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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}@wlv.ac.uk


   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 describes
which they operate. The part of the world with which
                                                             the various real world entities involved in that system and
an application is concerned is defined as that applica-
tion’s domain. This paper advocates that an application
                                                             relationships between them. The domain model provides
domain of a WSN can serve as a supplement to analysis,       a structural view of the system which we suggest using to
interpretation, and visualisation methods and tools. We      complement the information gained from analysing data
believe it is critical to elevate the capabilities of the    gathered by a WSN. The logical integration of a domain
data 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-Dimensional
Application Domain-driven (M-DAD) mapping frame-             vations as well as to predict future observations. It exploits
work that is suitable for mapping an arbitrary num-          the local semantics from the environment of each sensor. It
ber of sense modalities and is capable of utilising the      also takes advantage of human guidance and information
relations between different modalities as well as other
                                                             from other available sources, e.g. satellites. Furthermore,
parameters of the application domain to improve the
mapping performance. M-DAD starts with an initial
                                                             it maintains the overall coherence of reasoning about
user defined model that is maintained and updated             the gathered data and helps to estimate the degree of
throughout the network lifetime. The experimental            confidence using probabilistic domain models. The use
results demonstrate that M-DAD mapping framework             of knowledge made available by the domain model can
performs as well or better than mapping services with-
                                                             also be a key to meeting the energy and channel capacity
out 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 help
set of applications each with different characteristics and   early detection and reduction of the amount of ineffective
environmental constraints. As a consequence, scientists      data forwarding across the network, rather than sustaining
from different research fields have begun to realise the im-   the energy expense of transmitting ineffective messages
portance of identifying and understanding the characteris-   further along the path to the destination.
tics and special deployment needs of different application
                                                                                II. Related Work
domains. In many WSN deployments, the network owners
have 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 are
example, in forest fire applications [2], [3], information    starting to appear on the horizon. The authors of the
about 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-
sensed data
trast to our work, efforts such as BBQ [4] have adopted
                                                                 structural
an approach that assumes that intelligence is placed at         knowledge
the edge of the network, such as a sink, which is assumed                               process of      sensed data     model
                                                                                       model building                 refinement
to be less resource constrained than the sensor nodes. An
interrogation-based approach can not guarantee that all
                                                                       Figure 1.   Merging of inductive and deductive methods
anomalies will always be detected. Finally, this approach
was found to be effective with stable network topologies.
In highly dynamic network topologies the cost of checking       physical principles. Deductive methods rely on a precise
whether the estimation is accurate becomes excessively          application environment and the explicit knowledge, called
high. Such a model will require collecting values of all        structural knowledge, of the underlying domain using first
attributes 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, inductive
communication 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 be
cal environments frequently exhibit predictable stable and      treated using experimental data knowledge due to the lack
strong attribute correlations to improve compression of the     of other application domain knowledge. Nevertheless, the
data communicated to the sink node. This approach is            use of inductive information helps in the generation of data
subject 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, applications
the case that the data is always within the error bound.        have been observed to perform significantly better if they
They propose periodic updates to ensure models can not          use a combination of the two methods [7]. Figure 1 shows
be incorrect indefinitely. This approach is not suitable         how the inductive and deductive methods can be merged
for raw value reconstruction; for any time-step where the       to capture the advantages of both methods. After the
model has suffered from failures and is incorrect, the           structural knowledge is fed to the system model (deductive
corresponding raw value samples will be wrong. Finally, as      process), the sense data is used to refine and complement
the approach presented in [4], Ken can only handle static       the basic structural model of the application domain. This
network 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 between
ping service where groups of network nodes cooperate            the physical model and the sense data.
to produce local maps which are cached and merged at             M-DAD makes use of knowledge given by the domain
a sink node, producing a map of the global network.             model in the map generation process. Knowledge from
The sink node receives periodic map updates from each           domain models provides guidance for map generation
cluster head used to refine an up-to-date global map.            from high dimensional data set and has the potential to
The distributed mapping service is made of four modules:        significantly speed up the map generation process and
Application (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 domain
maps), In-network Processing (process raw data received         model. For instance, Hofierka et al. [8] incorporate the
