An Alignment Equation for Using Mind Map
An alignment equation for using mind maps to filter learning queries from
Google
Imran A. Zualkernan
American University of
Sharjah, UAE
izualkernan@aus.edu
Mohammed A. AbuJayyab
American University of
Sharjah, UAE
mjayyab@gmail.com
Abstract
Search engines like Google play a critical role in
life-long learning. However, the query capabilities of
such engines remain simple and often yield a result set
that is too large. In addition, search engines like
Google rely on page ranking algorithm that represents
the “collective consciousness” of millions of users.
Learning about specifics often involves context. This
paper shows how mind maps can be used as a
contextual mechanism to specify what needs to be
learned and to filter and retrieve the relevant sources
of learning from the internet. In specific, a concept of
“alignment” is introduced that filters only those
information sources that are globally aligned to the
mind map.
The filter is implemented as a
combinatorial optimization algorithm using Simulated
Annealing.
1. Introduction
As semantic internet [1] and specialized
repositories of learning objects (e.g., [2]) come of age
to include structured information about resources on
the internet, search engines like Google [3] remain the
most successful search engines for life-long learning.
Search engines typically work using page and link
similarity to conduct a search [4].
It has been explicitly suggested that Google assigns
“implicit” semantics to concepts [5]. Since page
ranking is based on million of users, the implicit
semantics assigned using these algorithms can be
termed “social semantics.” However, how does one
specify what an individual needs to learn in a specific
context? One line of research addresses how effective
answers to specific questions from a user can be
formulated [6]. Object ontologies [7] are also being
used to specify “what needs to be learned” in a
particular context. Mind maps for brain-storming [8]
have also been used as a part of literacy education [9].
Mind maps [10] and ontologies have also been
abstracted from existing documents to discover the
underlying latent semantic structure [11]. Conceptual
graphs (another graphical notation similar to mind
maps), have also been suggested for use in “semantic
queries” [12]. Finally, multiple techniques such as
topological analysis, filtering, search and using a
concept map to filter the results from a search engine
like Google have also been proposed [13].
The research presented in this paper relies on the
topology of a mind map and the response set retrieved
from a search engine like Google to arrive at a filtered
set of results that are “aligned” with the mind map
hence providing a user-specific “contextual” search
mechanism.
2. Formalization
Given a general purpose search engine (e.g.,
Google) that operates over a collection of web pages
and a mind map given by a directed graph G (V , E ) ,
where each viH V represents a concept in the mind
map, the goal of this research is to find a subset of web
pages that are “aligned” with the mind map.
More formally, a search engine returns an ordered
response set rs P1 ,..., Pk representing potentially
relevant pages. For a response set, i j implies that
page Pi is more relevant than Pj within the first k
search results. A query based on the mind map, returns
a set of response sets SRS {rs1 , rs2 , rs3 ..., rsl } where
each response set rsi is generated by a query of the
form vr ..vi where vr is a designated root node (or
the primary starting concept) and all subsequent nodes
in the query are on a path from vr to vi in graph G.
A set of response set SRS with a response set
bound of k is said to be aligned with a concept
Proceedings of the Sixth International Conference on Advanced Learning Technologies (ICALT'06)
0-7695-2632-2/06 $20.00 © 2006
IEEE
Yaser A. Ghanam
American University of
Sharjah, UAE
yghanam@gmail.com
map G if the following equation holds for each
rsi SRS
For each vi , v j , vk G
d (v i , v j ) d (v i , v k ) D ( rs i , rs j ) D ( rs i , rs k )
(1)
24*10 = 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 (121/240 = 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.
Where d is defined to be the number of hops between
vi and v j . D , on the other hand, is measured using
the Levenshtein or edit distance [14] between two
response sets rs i and rs j . 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
Figure 1. A mind map for an overview of java and
related technologies
There was a correlation (r = 0.462; p
Imran A. Zualkernan
American University of
Sharjah, UAE
izualkernan@aus.edu
Mohammed A. AbuJayyab
American University of
Sharjah, UAE
mjayyab@gmail.com
Abstract
Search engines like Google play a critical role in
life-long learning. However, the query capabilities of
such engines remain simple and often yield a result set
that is too large. In addition, search engines like
Google rely on page ranking algorithm that represents
the “collective consciousness” of millions of users.
Learning about specifics often involves context. This
paper shows how mind maps can be used as a
contextual mechanism to specify what needs to be
learned and to filter and retrieve the relevant sources
of learning from the internet. In specific, a concept of
“alignment” is introduced that filters only those
information sources that are globally aligned to the
mind map.
The filter is implemented as a
combinatorial optimization algorithm using Simulated
Annealing.
1. Introduction
As semantic internet [1] and specialized
repositories of learning objects (e.g., [2]) come of age
to include structured information about resources on
the internet, search engines like Google [3] remain the
most successful search engines for life-long learning.
Search engines typically work using page and link
similarity to conduct a search [4].
It has been explicitly suggested that Google assigns
“implicit” semantics to concepts [5]. Since page
ranking is based on million of users, the implicit
semantics assigned using these algorithms can be
termed “social semantics.” However, how does one
specify what an individual needs to learn in a specific
context? One line of research addresses how effective
answers to specific questions from a user can be
formulated [6]. Object ontologies [7] are also being
used to specify “what needs to be learned” in a
particular context. Mind maps for brain-storming [8]
have also been used as a part of literacy education [9].
Mind maps [10] and ontologies have also been
abstracted from existing documents to discover the
underlying latent semantic structure [11]. Conceptual
graphs (another graphical notation similar to mind
maps), have also been suggested for use in “semantic
queries” [12]. Finally, multiple techniques such as
topological analysis, filtering, search and using a
concept map to filter the results from a search engine
like Google have also been proposed [13].
The research presented in this paper relies on the
topology of a mind map and the response set retrieved
from a search engine like Google to arrive at a filtered
set of results that are “aligned” with the mind map
hence providing a user-specific “contextual” search
mechanism.
2. Formalization
Given a general purpose search engine (e.g.,
Google) that operates over a collection of web pages
and a mind map given by a directed graph G (V , E ) ,
where each viH V represents a concept in the mind
map, the goal of this research is to find a subset of web
pages that are “aligned” with the mind map.
More formally, a search engine returns an ordered
response set rs P1 ,..., Pk representing potentially
relevant pages. For a response set, i j implies that
page Pi is more relevant than Pj within the first k
search results. A query based on the mind map, returns
a set of response sets SRS {rs1 , rs2 , rs3 ..., rsl } where
each response set rsi is generated by a query of the
form vr ..vi where vr is a designated root node (or
the primary starting concept) and all subsequent nodes
in the query are on a path from vr to vi in graph G.
A set of response set SRS with a response set
bound of k is said to be aligned with a concept
Proceedings of the Sixth International Conference on Advanced Learning Technologies (ICALT'06)
0-7695-2632-2/06 $20.00 © 2006
IEEE
Yaser A. Ghanam
American University of
Sharjah, UAE
yghanam@gmail.com
map G if the following equation holds for each
rsi SRS
For each vi , v j , vk G
d (v i , v j ) d (v i , v k ) D ( rs i , rs j ) D ( rs i , rs k )
(1)
24*10 = 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 (121/240 = 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.
Where d is defined to be the number of hops between
vi and v j . D , on the other hand, is measured using
the Levenshtein or edit distance [14] between two
response sets rs i and rs j . 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
Figure 1. A mind map for an overview of java and
related technologies
There was a correlation (r = 0.462; p