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An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks
An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks
An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks
An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks
An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks
An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks
An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks
An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks
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An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks


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Wireless sensor networks (WSNs) havean intrinsic interdependency with the environments inwhich they operate. The part of the world with whichan application is concerned is defined as that …

Wireless sensor networks (WSNs) havean intrinsic interdependency with the environments inwhich they operate. The part of the world with whichan application is concerned is defined as that applica-tion’sdomain.Thispaperadvocatesthatanapplicationdomain of a WSN can serve as a supplement to analysis,interpretation,andvisualisationmethodsandtools.Webelieve it is critical to elevate the capabilities of thedata mapping services proposed in [1] to make use of the special characteristics of an application domain. Inthis paper, we propose an adaptive Multi-DimensionalApplication Domain-driven (M-DAD) mapping frame-work that is suitable for mapping an arbitrary num-ber of sense modalities and is capable of utilising therelations between different modalities as well as otherparameters of the application domain to improve themapping performance. M-DAD starts with an initialuser defined model that is maintained and updatedthroughout the network lifetime. The experimentalresults demonstrate that M-DAD mapping frameworkperforms as well or better than mapping services with-out its extended capabilities.

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  • 1. An Integrated Inductive-Deductive Framework for Data Mapping in Wireless Sensor Networks Mohammad Hammoudeh, Robert Newman, Sarah Mount, Christopher Dennett School of Computing and IT University of Wolverhampton Wolverhampton, UK Email: {m.h.h, r.newman, s.mount, c. dennett} Abstract—Wireless sensor networks (WSNs) have A domain model carries knowledge of an application do-an intrinsic interdependency with the environments in main. It is a conceptual model of a system which describeswhich they operate. The part of the world with which the various real world entities involved in that system andan application is concerned is defined as that applica-tion’s domain. This paper advocates that an application relationships between them. The domain model providesdomain of a WSN can serve as a supplement to analysis, a structural view of the system which we suggest using tointerpretation, and visualisation methods and tools. We complement the information gained from analysing databelieve it is critical to elevate the capabilities of the gathered by a WSN. The logical integration of a domaindata mapping services proposed in [1] to make use of model and sensory data from multiple heterogeneous sen-the special characteristics of an application domain. In sory sources can be effectively used to explain past obser-this paper, we propose an adaptive Multi-DimensionalApplication Domain-driven (M-DAD) mapping frame- vations as well as to predict future observations. It exploitswork that is suitable for mapping an arbitrary num- the local semantics from the environment of each sensor. Itber of sense modalities and is capable of utilising the also takes advantage of human guidance and informationrelations between different modalities as well as other from other available sources, e.g. satellites. Furthermore,parameters of the application domain to improve themapping performance. M-DAD starts with an initial it maintains the overall coherence of reasoning aboutuser defined model that is maintained and updated the gathered data and helps to estimate the degree ofthroughout the network lifetime. The experimental confidence using probabilistic domain models. The useresults demonstrate that M-DAD mapping framework of knowledge made available by the domain model canperforms as well or better than mapping services with- also be a key to meeting the energy and channel capacityout its extended capabilities. constraints of a WSN system. The energy efficiency of the system can be improved by utilising a domain model in the I. Introduction process of converting data into increasingly distilled and WSNs are being deployed for an increasingly diverse high-level representations. Finally, domain models helpset of applications each with different characteristics and early detection and reduction of the amount of ineffectiveenvironmental constraints. As a consequence, scientists data forwarding across the network, rather than sustainingfrom different research fields have begun to realise the im- the energy expense of transmitting ineffective messagesportance of identifying and understanding the characteris- further along the path to the destination.tics and special deployment needs of different application II. Related Workdomains. In many WSN deployments, the network ownershave some knowledge about the monitored environment WSN applications that incorporate the special charac-characteristics in which the target system operates. For teristics of the environment in which they operate areexample, in forest fire applications [2], [3], information starting to appear on the horizon. The authors of theabout the forest topography can be obtained from GIS BBQ [4] focus on using probabilistic models of the real-systems or satellites maps. world to provide approximate answers efficiently. In con-