from various cluster heads) and Routing (responsible for        topographic characteristics to give better daily and annual
data communication). This approach does not incorporate         mean precipitation predictions. The general lack of an
the 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 to
blend of both inductive and deductive models to establish       overcome the limitations of generating a map from a single
a successful mapping between sense data and universal           sense modality. A single sense modality map typically
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 points
among other types in multi-modal sensing applications.
                                                                               xi ∈ Ω, i ∈ [1, n] , Ω ⊂ Rn              (1)
In addition, high-throughput data sets also often contain
errors and noise arising from imperfections of the sensing     with function values yi ∈ R, and i ∈ [1, N ] we require a
devices. Maps generated from a combination of different         continuous function f : Ω −→ R to interpolate unknown
types of data are likely to lead to a more coherent map        intermediate points such that
by consolidating information on various aspects of the
monitored 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 n
assuming that sensing errors across different data sets         is the number of dimensions and Ω is a suitable domain
are largely independent and the probability an error is        containing the observation points. When rewriting this
supported by more than one type of data is small. A            definition in terms of relationships between sets we get
natural 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 with
to combine the maps generated from different types of           continuous functions
data. We may combine the maps in different ways such
as 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 the
of delivering better maps, multiple types of data can
                                                               n-dimensional Euclidean space where
be analysed concurrently under an integrated relational
model. 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 brevity.
by 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 generalisation
known 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 set
the distance between the interpolation location P and the
                                                               distance metric. Burley et al. [10] discuss the usefulness of
given 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 possible
between sets rather than in terms of the Euclidean dis-
                                                               to define GAs over an arbitrary number of geometric
tance between points. Using this distance metric, a new
                                                               dimensions and that it is therefore theoretically possible to
generalised interpolation function f that is suitable for an
                                                               work with any number of dimensions. This is done simply
arbitrary 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 multivariate
to 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 distance
functions do not need to satisfy the formal mathematical       B. Scale-based Local Distance Metric
requirements for the Euclidean distance definition. The           In this section we modify the distance metric defined
power of such a generalisation can be seen when we include     in Section III-A to include the knowledge given by the
the time variable as one dimension. The spatial data           domain model. The domain model helps to significantly
reduce the size of the support nodes set. The difference in     in the system. Equation 6 can now be extended to include
the size of the support nodes set can be several orders        the domain model parameters of arbitrary dimensional
of magnitude with increasing problem dimension. The            system. Then the dimension-based scaling metric can be
increase in the support size can lead to an increase in        defined as
the 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)
                                                                               i
interpolation 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 the
interpolation algorithm complexity as well as interpolation      IV. Distributed Self-Adaptation in Mapping
accuracy.                                                                                Services
  We define the term scale for determining the weight           A. Benefits of Self-Adaptation
of every given dimension with respect to P based on a            In this section we extend the capabilities of M-DAD
combined Euclidean distance criteria and the information       to overcome challenges imposed by the described external
already 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 adapt
the 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 with
is identical for all Si which means that all sets have the     contextual information to update the initial application
same 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 changes
to improve the interpolation results when applied to an        significantly over time which necessitate updating the
arbitrary number of dimensions. In M-DAD, the support          domain model to reflect the changes in the contextual
set, Ci , for P is calculated using mP . Symbolically, Ci is   knowledge provided by the physical constraints imposed
calculated 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 inexpensive
local model that selects the support set for calculating P ,   to deploy and maintain. This adaptation procedure will
d is an Euclidean distance function, Ej is an observation      recover, over time, the effects of user domain modelling
point 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 problem
of parameters. These parameters are usually a set of rela-     and considerable work is being done by the research
tionships between different dimensions or other application     community in that area. However, in this work we aim
domain characteristics such as obstacles. When predicting      to deal with a small set of adaptivity issues that have a
the 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 the
extended to multi-dimensional distance weighting systems
                                                               interpolation capability of the network to perform local
as 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 own
where K (P, Si ) is the distance from the interpolation        reading value (y ) using mP (eq. 7). Then, y is compared
position P to data set Si and n is the number of dimensions    to the node measured value, y. It is desirable that the
