 5946
486 http:www.java.com
9 1463
1046 http:www.java.comendo
wnloadmanual.jsp 8 1463
1046 http:www.anfyteam.comj
ava 8 848
36507 http:javaboutique.internet.
com 7 721
800 http:www.javaworld.com 8
953 12309
http:java.net 8 125
12636 http:www.microsoft.com
mscorpjava 8 53509
14 http:www.developer.comj
ava 7 927
14144 http:www.apl.jhu.edu~hal
ljava 6 234
120943
selected by the alignment algorithm
4. Conclusion
