High-Level Information Fusion with Bayesian Semantics

Paulo C. G. Costa, Kathryn Laskey, Kuo-Chu Chang, Wei Sun, Cheol Park, Shou MatsumotoCenter of Excellence in C4I & Department of Systems Engineering and Operations Research

George Mason UniversityFairfax, VA 22030

(pcosta,klaskey,kchang)@gmu.edu; wsun@c4i.gmu.edu; cparkf@gmu.edu; smatsum2@masonlive.gmu.edu

Abstract

In an increasingly interconnected world infor-mation comes from various sources, usuallywith distinct, sometimes inconsistent seman-tics. Transforming raw data into high-levelinformation fusion (HLIF) products, such assituation displays, automated decision sup-port, and predictive analysis, relies heavilyon human cognition. There is a clear lack ofautomated solutions for HLIF, making suchsystems prone to scalability issues. In thispaper, we propose to address this issue withthe use of highly expressive Bayesian mod-els, which can provide a tighter link betweeninformation coming from low-level sourcesand the high-level information fusion sys-tems, and allow for greater automation of theoverall process. We illustrate our ideas witha naval HLIF system, and show the results ofa preliminary set of experiments.

1 INTRODUCTION

Information fusion is defined as:. . . the synergistic integration of informa-

tion from dierent sources about the behav-ior of a particular system, to support deci-sions and actions relating to the system.1

A distinction is commonly made between low-level andhigh-level fusion. Low-level fusion combines sensor re-ports to identify, classify, or track individual objects.High-level fusion combines information about multipleobjects, as well as contextual information, to charac-terize a complex situation, draw inferences about theintentions of actors, and support process refinement.

In current information fusion systems, lower-level datafusion is typically accomplished by stove-piped sys-

1The International Society for Information Fusion,

http://isif.org

tems that feed information directly to human users.Subsequent generation of high-level information fu-sion (HLIF) products, such as situation displays, auto-mated decision support, and predictive analysis, reliesheavily on human cognition. The tacit underlying as-sumption is that humans are still the most ecientresource for translating low-level fusion products intodecision-relevant knowledge. While the current ap-proach works well for many purposes, it cannot scaleas the data influx grows. Automated assistance forHLIF tasks is urgently needed to mitigate cognitiveoverload and achieve the necessary throughput.

Stove-piped systems can be extremely ecient at ex-ploiting a specific technology applied to a limited andwell defined set of problems. Air Trac Control Sys-tems, for instance, employ radar technology in a veryeective way to provide reliable situation awarenessfor radar controllers via sophisticated low-level infor-mation fusion (LLIF) techniques. The synthetic radarscreen shown to trac controllers in a sector of an AreaControl Center (ACC) fuses multiple radar tracks.Data association algorithms infer whether geographi-cally close signals captured by various radars are com-ing from a single or multiple aircraft. Despite thesophistication of its low-level fusion components, theATC system relies heavily on humans for HLIF prod-ucts. For instance, controllers rely on their own under-standing of the overall picture to decide how to drivetheir tracks; area coordinators rely on their knowledgeto decide whether the outbound trac to a given air-port should be redirected due to an upcoming storm;and so on.

The ATC system is a good example of a highly so-phisticated stove-piped system that relies on humancognition for its major purpose: to ensure that thou-sands of airplanes in the US can share the airspacein a safe and eective way. As the volume of air-planes increases, more humans are needed to performHLIF tasks. After a point, the overhead of transferringbetween ever-smaller control sectors becomes a major

scalability issue. That is, cognitive limitations (eachhuman can control only airplanes at once) togetherwith the added complexity of adding extra cognitiveunits (a.k.a. trac controllers) become a major obsta-cle to growth. This scalability problem is common toHLIF systems in other domains as well.

In this paper, we propose to address the issue withthe use of highly expressive Bayesian models. Suchsystems provide a tighter link between low-level andhigh-level information fusion systems. Because theyare suciently expressive to reason about high-levelinformation, they provide a coherent framework forexpressing and reasoning with uncertain informationthat spans low and high level systems.