estimate of y minimises the standard deviation (σ). Nodes       votes υ disseminate the bill to the chamber and all nodes
modify 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 false
tions, nodes will change the weight of each dimension           positives. Once a bill is approved by one chamber, it is
to 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 chamber
initially given in the domain model in order to recover         heads must agree to identical version of the bill. When
the effect of inaccuracies in the given domain model or to       the bill is submitted to the president, the sink node, he
adapt 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 Evaluation
is calculated using mp . Finally, a prediction accuracy
criterion, ∆, 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 the
number 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 into
dimension 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 the
domain model independently from the network, the map-
                                                                metal body of the ship. The model was restricted to a
ping service may become unstable because of the inconsis-
                                                                small area of the ship deck which has two big doors. The
tency in the domain model defined on various nodes. Such
                                                                chosen part of the ship deck is modelled by a brass sheet
inconsistencies may lead to inconsistent system states and
                                                                which contains a hole segment excavation to model an
conflicting differences in calculating mapping values. To
                                                                opened door. A simple domain model was defined to carry
ensure mapping stability we propose a Virtual Congress
                                                                information about doors that when opened they impact
Algorithm 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 the
high-level collaboration environment in which the system        brass sheet with 10mm width and 2cm length. A FLIR
can achieve globally efficient behaviour under dynamic            ThermaCAM P65 Infrared (IR) camera [11] was used
environmental conditions. The network is viewed as a            to take sharp thermal images and produce an accurate
virtual congress where nodes are senators who vote for          temperature analysis and results. The IR camera delivers
legislating changes to the domain model in response to          320 × 240 IR resolution (640 × 480 pixels, full colour) at
locally detected environmental conditions. This algorithm       0.08C thermal sensitivity. Finally, a 1371o C blue flame
is an attractive solution as senators collaboratively decide    was placed on the middle of one edge of the brass sheet
upon their local knowledge on the behaviour and correct-        as a heat source. Brass (an alloy of copper and zinc) was
ness of the system. Logically related nodes, chambers, are      chosen for this experiment because it is a good thermal
granted 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 sheet
A 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 were
each senator must monitor the changes over time using           recorded in addition to a thermal image taken by the IR
equation ?? before putting them into a bill. Senators           camera. The mapping services were ran over a subset of
send their voting results to the proposing senator. The         the data collected from this experiment to observe how
proposing senator, upon receiving the required number of        the heat will diffuse in the brass sheet in the absence
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 on
the sheet with the segment hole excavation and sensor
thermal measurements as well as a IR camera image were
taken after applying heat on the brass sheet. The mapping
service were ran using the same size of the thermal data-set
used in the previous experiment. Three experimental runs
were 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 presence
of the obstacle and its characteristics. (2) Run the map-
ping service which integrates some of the domain model         some interpolation areas contain many sensor readings
knowledge. 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 needed
integrates 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-DAD
length, and strength.                                          mapping framework. M-DAD was given some information
                                                               about the application domain including the existence of
Results and discussion: Figure 2 shows the heat diffu-
                                                               the obstacle, its location and length. We observe that the
sion map generated by the IR camera. Given that the heat
                                                               map obtained by M-DAD conserves perfectly the global
is 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 reduced
and right side areas around the heat source, this figure
                                                               the prediction error and visually it accurately captured the
shows that the existence of the obstacle has an effect on
                                                               effect of the heat obstacle on heat diffusion through the
heat diffusion through the brass sheet. It its observed that
                                                               brass sheet. The M-DAD generated map is smoother than
the obstacle strongly reduced the temperature rise in the
                                                               that rendered with the distributed mapping services, only
area on its right side. This map has been randomly down-
                                                               in some sub-regions containing the obstacle and around
sampled to 1000 points, that is 1.5% of the total 455 × 147
                                                               the heat source location.
to be used by the mapping service to generate the total
heat map.
  Figure 3 shows the map generated by the distributed
mapping service described in [1]. Compared with Fig-
ure 2, the obtained map conserves perfectly the global
appearance and many of the details of the original map
with 98.5% less data. However, the area containing the
obstacle has not been correctly reconstructed and caused
hard edges around the location of heat source. This is due     Figure 5.     Interpolated heat map generated by M-DAD given
to attenuation between adjacent points and the fact that       obstacle location, width and length.
M-DAD vs. standard Shepard
  Figure 5 shows the map generated by M-DAD with a                                   45