  • 2. sensed datatrast to our work, efforts such as BBQ [4] have adopted structuralan approach that assumes that intelligence is placed at knowledgethe edge of the network, such as a sink, which is assumed process of sensed data model model building refinementto be less resource constrained than the sensor nodes. Aninterrogation-based approach can not guarantee that all Figure 1. Merging of inductive and deductive methodsanomalies will always be detected. Finally, this approachwas found to be effective with stable network topologies.In highly dynamic network topologies the cost of checking physical principles. Deductive methods rely on a precisewhether the estimation is accurate becomes excessively application environment and the explicit knowledge, calledhigh. Such a model will require collecting values of all structural knowledge, of the underlying domain using firstattributes at one location at each time step, and the cost of principles to create a model of the problem typically yield-doing so will most likely reduce any savings in source-sink ing governing equations [6]. On the other hand, inductivecommunication that might result. methods utilises experimental data as the only source of Motivated by BBQ, Ken [5] exploits the fact that physi- available knowledge [6]. Some applications can only becal environments frequently exhibit predictable stable and treated using experimental data knowledge due to the lackstrong attribute correlations to improve compression of the of other application domain knowledge. Nevertheless, thedata communicated to the sink node. This approach is use of inductive information helps in the generation of datasubject to failure as basic suppression. It does not have consistency checks based on the structural knowledge ab-any mechanism to distinguish between node failure and stractions given in the domain model. Finally, applicationsthe case that the data is always within the error bound. have been observed to perform significantly better if theyThey propose periodic updates to ensure models can not use a combination of the two methods [7]. Figure 1 showsbe incorrect indefinitely. This approach is not suitable how the inductive and deductive methods can be mergedfor raw value reconstruction; for any time-step where the to capture the advantages of both methods. After themodel has suffered from failures and is incorrect, the structural knowledge is fed to the system model (deductivecorresponding raw value samples will be wrong. Finally, as process), the sense data is used to refine and complementthe approach presented in [4], Ken can only handle static the basic structural model of the application domain. Thisnetwork topologies and does not make use of redundancy. refinement procedure can be done continuously through- The authors of [1] propose a distributed data map- out the network life to keep consistent mapping betweenping service where groups of network nodes cooperate the physical model and the sense produce local maps which are cached and merged at M-DAD makes use of knowledge given by the domaina sink node, producing a map of the global network. model in the map generation process. Knowledge fromThe sink node receives periodic map updates from each domain models provides guidance for map generationcluster head used to refine an up-to-date global map. from high dimensional data set and has the potential toThe distributed mapping service is made of four modules: significantly speed up the map generation process andApplication (contains the user defined applications, e.g. deliver more accurate maps. To the best of our knowledge,isopleth maps), Interpolation (a building block to generate only few previous studies have considered the domainmaps), In-network Processing (process raw data received model. For instance, Hofierka et al. [8] incorporate thefrom various cluster heads) and Routing (responsible for topographic characteristics to give better daily and annualdata communication). This approach does not incorporate mean precipitation predictions. The general lack of anthe characteristics of the application domain. appropriate data mapping framework for exploiting these rich sense data resources motivates this work. III. M-DAD Mapping Framework Details Moreover, M-DAD mapping framework performs map- The proposed mapping framework, M-DAD, utilises a ping from related multiple types of the sense data toblend of both inductive and deductive models to establish overcome the limitations of generating a map from a singlea successful mapping between sense data and universal sense modality. A single sense modality map typically