This paper describes our approach by way of a casestudy in information fusion for Maritime DomainAwareness. Section 2 motivates the use of explicitprobabilistic semantics and explains the main conceptsbehind our approach. Section 3 introduces the Mar-itime Domain Ontology we used in our experiments.The experiments are described in Section 4. Section 5concludes with a discussion.

2 Semantics in HLIF

Humans are more eective than computers at gather-ing various pieces of information and correlating theminto a coherent picture, but still have a high error rate.For example, an intelligence analyst can correlate im-ages and videos of a road with observers reports thata convoy has passed in the early afternoon, and con-clude that this was the same convoy that participatedin a terrorist attack 10 miles down that road. Theseconclusions are based on an implicit understanding ofhow trucks and cars are represented in each type ofmedia (video, imagery, human reports), as well as thetemporal and spatial relationships between cars, roads,convoys, etc. For a computer program to perform thesame inferences from the same set of sources, it mustpossess the same kind of knowledge. Conveying suchknowledge to a computer program requires a means tomake the humans tacit knowledge explicit and formal,so it can be retrieved and used when needed.

Ontologies are the current paradigm for specifying do-main knowledge in an explicit and formal way. One ofthe most cited definitions of ontologies is the specifica-tion of a conceptualization. [1] To perform automatedfusion in the above example, concepts such as cars,roads, convoys, people, etc., as well as their relation-ships, must be formalized in a way that computers canstore, retrieve, and use. Not surprisingly, ontologieshave been widely considered in the domain of informa-tion fusion as a means to enable automated systems toperform HLIF tasks (e.g. [2, 3, 4]).

Most languages for expressing ontologies, such as themost popular variant of the W3C RecommendationOWL [5], are based on Description Logic [6]. Otherontology languages such as KIF2 and the ISO Stan-dard Common Logic3 , are based on first-order logic.Classical logic has no standard means to represent un-certainty. This is a major drawback for HLIF sys-tems, which must operate in environments in whichuncertainty is pervasive. Inputs from LLIF systemscome with uncertainty, as do the high-level domain re-lationships that analysts use to draw inferences abouta complex situation.

Although LLIF algorithms often have a basis in prob-ability theory, it is common to report results accord-ing to a threshold rule without any confidence qual-ifier. This is often justified by cognitive limitationsof human decision makers. As an example, suppose avideo analysis report assigns 86% probability of personJoe being inside a car driving towards place A. If thethreshold for the input source was 85%, a LLIF sys-tem might simply report the statement without quali-fication, and a HLIF system might treat this as a truestatement. Such threshold rules lose uncertainty infor-mation. Other information sources, each with its owninternal processing and threshold rules, might provideadditional reports about Joe, A, and other aspects ofthe situation relevant to inferences about Joes destina-tion. Without uncertainty qualifiers, it is dicult forthe HLIF system to draw sound inferences about Joesdestination. Other limitations of HLIF with respectto the handling of uncertainty are discussed within thecontext of the International Society of Information Fu-sions working group on Evaluation of Technologies forUncertainty Reasoning (ETURWG)4 [7, 8].

Representing uncertainty with ontologies is an activearea of research, especially in the area of the Seman-tic Web (e.g., [9, 10]). HLIF requires reasoning withuncertain information about complex situations withmany interacting objects, actors, events and processes.Automating HLIF therefore requires expressive rep-resentation formalisms that can handle uncertainty.Probabilistic ontologies [11, 12], extend traditional on-tologies to capture both domain semantics and associ-ated uncertainty about the domain. The probabilisticontology language PR-OWL [12] is based on multi-entity Bayesian Networks [13].

2.1 Multi-Entity Bayesian Networks

MEBNs represent the world as a collection of inter-related entities and their respective attributes. Knowl-

2http://www-ksl.stanford.edu/knowledge-sharing/kif/

3http://www.iso-commonlogic.org/

4http://eturwg.c4i.gmu.edu/

edge about attributes of entities and their relation-ships is represented as a collection of repeatable pat-terns, known as MEBN Fragments (MFrags). A setof MFrags that collectively satisfies constraints ensur-ing a unique joint probability distribution is a MEBNTheory (MTheory).

