Information Fusion in a Cooperative Multi-agent
System for Web Information Retrieval
K. B. Shaban
O. A. Basir
K. Hassanein
M. Kamel
School of Engineering
University of Guelph
Guelph, Ontario, Canada
N1G 2W1
[email protected]
School of Engineering
University of Guelph
Guelph, Ontario, Canada
N1G 2W1
[email protected]
School Of Business
McMaster University
Hamilton, Ontario, Canada
L8S 4L8
[email protected]
Systems Design Engineering
University of Waterloo
Waterloo, Ontario, Canada
N2L 3G1
[email protected]
Abstract – As an attempt to solve some contemporary web
information retrieval problems, a construction of a
cooperative multiagent system is proposed. This paper
introduces the system and presents the use of a unique
aggregation and fusion technique that is employed to
attain reliable delivery performance. The intelligent
methodology to fuse agents’ decisions, the team consensus
approach, models the interaction and bring a society into
a consensus. After each agent in the group gathers
information relevant to a user’s query, the group engages
in an uncertainty estimation stage. This process allows
each agent to assess its self-uncertainty and the
conditional uncertainties of other agents. The procedure
facilitates the computation of a weighting scheme that
operates recursively on information collected by these
agents until the group reaches a consensus. Whenever a
new task is received, the uncertainty estimates of agents
are updated and used to compute a new weighting scheme.
Keywords: Information fusion, decision fusion, team
consensus, cooperative multiagent systems, web
information retrieval.
1 Introduction
As the value and range of information available on the
Internet has grown, so the need to manage this information
effectively has grown, and has given a rise to what is
known as the Internet information overload (or overkill)
problem. Put simply, the volume of information available
via the World Wide Web (WWW, or Web) represents a
very real problem. The potential of this problem is
immediately apparent to anyone with more than the most
superficial experience of using the WWW.
The
information overload problem can be characterized in two
management processes; Information filtering, and
Information gathering. It is of a great benefit to take the
burdens off users’ shoulders and automate these tasks [7].
There are many publicly available information retrieval
tools (i.e., search engines, web directories, etc.), but users
ISIF © 2002
are not necessarily satisfied with their different retrieval
speeds, qualities of retrieved information, formats of
inputting queries and presenting results, database sizes,
and on-line availabilities [6]. These tools are even
contributing to the information overload problem, as they
require the end user to constantly direct the management
process. Users have to look for the desired information,
sort the wheat form the chaff, and focus on information
they need. Moreover, the gathering, organization, and
handling process in these systems is focused on the low
information (or even data) representations instead of the
higher knowledge levels, and that is considered as a strong
factor leads to theses systems retrieval impreciseness [11]
A construction of a cooperative multiagent system
(MAS) for web information retrieval is being proposed.
The system shall overcome pitfalls current Web-based
information retrieval tools are facing. It consists of a
distributed group of entities (Intelligent Agents1) that
mimic everyday life of information seekers. Each member
of this group has the ability to be goal and pattern driven,
autonomous, and rational in a cooperative and interactive
setting. Agents are responsible for perceiving users’
desires, setting goals, exploiting all efforts to achieve these
goals, filtering and customizing results, and presenting
them in appropriate formats. They may also have more
interesting features such as tracking their perspective
users’ browsing behaviours, and trying to anticipate what
items may be of interest through building profiles of the
accumulated knowledge (see figure 1).
At a certain level of abstraction, many MAS
applications share common features, e.g., collaboration.
Individual agents are designed and built to enact particular
roles. These agents are autonomous, goal directed entities,
which are responsive to their environment. They must
1
Definition of multiagent systems, intelligent agents, and details of everevolving technology are beyond the scope of this article. However, the
reader is referred to the literature to gain familiarity to the subject [3, 4].
There are several definitions of agents and multiagent systems, and one
can also describe rather than define agents in terms of their task,
autonomy, communication capabilities, etc.
1256
typically interact in order to carry out their roles. Such
interactions are a natural consequence of the inevitable
interdependencies, which exist between the agents, their
environment, and their design objectives.
One important aspect of the cooperation property is the
ability to reach a consensus in decisions made by the
different agents at different levels of information
abstraction.