                                                                                     40
more complex domain model than the previous M-DAD
                                                                                     35

version (Figure 4). In this version we give M-DAD the                                30




                                                                Standard Deviation
obstacle width. We notice a better approximation to the                              25


real surface near the obstacle. The new details included in                          20


the domain model removed two artifacts from both ends                                15



of the obstacle. This is due to the inclusion of the obstacle                        10


                                                                                     5                                         Standard Shepard   M-DAD
width in weighting sensor readings when calculating P
                                                                                     0

which further reduces the effect of geographically nearby                                  0   2     4
                                                                                                             Location
                                                                                                                        6      8                      10



sensors that are disconnected from P by an obstacle.            Figure 6.     The standard deviation of temperature values at 10
Conclusion: 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, nodes
mapping services.
                                                                that have close humidity reading to that of P .
Experiment 2: Mapping from Related Multiple
                                                                Conclusion: This experiment proves that mapping from
Dimensions
                                                                related multiple dimensions can improve the generated
Aim: The aim of this experiment is to study if mapping
                                                                map quality. This observation is confirmed by the data
from related multiple types of the sense data can lead to
                                                                shown in Figure 6. The results from this experiment and
an improved mapping performance by overcoming some
                                                                Experiment 1 confirms the general theory of M-DAD
of 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 Model
Cold 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 model
temperature 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 in
sheet. 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 contains
data 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 to
the removed temperature reading using the rest of the           predict, but can be estimated using published metrics such
data set; (3) the standard deviation was calculated for         that in [12]. It was assumed that the obstacle is continuous
the temperature value resulted from 2 and 3; (4) steps 1        and the existence of this obstacle between two directly
to 4 were repeated for each of the 10 sensors temperature       communicating nodes will break the wireless links between
readings                                                        them. The local semantics of the application domain were
Results 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 through
ature map using the humidity map. Figure 6 shows the            an intermediate node(s) as there exists an obstacle between
standard deviation of the calculated temperature values         the two communicating nodes.
by M-DAD and the distributed mapping services. It is            Results and discussion: Table I shows three M-DAD
observed that M-DAD reduced the standard deviation by           mapping runs each with different node distributions. We
between 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
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 the
and 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
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                                                                     “Experimental applications of hierarchical mapping services in
described here is highly dependent on the nodes location             wireless sensor networks,” in SENSORCOMM ’08: Proceedings
                                                                     of the 2008 Second International Conference on Sensor Tech-
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for 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 Security
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  We notice that in the three mapping runs, zero bills               models,” in ICDE ’06: Proceedings of the 22nd International
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                                                                 [6] P. Hertkorn and S. Rudolph, “From data to models: Synergies
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                                                                 [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 und
and 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 with
tributed 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, http://software.kjinnovation.com/
using the nearest neighbour triangulation RF connectivity            InterpMethods.pdf.
map as one dimension to predict the heat map. Therefore,        [10] M. Burley, K. Bechkoum, and G. Pearce, “A formative survey
the 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,” http://www.flir.com.hk/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 different
sense modalities. M-DAD spontaneously responses to sys-