An MFrag is a parametrized fragment of a directedgraphical probability model. It represents probabilis-tic relationships among uncertain attributes of and re-lationships among domain entities. MFrags are tem-plates that can be instantiated to form a joint prob-ability distribution involving many random variables.Such a ground network is called a situation-specificBayesian network (SSBN).

MEBN provides a compact way to represent re-peated structures in a Bayesian Network. There isno fixed limit on the number of random variableinstances, which can be dynamically generated asneeded. The ability to form a consistent compositionof parametrized model fragments makes MEBN wellsuited for knowledge fusion applications [14]. MEBNinference can be performed by instantiating relevantMFrags and assembling them into SSBNs to reasonabout a given situation. As evidence arrives, it isfused into the SSBN to provide updated hypotheseswith associated levels of confidence. These are veryconvenient features for representing diverse informa-tion coming from various sensors, which make MEBNattractive as a logical basis for probabilistic ontologies.

2.2 PR-OWL Probabilistic Ontologies

There are basically three aspects that must be ad-dressed for a representational and reasoning frame-work in support of eective higher-level knowledge fu-sion:

1. A rigorous mathematical foundation,

2. The ability to represent intricate patterns of un-certainty, and

3. Ecient and scalable support for automated rea-soning.

Current ontology formalisms deliver a partial answerto items 1 and 3, but lack a principled, standardizedmeans to represent uncertainty. This has spurred thedevelopment of palliative solutions in which probabil-ities are simply inserted in an ontology as annotations(e.g. marked-up text describing some details relatedto a specific object or property). These solutions ad-dress only part of the information that needs to berepresented, and too much information is lost to thelack of a good representational scheme that capturesstructural constraints and dependencies among proba-bilities. A true probabilistic ontology must be capableof properly representing those nuances. More formally:

Definition 1 (from [11]): A probabilisticontology (PO) is an explicit, formal knowl-edge representation that expresses knowledgeabout a domain of application. This includes:

Types of entities that exist in the do-main;

Properties of those entities; Relationships among entities; Processes and events that happen withthose entities;

Statistical regularities that characterizethe domain;

Inconclusive, ambiguous, incomplete,unreliable, and dissonant knowledge re-lated to entities of the domain; and

Uncertainty about all the above forms ofknowledge;

where the term entity refers to any concept(real or fictitious, concrete or abstract) thatcan be described and reasoned about withinthe domain of application.

POs provide a principled, structured, sharable formal-ism for describing knowledge about a domain and theassociated uncertainty and could serve as a formal ba-sis for representing and propagating fusion results ina distributed system. They expand the possibilities ofstandard ontologies by introducing the requirement ofa proper representation of the statistical regularitiesand the uncertain evidence about entities in a domainof application. POs can be implemented using PR-OWL5, a Probabilistic Web Ontology Language thatextends OWL with constructs for expressing first-orderBayesian theories. PR-OWL structures map to MEBNstructures, so PR-OWL provides a means to expressMEBN theories in OWL.

2.3 The UnBBayes MEBN/PR-OWL Plugin

In order to develop and use POs, we have devel-oped a MEBN/PR-OWL plugin to the graphicalprobabilistic package UnBBayes6, an open source,JavaTM-based application developed at the Universityof Brasilia. The plugin provides both a GUI for build-ing probabilistic ontologies and a reasoner based on theMEBN/PR-OWL framework [15, 16]. Reasoning inthe UnBBayes MEBN/PR-OWL plugin involves SSBNconstruction, which can be seen type of proposition-alization, and the subsequent inferential process overthe resulting SSBN. Figure 1 shows a screenshot of theUnBBayes MEBN/PR-OWL plugin.

5http://www.pr-owl.org

6http://unbbayes.sourceforge.net

Figure 1: The UnBBayes MEBN/PR-OWL plugin

Many HLIF problems involve spatio-temporal enti-ties, and require reasoning with discrete and continu-ous, possibly non-Gaussian, variables. To support thisrequirement, a capability for hybrid MTheories wasadded to the UnBBayes MEBN/PR-OWL plugin. Theplugin can handle MTheories in which continuous vari-ables can have discrete or continuous parents, but nodiscrete variable is allowed to have a continuous par-ent. To specify hybrid models, constructs were addedto the local distribution scripting language for contin-uous distributions. The SSBN construction algorithmfor building the ground model is basically unchangedexcept that local distributions can be continuous.