There is always a certain amount of
uncertainty associated with decisions made by these
agents. This uncertainty problem can prevent information
retrieval agents from answering complex queries, or
preclude personal agents from figuring out ambiguous user
actions.
Generally speaking, uncertainty in agent
decisions can be attributed to two main aspects, namely,
deficiency in agent decision-making capability, and
application information ambiguity. The first aspect is
generally due to agent design/implementation defects.
The second aspect is due to information overload. For
example, in an environment such as the Internet,
properties like inaccessibility, non-deterministic, and
dynamic nature of the information space, are sources of
agent imprecise decisions. Each one of these sources may
induce a certain amount of uncertainty to the agents’
assessments and may cause them to acquire the wrong
knowledge, which may lead to unfavourable results. Thus,
procedures to reduce uncertainty are crucial for improving
the capability, increasing the reliability, and widening the
applicability of such systems.
agents. The procedure facilitates the computation of a
weighting scheme that operates recursively on decisions
made by these agents until the group reaches a consensus.
Whenever a new task is received, the uncertainty estimates
of agents are updated and used to compute a new
weighting scheme. The approach is computationally
tractable, and analytical as well as comparative studies
have demonstrated that the approach can be applied to
many practical information fusion and integration
applications [8].
The breakdown of the paper as follows; section 2
formally state the decision fusion problem; section 3
illustrates types of cooperative agents’ team settings and
suggest the use of the team consensus arrangement;
section 4 discuss the team consensus approach and its
hypothetical assumptions in assessing agents importance
weights; section 5 introduce the concept of how weights
can be used to reflect uncertainties; section 6 provides how
uncertainty estimations of agent decisions can be acquired
and used to assign weights coefficients; section 7 gives an
illustrative case of the whole fusion procedure where a
consensus decision can be noticed; section 7 concludes the
paper.
User
In order to reduce both aspects of uncertainty, one may
intuitively suggest building ingenious agents and
structuring their environment. However, the use of agents
capable of digesting the gigantic knowledge on the
Internet and produce accurate answers to all users’
enquiries may not be achievable, or at least may result in
very costly systems. Moreover, practically speaking, it is
not always possible to structure the agent-working
environment in such a way that reduces uncertainty. As in
the Internet, where the majority of information resources
are dynamically changing, it is unfeasible to construct an
inclusive knowledge space. A more practical approach is
to view these agents as a collaborative society of agents
that communicate their assessments and engage in a
discourse so as to reach a consensus with respect to the
best decision possible. By combining decisions made by
different agents, more effective decision-making can be
achieved.
There are several attractive decision fusion
methodologies, from different disciplines, based on
statistical methods, probability techniques, artificial
intelligence approaches, and others [1]. This article
presents the use of an intelligent approach, the team
consensus approach, which has been applied in multisensory data fusion [9]. The approach tries to bring team
into a consensus by having agents engage in an uncertainty
estimation stage whenever a group decision is required.
This process allows each agent to assess its selfuncertainty and the conditional uncertainties of other
Personal
Agent
Resource
“Information
Retrieval” Agent
User
Personal
Agent
Intermediate
“Fusion” Agent
Environment
“The Web”
Figure 1. Envisioned View of the System
2 Fusion Problem Formulation
Consider a group of N agents, indexed by the set A = { A1,
A2, …, AN}, gathering information from their perspective
environment (e.g., the Web). Here, a decision theory
formulation is utilized where each agent Ai observes a
subset θi over a universal information space given by Θ.
1257
An information structure ηi is used to relate θi to a belief
zi. Thus,
zi = ηi (θi )
7: display
(1)
where zi ∈ ℑ , the knowledge space.
1
Upon receiving a query q, Ai chooses an answer ai from
a set of possible answers Γ i= (γ1, ..., γM). This answer is
related to the belief zi by a decision function δi as
ai = δi (zi)
6: get final answer
1 / Personal Agent *
1: enquire
1 / Fusion Agent
2: request
1
User
3: query
(2)
5: get answer
*
Each agent processes its own beliefs, which might be
different from the beliefs of other agents, and uses them to
rank its answers. Collectively, the n-tuple pair η = (η1, …,
ηn), and δ = (δ1, …, δn), respectively, are the information
structure and the decision rule of the group.