  • 3. reveals only a small number of aspects of the monitored interpolation problem can be stated as follows:phenomena and is unable to infer the correct relations Given a set of randomly distributed data pointsamong other types in multi-modal sensing applications. xi ∈ Ω, i ∈ [1, n] , Ω ⊂ Rn (1)In addition, high-throughput data sets also often containerrors and noise arising from imperfections of the sensing with function values yi ∈ R, and i ∈ [1, N ] we require adevices. Maps generated from a combination of different continuous function f : Ω −→ R to interpolate unknowntypes of data are likely to lead to a more coherent map intermediate points such thatby consolidating information on various aspects of themonitored phenomena. Additionally, the effects of data f (xi ) = yi where i ∈ [1, N ] . (2)noise on generated maps will be dramatically reduced, We refer to xi as the observation points. The integer nassuming that sensing errors across different data sets is the number of dimensions and Ω is a suitable domainare largely independent and the probability an error is containing the observation points. When rewriting thissupported by more than one type of data is small. A definition in terms of relationships between sets we getnatural approach is to make use of the relation between the following:the multiple types of sense data to generate a map is Given N ordered pairs of separated sets Si ⊂ Ω withto combine the maps generated from different types of continuous functionsdata. We may combine the maps in different ways suchas accepting a value at an observation point only when fi : Si −→ R, i ∈ [1, N ] (3)it is commensurate with all maps as defined in the given we require a multivariate continuous function f : Ω −→ R,model. More interestingly, and allegedly with guarantees defined in the domain Ω = S1 ∪ S2 ∪ ... ∪ Sn−1 ∪ Sn of theof delivering better maps, multiple types of data can n-dimensional Euclidean space wherebe analysed concurrently under an integrated relationalmodel. The latter method is novel in the sense that most f (xi ) = fi (xi ) ∀xi ∈ Si where i ∈ [1, N ] (4)existing n-dimensional interpolation schemes are defined The proof is omitted for applying one-dimensional interpolation in each separate Using the point to set distance generalisation, the func-coordinate dimension without taking advantage of the tion f can be determined as a natural generalisationknown relations between diverse dimensions [9]. of methods developed for approximating univariate func-A. Multivariate Spatial Interpolation in M-DAD tions. Well-known univariate interpolation formulas are extended to the multivariate case by using Geometric Most spatial data interpolation methods are based on Algebra (GA) in a special way while using a point to setthe distance between the interpolation location P and the distance metric. Burley et al. [10] discuss the usefulness ofgiven set of data points. M-DAD defines a new metric GA for adapting univariate numerical methods to multi-for distance, suitable for higher dimensions, in which the variate data using no additional mathematical derivation.concept of closeness is described in terms of relationships Their work was motivated by the fact that it is possiblebetween sets rather than in terms of the Euclidean dis- to define GAs over an arbitrary number of geometrictance between points. Using this distance metric, a new dimensions and that it is therefore theoretically possible togeneralised interpolation function f that is suitable for an work with any number of dimensions. This is done simplyarbitrary number of variables is defined. by replacing the algebra of the real numbers by that of In multivariate interpolation every set Si corresponds the GA. We apply the ideas in [10] to find a multivariateto an input variable i.e. a sense modality, called i, and analogues of univariate interpolation functions.referred to as a dimension. In M-DAD, the distancefunctions do not need to satisfy the formal mathematical B. Scale-based Local Distance Metricrequirements for the Euclidean distance definition. The In this section we modify the distance metric definedpower of such a generalisation can be seen when we include in Section III-A to include the knowledge given by thethe time variable as one dimension. The spatial data domain model. The domain model helps to significantly
  • 4. reduce the size of the support nodes set. The difference in in the system. Equation 6 can now be extended to includethe size of the support nodes set can be several orders the domain model parameters of arbitrary dimensionalof magnitude with increasing problem dimension. The system. Then the dimension-based scaling metric can beincrease in the support size can lead to an increase in defined asthe computation and processing times of the interpola-tion algorithm and lead to the same drawbacks of global mP = L (K(P, Si ), δ (Si )) i ∈ [0, n] (7) iinterpolation methods. Therefore, the proposed metric where Si = CP and CP is the dimension containing P .attempts to balance the size of the support sets with theinterpolation algorithm complexity as well as interpolation IV. Distributed Self-Adaptation in Mappingaccuracy. Services We define the term scale for determining the weight A. Benefits of Self-Adaptationof every given dimension with respect to P based on a In this section we extend the capabilities of M-DADcombined Euclidean distance criteria and the information to overcome challenges imposed by the described externalalready known about the application domain a prior net- system changes, e.g. topographical changes, through ap-work deployment. While the term weight is reserved for