For inference in a hybrid SSBN, the plugin implementsthe direct message passing (DMP) algorithm [17] tocompute, propagate, and integrate messages. DMPcombines the unscented transformation [18] and thetraditional message-passing algorithm to deal with ar-bitrary, not necessary linear, functional relationshipsbetween continuous variables in the network. DMPgives exact results for polytree conditional linear Gaus-sian (CLG) networks and approximate results for net-works with loops (via loopy propagation), networkswith non-linear relationships (via the unscented trans-formation) and networks with non-Gaussian variables

(via mixtures of Gaussians). Mixtures of Gaussian dis-tributions are used to represent continuous messages.The number of mixture components can be as largeas the size of the joint state space of all discrete par-ents. To achieve scalability, the algorithm can restrictthe number of mixture components in the messages tosatisfy a predefined error bound [19].

Specifically, without loss of generality, suppose a typi-cal hybrid model involving a continuous node X with adiscrete parent node D and a continuous parent nodeU. As shown in Figure 2, messages sent between thesenodes are: (1) message from D to X, denoted asX(D); (2) message from U toX, denoted as X(U);(3) message from X to D, denoted as X(D); and(4) message from X to U , denoted as X(U).

Figure 2: Example hybrid model

In general, for a polytree network, any node X dseparates evidence into {e+, e}, where e+ and eare evidence from the sub-network aboveX and be-low X respectively. The and message maintainedin each node are defined as,

(X) = P (eX |X) (1)

and

(X) = P (X| e+X) (2)

With the two messages, it is straightforward to seethat the belief of a node X given all evidence is justthe normalized product of and values, namely,

BEL(X) = P (X|e) = P (X|e+X , eX)

= (X)(X) (3)

where is a normalizing constant. It can be shownthat for a hybrid network, the message can be re-cursively computed as,

(X) =X

D

Z

UP (X|D,U)X(D)X(U)dU

=X

D

X(D)

Z

UP (X|D,U)X(U)dU

(4)

where the integral of P (X|D = d, U)X(U) over Uis equivalent to a functional transformation of X(U),which is a continuous message in the form of a Gaus-sian mixture.

Similarly, the message for the discrete parents canbe obtained as

X(D = d) =

Z

X(X)

Z

UP (X|D = d, U)X(U)dUdX

(5)where

RU P (X|D = d, U)X(U)dU is a functional

transformation of a distribution over U to X.

On other hand, the message for continuous parentU can be computed as

X(U) =

Z

X(X)

X

D

P (X|D,U)X(D)X(D)dX

=X

D

X(D)

Z

X(X)P (X|D,U)dX

(6)

Equations (3) to (6) form a baseline for computingdirect messages between mixed variables.

As mentioned earlier, with the unscented transforma-tion, this method can be modified for arbitrary non-linear non-Gaussian hybrid models. In addition, thealgorithm is scalable by combining the mixture com-ponents in the messages with any given error bound

3 Maritime Domain Awareness PO

In 2008, the Department of Defense issued a direc-tive to establish policy and define responsibilities forMaritime Domain Awareness (MDA).7 The directivedefines MDA as the eective understanding of theglobal maritime domain and its impact on the secu-rity, safety, economy, or environment of the UnitedStates. The ability to automatically integrate in-formation and recommendations from multiple intel-ligence sources in a complex and ever-changing envi-ronment to produce a dynamic, comprehensive, andaccurate battlespace picture is a critical capability forMDA. This section reports on a prototype probabilis-tic ontology for maritime domain awareness (MDA-PO). This model, which is depicted in Figure 3, wasdeveloped as part of the PROGNOS project [20, 21],with the assistance of two retired Navy ocers whoserved as subject-matter experts.

Figure 4 depicts one of the MFrags of the MDA-PO,the AggressiveBehavior MFrag. As the name implies,this is a chunk of knowledge that captures some ofthe concepts and relationships that are useful to in-fer whether a ship is displaying aggressive behavior.The three dierent types of MFrag nodes can be seen:Context, Input, and Resident nodes.