/ Retrieval Agent
1
4: answer
The decision integration problem can be stated as
finding the group answer a ∈ Γ that constitutes the
group preference. To achieve that, a ranking function that
places a preference ordering on the answers of each agent
is defined as Ri(δi (zi ), q): Γ × Θ → ℜ for each Ai ∈ A,
and
k∈Γi
*
:ExternalResource
Figure 2 (a) Collaboration Diagram of Centralized Team
Ri (γk) = 1. The actual form of each ranking
function can vary considerably depending on the nature of
the decision problem and the tactic agents follow. For
instance, information retrieval agents might be equipped
with different computational methods (e.g., LSI1, VSR2,
etc.) for automated indexing, representations, and then
ranking their findings.
10: display
1
9: get final answer
1 / Personal Agent *
1: enquire
2: request 1
User
A global ranking function RG, i.e., the group ranking
function, is then defined to aggregate the expected
rankings of all members, RG = f(R1, …, Rn). The
performance of the agents as a group is influenced by this
function. The actual form of this function will be shown
in section 4.
*
/ Retrieval Agent *
1
1
2
Latent Semantic Indexing [2].
Vector Space Representation [13].
*
* / Retrieval Agent
5: query
6: get answer
7: answer
*
:ExternalResource
1
3: query
8: get answer
3 System Collaboration Model
Agents’ groups can be categorized in terms of
relationships and interactions between members into two
types, namely, non-recursive and recursive arrangements.
In the non-recursive organizations, information flow
between members of the group is always permitted in only
one direction. The standard UML collaboration diagram
[10] in figure 2a is a snapshot of one variation of this type
of setting, the centralized team. Another example of the
non-recursive type is also modeled and showed in figure
2b. This setting can be realized by assuming a natural
precedence order in which the members of the group
communicate their answers. In this group, the decision of
the ith member depends only on its internal beliefs and the
decision of the (i – 1)th member.
1 / Fusion Agent
1
4: answer
*
:ExternalResource
Figure 2 (b) Collaboration Diagram of Sequential Team
In the recursive category, however, each member of the
group can engage in a discourse with other members of the
group. They are suggesting and verifying each other’s
answers. This provides a powerful means to resolve
environment ambiguities, a proficiency that makes the
recursive groups the best choice for integrating
information provided by multiple agents. This type of
network is called the group consensus and was suggested
by DeGroot [5] to aggregate multiple opinions into one
decision that constitutes the group consensus (Figure 2c).
This consensus is achieved by allowing all group members
1258
to linearly pool their assessments in a recursive manner.
This model is simple and intuitively appealing, and it will
be used here to aggregate agents’ knowledge.
18: display
1
User
limit theorems of Markovian chains to determine whether
the group will converge to a common ranking, which
represents the group consensus, and if so what is the value
of this ranking. It has been shown and proven in [5, 12]
that the group will converge to a common ranking if and
only if there exists a vector π such that.
17: get final answer
1 / Personal Agent *
1: enquire
2: request 1
4: query
subject to
1
πi = 1
(5)
N
RG(γk) =
*
*
/ Retrieval Agent *
6: answer 10: get answer
14: answer 12: get answer
1
πi × Ri(γk)
(6)
As the weights, wij, of this model are estimated
subjectively by each member of the group, they are meant
to reflect experience, honesty, etc. Nonetheless, they can
also be used to reflect the uncertainty of agents about their
decisions. It is fully obvious that this uncertainty is
different in various situations, differs from agent to agent,
and it will manifest in the ranking assessments of each
agent. In this way, weights will be adaptive and have
some dynamic behaviour, in the sense that they portray the
changes in the state of knowledge in the group. Weights
are assigned accordingly as to exhibit their self and peers
confidence degree.
5: answer
13: answer
*
:ExternalResource
*
:ExternalResource
i =1
* / Retrieval Agent
9: give answer
11: give answer
And the common group ranking, for each γk∈ Γ denoted
by RG(γk), k = 1, …, M, is given by
7: get answer
15: get answer
1
(4)
i∈A
3: query
8: get answer
16: get answer
π × w=π
1 / Fusion Agent
Figure 2 (c) Collaboration Diagram of Consensus Team
4 Team Consensus for Fusion
5 Uncertainty Estimation
In this model, each individual agent must first assess its
The objective here is to seek a function that, by processing
the decisions made by a group of agents, can estimate their
uncertainties. This function should reflect the contrasts of
agents’ decisions. Given the uncertainty levels of all
agents, one only needs to adjust the weights of the agents
such that the more uncertain an agent is lesser weight it
receives.