plying self-adaptation intelligence to continuously adaptthe relevance of a data site by calculating the Euclidean to erratic changes in the application domain conditions.distance from that location to P . A special case is when fi At run time, M-DAD integrates the sensory data withis identical for all Si which means that all sets have the contextual information to update the initial applicationsame scale. domain model provided by network owners to maintain For the purposes of M-DAD we define a new scale-based a coherent logical picture of the world over time. Self-weighting metric, mP , which uses the information given adaptation is particularly useful in long-term WSNs de-by domain model to alter the distance weighting function ployments where the environmental conditions changesto improve the interpolation results when applied to an significantly over time which necessitate updating thearbitrary number of dimensions. In M-DAD, the support domain model to reflect the changes in the contextualset, Ci , for P is calculated using mP . Symbolically, Ci is knowledge provided by the physical constraints imposedcalculated as by the local environmental conditions where sensors are located. This allows mapping services to evolve at run- Ci = L (d (P, Ej ) , δ (Si )) ∀Ej ∈ Si (5) time with less intervention of the user and leads to near-where Si is a set of observation points, i ∈ [1, N ], L is a optimal and flexible design that is simple and inexpensivelocal model that selects the support set for calculating P , to deploy and maintain. This adaptation procedure willd is an Euclidean distance function, Ej is an observation recover, over time, the effects of user domain modellingpoint in the dimension Si , and δ(Si ) a set of parameters inaccuracies.for dimension Si . Each dimension can have different set We realise that self-adaptation is a challenging problemof parameters. These parameters are usually a set of rela- and considerable work is being done by the researchtionships between different dimensions or other application community in that area. However, in this work we aimdomain characteristics such as obstacles. When predicting to deal with a small set of adaptivity issues that have athe value of a point in dimension Si we refer to that significant effect on the mapping services.dimension as SP . B. Adaptability Implementation in M-DAD Uni-dimensional distance weighting functions can be To implement adaptability in M-DAD we exploit theextended to multi-dimensional distance weighting systems interpolation capability of the network to perform localas follows training of the map generation service. Each node uses ω = K (P, Si ) , i ∈ [0, n] (6) the readings of its surrounding nodes to predict its ownwhere K (P, Si ) is the distance from the interpolation reading value (y ) using mP (eq. 7). Then, y is comparedposition P to data set Si and n is the number of dimensions to the node measured value, y. It is desirable that the
  • 5. estimate of y minimises the standard deviation (σ). Nodes votes υ disseminate the bill to the chamber and all nodesmodify the size of the support set to include the minimum implement the new changes that have been agreed on.number of nodes needed to predict y with a certain level The value of υ was empirically estimated to be over 50%of accuracy. Furthermore, in multi-dimensional applica- of chamber population because it helps to avoid falsetions, nodes will change the weight of each dimension positives. Once a bill is approved by one chamber, it isto improve the prediction accuracy of y . In fact, nodes sent to other chamber heads who may accept or reject it.will alter the relationships between different dimensions In order for the bill to become a state law, all chamberinitially given in the domain model in order to recover heads must agree to identical version of the bill. Whenthe effect of inaccuracies in the given domain model or to the bill is submitted to the president, the sink node, headapt to emerging environmental changes. In that, these may choose to sign the bill, thereby making it a state law.model updates influence the estimation results because y V. Experimental Evaluationis calculated using mp . Finally, a prediction accuracycriterion, ∆, is defined as the average σj where σj = Experiment 1: Incorporation of the Domain 2 Model in the Mapping Services i (yi − yi ) j ∈ [1, n] and i ∈ [1, N ] where n is thenumber of dimensions and N is the number of readings in Aim: The aim of this experiment is to study the effect of σj integrating the knowledge given by the domain model intodimension j. Then ∆ is written as ∆ = n j ∈ [1, n].