Resident nodes are the random variables that formthe core subject of an MFrag. The MFrag defines alocal distribution for each resident node as a functionof the parents of the resident node in the fragmentgraph. They can be discrete or continuous. There arethree discrete nodes in this MFrag, which are depictedas yellow rounded rectangles in the picture, and fivecontinuous nodes, depicted as rounded rectangles withdouble lines.

As an example of how the representation works, re-ports on the propeller turn count of a ship will be anindicator of whether the ship speed is changing or not.Also, there will be dierent probability distributionsfor speedChange(ship) if the ship is behaving aggres-sively or not (i.e. if the state of node hasAggressive-Behavior(ship) is true or false).

Input nodes, depicted as gray trapezoids in the figure,serve as pointers referring to resident nodes in otherMFrags. Input nodes influence the local distributionsof resident, but their own distributions are defined inthe MFrags in which they are resident.

In a complete MTheory, every input node must pointto a resident node in some MFrag. For instance, thehasBombPortPlan(ship) input node influences the dis-tribution of all the hasAggressiveBehavior(ship) nodes

7www.dtic.mil/whs/directives/corres/pdf/200502p.pdf

Figure 3: The MDA-PO

that would be instantiated in an SSBN constructionprocess.

Context nodes are Boolean (i.e., true/false) randomvariables representing conditions that must be satisfiedfor the probability distribution of an MFrag to apply.Like input nodes, context nodes also have distributionsdefined in other MFrags.

By allowing uncertainty on context nodes, MEBN canrepresent several types of sophisticated uncertaintypatterns, such as relational uncertainty or existenceuncertainty. There is only one context node in the Ag-gressiveBehavior MFrag, seen in the figure as a greenpentagon.

The MDA-PO is described in detail in [22]. In PROG-NOS, the MDA-PO was also used to build the modelused to run the test and evaluation process, which weexplain in the next Section.

4 Experimental Results

The main objective of the set of experiments presentedin this paper was to assess the accuracy, scalability,and overall performance of the SSBN construction andDMP algorithms combined. As a benchmark, we usedthe UnBBayes implementation of the Junction Tree(JT) algorithm, which is a well-known belief propa-gation method for Bayesian networks [23] and the fo-

Figure 4: The Aggressive Behavior MFrag

cus of various eorts on algorithm optimization (e.g.[24, 25]).

4.1 Setup and Metrics

Obtaining a real data set for maritime HLIF was notan option for our team. Therefore, we generated vari-ous synthetic datasets through an agent-based simula-tion module, depicted in Figure 5. The module gener-ates simulated scenarios, including entities (e.g., ships,people) and their features. The simulated scenariosserve as the ground truth for evaluating performance.The simulation module also generates reports of thekind the eventual operational system is expected toreceive, thus exercising the interfaces and the reason-ing module in a realistic manner [21].

The simulation is based on maritime activities (regularand suspicious) with the objective of prevention anddisruption of terrorist attacks, sabotage, espionage, orsubversive acts. Therefore, the agents on the simu-lation tool simulate commercial, fishing, recreational,and other types of ships in their normal and suspiciousbehaviors. Suspicious behaviors are characterized byships that do not follow their regular or most prob-able routes according to their origin and destination,by ships that meet in the middle of the ocean for noapparent reason, etc.

For the experiments, the simulation engine generated9 types of scenarios with dierent combinations of thenumber of ships and the associated entities (e.g. or-ganizations, people, etc.). The maximum size of thedataset was limited to 10K entities. After generatingeach dataset, we added noise as to assess robustnessto model misspecification. The scenario for the ex-periments emulates a U.S. Navy destroyer conductingMaritime Security Operations in a relatively busy area.This is a needle in a haystack type of problem, inwhich the destroyer has information about dozens ofships within a certain radius, but can only verify a few

of them. In this case, the HLIF system must integratethe data coming from the ship sensors with informa-tion coming from other sources, such as intelligence re-ports, signals intelligence, HUMINT, and others. Weemulate this in the experiments with area queriesin which all ships within a 60NM radius are queriedby the system. More precisely, information on all nknown ships within that radius trigger the instantia-tion of MFrags storing pertinent knowledge, includingthe one containing the shipOfInterest(ship) node. Thesystem would then query the n shipOfInterest(ship)nodes that were instantiated.