∀ γk ∈ Γ i. It is then
own expected rankings
confronted with the decisions of the other group members
and revises its own by making an assessment of each
group member’s relative importance, expertise, honesty,
etc. Specifically, each revised expected ranking is deemed
to be of the form
*
R i (γk),
N
*
R i (γk) =
wij Rj(γk)
(3)
j =1
where wij is a positive importance weight assigned by the
ith member to the jth member and
N
j =1
wij = 1, ∀ i, j ≤
N.
Each agent revises its opinion in this manner where it
should update its own decision in light of the revisions
made by others. The process continues until further
revision no longer changes the expected ranking of any
member. Since w is an N × N stochastic matrix, it can be
viewed as the one-step transition probability matrix of
Markovian chain with N states and stationary transition
probability. This interpretation enables one to use the
In a communicative group of agents, two types of
uncertainties seem to emerge. The first uncertainty is
local to the agent and reflects the quality of decisions it
makes. The second uncertainty is global and manifests the
cooperation of agents in terms of knowledge exchange.
Given their answers as well as of other agents, they will be
able to adjust their uncertainty level.
The latter
mechanism mimics how agents improve their state of
knowledge by learning from each other.
There are two types of uncertainties that can be used to
model this estimation process: the self-uncertainty and the
conditional-uncertainty. The self-uncertainty measures
how uncertain the agent about its decisions or how random
are the choices of the agent. The more certain is an agent
the higher contrast are its choices. Let Ui|i indicate the
1259
self-uncertainty of Ai . Ui|i is computed based on the local
knowledge of the agent as
Similarly, taking the partial derivative of Vi with respect
to the Lagrange multiplier ρ and equating with zero yields
M
Ui|i = -
Ri (γk) logM Ri(γk)
(7)
Combining eqs. (13) and (14) yields
The conditional-uncertainty, however, is a measure of
the state of uncertainty of an agent given the answers of
other agent. This measure can be used to capture the
essence of knowledge relevancy between agents.
M
Ri (γk| Γ j) logM Ri(γk| Γ j)
j∈A
ρ
=1
2× U 2j|i
(15)
2
U −j|i2
j∈ A
(16)
It then follows that
(8)
k =1
ρ=
In general, for a team of N agents, these uncertainties
are arranged in a matrix form as
Substituting eqs. (16) and (13) gives the agent
weighting coefficient, wij, as follows:
U1 | 1 U2 | 1 . . . UN | 1
U1 | 2 U2 | 2 . . . UN | 2
... ... ... ...
U=
U1 | N U2 | N . . . UN | N
(14)
j∈A
k =1
Ui|j = -
wij = 1
(9)
wij =
1
U
2
j |i
(17)
U −2
k ∈A k |i
7 Illustrative Scenario
6 Uncertainty Based Weightings
Now, given the uncertainty matrix U, each agent of the
group can determine appropriate weights for itself and
other agents. This can be achieved by minimizing the sum
of squares of its self-uncertainty and conditional
uncertainties associated with other agents. This implies
that each agent will assign high weights to agents with low
conditional-uncertainties and low weights to those with
high conditional-uncertainties. The minimization problem
may be stated as follows:
Minimize Ti =
w ij × U j |i ,
2
2
Consider a multiagent system consists of three information
retrieval agents each observing a limited portion of the
Web. For simplicity, a maximum of four answers from
each agent will be considered (Table 1).