∆ must always be minimised to achieve the best mapping the mapping services.results. Procedure: In this experiment the effective thermal dif- fusivity in a cargo ship is studied. Some aspects of a cargo However, when individual nodes alter their programmed ship fire were modelled, particularly, heat diffusion in thedomain model independently from the network, the map- metal body of the ship. The model was restricted to aping service may become unstable because of the inconsis- small area of the ship deck which has two big doors. Thetency in the domain model defined on various nodes. Such chosen part of the ship deck is modelled by a brass sheetinconsistencies may lead to inconsistent system states and which contains a hole segment excavation to model anconflicting differences in calculating mapping values. To opened door. A simple domain model was defined to carryensure mapping stability we propose a Virtual Congress information about doors that when opened they impactAlgorithm to manage global model updates locally. the heat diffusion in the ship body. The hole segment The Virtual Congress Algorithm (VCA) provides a that represents an opened door was excavated in thehigh-level collaboration environment in which the system brass sheet with 10mm width and 2cm length. A FLIRcan achieve globally efficient behaviour under dynamic ThermaCAM P65 Infrared (IR) camera [11] was usedenvironmental conditions. The network is viewed as a to take sharp thermal images and produce an accuratevirtual congress where nodes are senators who vote for temperature analysis and results. The IR camera deliverslegislating changes to the domain model in response to 320 × 240 IR resolution (640 × 480 pixels, full colour) atlocally detected environmental conditions. This algorithm 0.08C thermal sensitivity. Finally, a 1371o C blue flameis an attractive solution as senators collaboratively decide was placed on the middle of one edge of the brass sheetupon their local knowledge on the behaviour and correct- as a heat source. Brass (an alloy of copper and zinc) wasness of the system. Logically related nodes, chambers, are chosen for this experiment because it is a good thermalgranted some power to impute the local changes, federal conductor.laws, that is not detected by all nodes in the network. The first experiment was ran using the brass sheetA senator may introduce a proposal in the chamber as a before the hole segment excavation. After applying heat,bill. To prevent overloading the chamber with proposals, thermal measurements from the Toradex Oak sensors wereeach senator must monitor the changes over time using recorded in addition to a thermal image taken by the IRequation ?? before putting them into a bill. Senators camera. The mapping services were ran over a subset ofsend their voting results to the proposing senator. The the data collected from this experiment to observe howproposing senator, upon receiving the required number of the heat will diffuse in the brass sheet in the absence
  • 6. Figure 2. Heat diffusion map taken by ThermaCAM P65 Infrared Figure 3. Heat map generated by the standard mapping service(IR) camera. defined in [1].of any obstacles. The same experiment was repeated onthe sheet with the segment hole excavation and sensorthermal measurements as well as a IR camera image weretaken after applying heat on the brass sheet. The mappingservice were ran using the same size of the thermal data-setused in the previous experiment. Three experimental runswere performed: (1) Run the mapping services without Figure 4. Interpolated heat map generated by M-DAD given obstacle location and length.any domain model knowledge. Particularly, the presenceof the obstacle and its characteristics. (2) Run the map-ping service which integrates some of the domain model some interpolation areas contain many sensor readingsknowledge. Particularly, the presence of the obstacle, its with almost the same elevation. That asserts that modifi-position, and length. (3) Run the mapping service which cations to map generation services are sometimes neededintegrates all the knowledge given by the domain model. in order to interactively correct the mapping parameters.Particularly, the presence of the obstacle, its position, Figure 4 shows the map generated by the M-DADlength, and strength. mapping framework. M-DAD was given some information about the application domain including the existence ofResults and discussion: Figure 2 shows the heat diffu- the obstacle, its location and length. We observe that thesion map generated by the IR camera. Given that the heat map obtained by M-DAD conserves perfectly the globalis applied at the middle of the top edge of the brass sheet appearance as the distributed mapping service (Figure 2).and the location of the obstacle, by comparing the left side However, using the given local semantics, M-DAD reducedand right side areas around the heat source, this figure the prediction error and visually it accurately captured theshows that the existence of the obstacle has an effect on effect of the heat obstacle on heat diffusion through theheat diffusion through the brass sheet. It its observed that brass sheet. The M-DAD generated map is smoother thanthe obstacle strongly reduced the temperature rise in the that rendered with the distributed mapping services, onlyarea on its right side. This map has been randomly down- in some sub-regions containing the obstacle and aroundsampled to 1000 points, that is 1.5% of the total 455 × 147 the heat source be used by the mapping service to generate the totalheat map. Figure 3 shows the map generated by the distributedmapping service described in [1]. Compared with Fig-ure 2, the obtained map conserves perfectly the globalappearance and many of the details of the original mapwith 98.5% less data. However, the area containing theobstacle has not been correctly reconstructed and causedhard edges around the location of heat source. This is due Figure 5. Interpolated heat map generated by M-DAD givento attenuation between adjacent points and the fact that obstacle location, width and length.