All experiments were performed in a dedicated com-puter with an Intel quad-core i7TMprocessor with 8GB of RAM, and running MS Windows 7TM64bit.

Accuracy is assessed by the quadratic scoring rule [26]:

B(r, i) =CX

j=1

(yj rj)2

where yj = 1 when the jth event is correct and 0 oth-erwise. C is the number of classes. This is a properscoring rule, i.e., the score is minimized when the as-sessed probability is equal to the actual frequency.

To assess scalability, we measured the computationtime as a function of the generated SSBN size andthe number of ships involved in a query.

4.2 Preliminary Results

The results for accuracy are depicted in Table 1. Fromthe obtained scores, it is clear that the Hybrid sys-tem performed better in capturing both the cases inwhich the shipOfInterest(ship) node state was true( 10.36% better) in the ground truth, as well as thosein which the node state was false ( 14.02% better).

Table 1: Results for AccuracyQueries on the

Ship of Interestnode

HybridSystem

DiscreteSystem

Ship of Interest =true (ground truth)

0.88203 0.79947

Ship of Interest =false (ground truth)

0.89439 0.78439

These results are consistent with expectations, giventhe inherent inaccuracies in discretizing the continuousrandom variables in the MDA-PO. The 10 to 14% im-provement from the hybrid with respect to the discretemodel was consistent all over the 9 datasets. However,since the datasets were all generated from the samemodel, it is dicult to assess robustness with this runof experiments. In any case, more complex relation-ships between nodes are likely to increase the dierence

Figure 5: PROGNOS simulation module

in accuracy between the JT and the DMP systems.

Figure 6 below shows the results of the area query ex-periments. The x-axis conveys the number of nodesgenerated by each query, which tends to be correlatedwith the number of ships. However, it was not uncom-mon to see a few ships generating a large network orvice-versa. The y-axis depicts query time in millisec-onds.

Figure 6: Area Query Time vs. Network Size

Regarding performance, most of the generated net-works were between 100 and 500 nodes, and generallyyielded a query time below 2 seconds for DMP and 5seconds for JT. The maximum query time for JT was7.3 seconds, while the DMP system worst case was 6.4seconds for a query. The results also show lower vari-ance for DMP query times for a given network size.

Figure 7 shows results for query time vs. number ofships within the 60NM area.

Figure 7: Query Time vs. Number of Ships

This was a dierent run of experiments, in which thefocus was on keeping a controlled number of shipswithin the query area. This allowed an assessment ofhow each system reacted to the controlled increase inthat number. The performance of JT stayed relativelysteady, while the DMP system performed much betterfor simpler problems but approached the performanceof JT when the number of ships was above twenty.

These results were also expected, since our implemen-tation of DMP was not as optimized as the JT imple-mentation in UnBBayes. More specifically, the DMPalgorithm was initially implemented in MATLABTM,and the translation to JavaTMwas not tuned for per-formance. Yet, the graph suggests a linear increase inthe range considered.

5 Discussion

The experiments were meant to simulate an HLIF sys-tem within a relatively simple scenario. In spite of theoverall size of the experiments and the fact that it wasconducted within a controlled environment, the per-formance figures are promising. There remain manyways to improve the ecacy of the algorithm. As pre-viously mentioned, the main objective of the testingand evaluation was to assess the gains in accuracy,which clearly lived up to our expectations.

The results also show promise for the feasibility of us-ing probabilistic ontologies as a driver for HLIF sys-tems. Our future steps towards this goal are to con-tinue the optimization of the algorithms, and to seekout new forms of knowledge acquisition techniques.The latter involves automated learning, which hasbeen the subject of our latest research eorts. Wealso plan to address the research on rare events, andto work with other datasets.

Acknowledgements

The PROGNOS project was partially funded by theOce of Naval Research. The authors acknowledgeRichard Haberlin and Michael Lehocky who served assubject-matter experts for developing the MDA-PO,and Rommel Carvalho, for his various contributionsto the PROGNOS project.

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