(10)
j∈A
N
subject to
and wij ≥ 0
wij=1,
(11)
j =1
Vi =
w ij × U j|i - ρ
2
2
j∈A
wij − 1
j∈A
(12)
where ρ is the Lagrange multiplier. Taking the partial
derivative of Vi with respect to wij and equating it to zero
yields
wij =
ρ
2× U 2j|i
γ1
γ2
γ3
γ4
R1(γk)
0.8
0.17
0.03
N/A
R2(γk)
0.333
0.333
N/A
0.333
R3(γk)
N/A
0.6
0.2
0.2
R1(γk| Γ2)
0.75
0.1
0.1
0.05
R1(γk| Γ3)
0.9
0.04
0.04
0.02
R2(γk| Γ1)
0.6
0.2
0.05
0.15
R2(γk| Γ3)
0.2
0.4
0.1
0.3
R3(γk| Γ1)
0.3
0.4
0.1
0.2
R3(γk| Γ2)
0.1
0.5
0.1
0.3
Table 1. Illustrative Scenario
The above minimization problem subject to the above
constraints is equivalent to minimization of
R\Γ
Γ
After receiving a query, every agent ranks its findings
based on local information. These assessments need not to
be the same as agents’ knowledge and reasoning
capabilities various. After the first information exchange
course finishes, each agent will provide new ranked
answers. The uncertainty matrix for this group as
computed using equations (7) and (8) is:
(13)
1260
agent 1 would benefit the most (in terms of uncertainty)
from these results. Similarly, one can point to other
interesting facts about the relational behaviour of the
group by considering the rest of the conditionaluncertainties in the uncertainty matrix.
0.53 0.77 0.92
U = 0.6
1.0
0.84
0.31 0.92 0.86
Then each agent of the group uses this matrix to
determine appropriate weights for itself as well as for
other agent in the group. Whenever new decision task is
required, uncertainties are recalculated and used to update
the weight matrix accordingly.
The computed weight matrix, computed using equation
(17) is:
0.55 0.26 0.18
w = 0.53 0.2
0.27
0.8 0.09 0.11
The vector π computed from the above weighting
matrix, using equation (4) is:
π = [0.6 0.2 0.2]
By linearly combining the assessments of the three
agents, using equation (6) the group will converge to the
following group ranking:
R\Γ
Γ
γ1
γ2
γ3
γ4
RG(γk)
0.55
0.29
0.06
0.1
Clearly in this case, the group will favor γ1 as its
ranking is greater than all other answers, and the answers
will be ordered according to the global ranking as γ1, γ2, γ4,
and γ3 respectively.
From the above case the following observations can be
noticed. First, the self-uncertainties of the three agents
(the diagonal of the matrix U) are different, and the second
agent has the highest self-uncertainty level. This is in
agreement with its ranking assessment in Table 1. It is
clear from the table that the three agents have different
assessments as to what is the answer to the query. The
information gathered by agent 2 did not enable it to have
any preference, which might rationalize why it has the
highest self-uncertainty level. Other reasons may also be
blamed for getting such answers (e.g., design/implantation
defects). On the other hand, the other two agents seem to
have more preference; Agent 1 is more toward the first
answer γ1, while Agent 3 has no clue of the first answer,
and giving a high rank to the second answer γ2.
8
Conclusion
The development of a multiagent system is deemed to
be the key to solve some of contemporary Web
information retrieval problems. Justifications and a brief
introduction to the system were offered in this article.
Following that, a presentation of an intelligent information
fusion approach, the team consensus approach, to integrate
agents’ decisions was given. The approach treats the
agents as a group of experts cooperating with each other to
perform a common goal. After each agent in the group
makes its own decisions concerning the given task, the
group engages in an uncertainty estimation stage. This
process allows each agent to assess its self-uncertainty and
the conditional uncertainties of other agent. The process
facilitates the computation of a weighting scheme that
operates recursively on agent beliefs until the group
reaches a consensus. Whenever new group decision is
required, the uncertainty estimates of agents are updated
and used to compute a new weighting scheme. An
illustrative scenario to demonstrate the whole procedure is
also given.
As a future extension of the work, other factors than
uncertainties could be considered. For instance, an
experience factor reflecting how successful an agent has
been during a considered period of time is worth
including. Sometimes an agent should not be penalized
based just on its decisions uncertainty.
Moreover,
uncertainty could even be neglected if qualities of all or
most decisions are good.
The other suggestion is to extend the fusion technique
so that can be applied in different levels and shapes of
information abstractions. Integrating knowledge in forms
other than decisions will be definitely needed in most of
multiagent application processes.
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they are given the answers the third agent. It indicates that
when agent 3 passed its results to agent 1 and agent 2,
1261
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