  • 7. M-DAD vs. standard Shepard Figure 5 shows the map generated by M-DAD with a 45 40more complex domain model than the previous M-DAD 35version (Figure 4). In this version we give M-DAD the 30 Standard Deviationobstacle width. We notice a better approximation to the 25real surface near the obstacle. The new details included in 20the domain model removed two artifacts from both ends 15of the obstacle. This is due to the inclusion of the obstacle 10 5 Standard Shepard M-DADwidth in weighting sensor readings when calculating P 0which further reduces the effect of geographically nearby 0 2 4 Location 6 8 10sensors that are disconnected from P by an obstacle. Figure 6. The standard deviation of temperature values at 10Conclusion: This experiment proves that the incorpo- locations calculated by M-DAD using the humidity map.ration of the domain model in the mapping service sig-nificantly improves the performance of the distributed nodes which are more related to P , for example, nodesmapping services. that have close humidity reading to that of P .Experiment 2: Mapping from Related Multiple Conclusion: This experiment proves that mapping fromDimensions related multiple dimensions can improve the generatedAim: The aim of this experiment is to study if mapping map quality. This observation is confirmed by the datafrom related multiple types of the sense data can lead to shown in Figure 6. The results from this experiment andan improved mapping performance by overcoming some Experiment 1 confirms the general theory of M-DADof the limitations of generating a map from a single sense defined in Section III.modality.Procedure: 10 Toradex Sensors equipped with humidity Experiment 3: Adaptations to Changes in the Do-and temperature sensors were placed over the brass sheet. main ModelCold water was sprayed onto the brass sheet to increase Aim: The aim of this experiment is the study the effective-the humidity in order to make relationships between the ness of the proposed VCA in modifying the domain modeltemperature and humidity more visible. Then, a blue flame to better fit the current state of the application domain.was placed on the middle of the top edge of the brass Procedure: The same experimental setup described insheet. Finally, the following steps were performed: (1) Experiment 1 is used here. The obstacle length was in-one temperature reading was removed from the collected creased from 2cm to 3.6cm. Then, the bill which containsdata set; (2) the distributed mapping service was used the best detected obstacle length value, the federal laws,to calculate the removed temperature reading using the and the state laws were examined. Wireless communica-rest of the data set; (3) M-DAD was used to calculated tions breaks caused by an obstacle attenuation are hard tothe removed temperature reading using the rest of the predict, but can be estimated using published metrics suchdata set; (3) the standard deviation was calculated for that in [12]. It was assumed that the obstacle is continuousthe temperature value resulted from 2 and 3; (4) steps 1 and the existence of this obstacle between two directlyto 4 were repeated for each of the 10 sensors temperature communicating nodes will break the wireless links betweenreadings them. The local semantics of the application domain wereResults and discussion: The relationship between the defined to interpret the break of direct wireless links be-humidity and temperature was used to create a temper- tween two nodes while being able to communicate throughature map using the humidity map. Figure 6 shows the an intermediate node(s) as there exists an obstacle betweenstandard deviation of the calculated temperature values the two communicating M-DAD and the distributed mapping services. It is Results and discussion: Table I shows three M-DADobserved that M-DAD reduced the standard deviation by mapping runs each with different node distributions. Webetween 0.17% to 12% compared to the standard mapping test three different randomly distributed nodes topolo-service. This is done by constructing the support set from gies because obstacle detection according to the model
  • 8. Table I tem changes. It starts with an initial model then it adapts The obstacle length (in pixels) in the best proposed bill and updates itself to give more precise image about theand the federal laws in three M-DAD mapping runs at 1000 nodes density. real world through a training procedure. Experimental results shows that M-DAD improves the mapping quality Run Num of bills Best bill Federal law 1 17 59.57 52.0 in terms of maps predictive error and smoothness. 2 19 60.0 57.74 References 3 14 60.0 52.0 [1] M. Hammoudeh, J. Shuttleworth, R. Newman, and S. Mount, “Experimental applications of hierarchical mapping services indescribed here is highly dependent on the nodes location wireless sensor networks,” in SENSORCOMM ’08: Proceedings of the 2008 Second International Conference on Sensor Tech-and density around the obstacle. Table I shows the number nologies and Applications, 2008, pp. 36–43.of proposed bills, the best proposed bill and the agreed bill [2] M. Hefeeda and M. Bagheri, “Wireless sensor networks for earlyfor each mapping run. We notice that the obstacle length detection of forest fires,” in International Workshop on Mobile Ad hoc and Sensor Systems for Global and Homeland Securitywas always detected accurately and that the best proposed (MASS-GHS 07), Italy, October 2007.bill was not always agreed locally. This is partially due to [3] C. Hartung, R. Han, C. Seielstad, and S. Holbrook, “Firewxnet:the cluster formation process which is able to deal with a multi-tiered portable wireless system for monitoring weather conditions in wildland fire environments,” in MobiSys ’06: Pro-obstacles (see [13]). Nonetheless, the average VCA agreed ceedings of the 4th international conference on Mobile systems,bills in the three mapping runs was 53.91 pixels which is applications and services, 2006, pp. 28–41.close to the actual obstacle length (60 pixels). Adapting [4] A. Deshpande, C. Guestrin, S. Madden, J. Hellerstein, and W. Hong, “Model-driven data acquisition in sensor networks,” into the new obstacle length improves the produced map VLDB ’04: Proceedings of the Thirtieth international conferencequality. Quantitatively, the RMS difference between the on Very large data bases. VLDB Endowment, 2004, pp. 588–maps generated with 30 and 60 pixels obstacle length 599. [5] D. Chu, A. Deshpande, J. Hellerstein, and W. Hong, “Approx-increased by 1.0. imate data collection in sensor networks using probabilistic We notice that in the three mapping runs, zero bills models,” in ICDE ’06: Proceedings of the 22nd Internationalbecame federal laws. This is because all the changes in the Conference on Data Engineering, 2006, p. 48. [6] P. Hertkorn and S. Rudolph, “From data to models: Synergiesapplication domain were local to part of the network and of a joint data mining and similarity theory approach,” in SPIEthe majority of the clusters did not sense these changes. Aerosense 1999 Conference On Data Mining and KnowledgeThis illustrates the mutual benefit of localising the VCA Discovery, 1999. [7] ——, “Dimensional analysis in case-based reasoning,” in Inter-and distributing it over two levels: the local/cluster level; national Workshop on Similarity Methods, S. I. fr Statik undand the global/network level. Dynarnik der Loft-und Raumfahrtkonstruktionen, Ed., 1998,Conclusion: This experiment shows that VCA helps to pp. 163–178. [8] J. Hofierka, J. Parajka, H. Mitasova, and L. Mitas, “Multivari-adapt to some changes in the domain model in a dis- ate interpolation of precipitation using regularized spline withtributed manner. This experiment is an instance of the tension,” Transactions in GIS, vol. 6, pp. 135–150, 2002.general case studied in Experiment 2, particularly, we are [9] K. C. Johnson, Multidimensional Interpolation Methods, KJ Innovation, 2006, the nearest neighbour triangulation RF connectivity as one dimension to predict the heat map. Therefore, [10] M. Burley, K. Bechkoum, and G. Pearce, “A formative surveythe improved mapping performance proved in this exper- of geometric algebra for multivariate modelling,” in UK Society for Modelling and Simulation, 2006, pp. 37–40.iment confirms the results found in Experiment 2. [11] F. Systems, “Thermacam p65,” print.htm, 2008, [Online; accessed 6-November-2008]. VI. Conclusion [12] Extricom, Application Note - Wired and Wireless LAN Security, In this paper we propose a new mapping framework Juniper Networks, November 2007. [13] M. Hammoudeh, A. Kurtz, and E. Gaura, “MuMHR: multi-called M-DAD. M-DAD is capable of dealing with an path, multi-hop, hierarchical routing,” in International Con-arbitrary number of sense modalities, performs distributed ference on Sensor Technologies and Applications (SENSOR-self-adaptation, exploits the application domain model, COMM2007), 2007.and generates maps using relationships between differentsense modalities. M-DAD spontaneously responses to sys-