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

  • 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}@wlv.ac.uk 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 describes which they operate. The part of the world with which the various real world entities involved in that system and an application is concerned is defined as that applica- tion’s domain. This paper advocates that an application relationships between them. The domain model provides domain of a WSN can serve as a supplement to analysis, a structural view of the system which we suggest using to interpretation, and visualisation methods and tools. We complement the information gained from analysing data believe it is critical to elevate the capabilities of the gathered by a WSN. The logical integration of a domain data 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-Dimensional Application Domain-driven (M-DAD) mapping frame- vations as well as to predict future observations. It exploits work that is suitable for mapping an arbitrary num- the local semantics from the environment of each sensor. It ber of sense modalities and is capable of utilising the also takes advantage of human guidance and information relations between different modalities as well as other from other available sources, e.g. satellites. Furthermore, parameters of the application domain to improve the mapping performance. M-DAD starts with an initial it maintains the overall coherence of reasoning about user defined model that is maintained and updated the gathered data and helps to estimate the degree of throughout the network lifetime. The experimental confidence using probabilistic domain models. The use results demonstrate that M-DAD mapping framework of knowledge made available by the domain model can performs as well or better than mapping services with- also be a key to meeting the energy and channel capacity out 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 help set of applications each with different characteristics and early detection and reduction of the amount of ineffective environmental constraints. As a consequence, scientists data forwarding across the network, rather than sustaining from different research fields have begun to realise the im- the energy expense of transmitting ineffective messages portance of identifying and understanding the characteris- further along the path to the destination. tics and special deployment needs of different application II. Related Work domains. In many WSN deployments, the network owners have 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 are example, in forest fire applications [2], [3], information starting to appear on the horizon. The authors of the about 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 data trast to our work, efforts such as BBQ [4] have adopted structural an approach that assumes that intelligence is placed at knowledge the edge of the network, such as a sink, which is assumed process of sensed data model model building refinement to be less resource constrained than the sensor nodes. An interrogation-based approach can not guarantee that all Figure 1. Merging of inductive and deductive methods anomalies will always be detected. Finally, this approach was found to be effective with stable network topologies. In highly dynamic network topologies the cost of checking physical principles. Deductive methods rely on a precise whether the estimation is accurate becomes excessively application environment and the explicit knowledge, called high. Such a model will require collecting values of all structural knowledge, of the underlying domain using first attributes 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, inductive communication 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 be cal environments frequently exhibit predictable stable and treated using experimental data knowledge due to the lack strong attribute correlations to improve compression of the of other application domain knowledge. Nevertheless, the data communicated to the sink node. This approach is use of inductive information helps in the generation of data subject 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, applications the case that the data is always within the error bound. have been observed to perform significantly better if they They propose periodic updates to ensure models can not use a combination of the two methods [7]. Figure 1 shows be incorrect indefinitely. This approach is not suitable how the inductive and deductive methods can be merged for raw value reconstruction; for any time-step where the to capture the advantages of both methods. After the model has suffered from failures and is incorrect, the structural knowledge is fed to the system model (deductive corresponding raw value samples will be wrong. Finally, as process), the sense data is used to refine and complement the approach presented in [4], Ken can only handle static the basic structural model of the application domain. This network 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 between ping service where groups of network nodes cooperate the physical model and the sense data. to produce local maps which are cached and merged at M-DAD makes use of knowledge given by the domain a sink node, producing a map of the global network. model in the map generation process. Knowledge from The sink node receives periodic map updates from each domain models provides guidance for map generation cluster head used to refine an up-to-date global map. from high dimensional data set and has the potential to The distributed mapping service is made of four modules: significantly speed up the map generation process and Application (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 domain maps), In-network Processing (process raw data received model. For instance, Hofierka et al. [8] incorporate the from various cluster heads) and Routing (responsible for topographic characteristics to give better daily and annual data communication). This approach does not incorporate mean precipitation predictions. The general lack of an the 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 to blend of both inductive and deductive models to establish overcome the limitations of generating a map from a single a 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 points among other types in multi-modal sensing applications. xi ∈ Ω, i ∈ [1, n] , Ω ⊂ Rn (1) In addition, high-throughput data sets also often contain errors and noise arising from imperfections of the sensing with function values yi ∈ R, and i ∈ [1, N ] we require a devices. Maps generated from a combination of different continuous function f : Ω −→ R to interpolate unknown types of data are likely to lead to a more coherent map intermediate points such that by consolidating information on various aspects of the monitored 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 n assuming that sensing errors across different data sets is the number of dimensions and Ω is a suitable domain are largely independent and the probability an error is containing the observation points. When rewriting this supported by more than one type of data is small. A definition in terms of relationships between sets we get natural 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 with to combine the maps generated from different types of continuous functions data. We may combine the maps in different ways such as 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 the of delivering better maps, multiple types of data can n-dimensional Euclidean space where be analysed concurrently under an integrated relational model. 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 brevity. by 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 generalisation known 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 set the distance between the interpolation location P and the distance metric. Burley et al. [10] discuss the usefulness of given 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 possible between sets rather than in terms of the Euclidean dis- to define GAs over an arbitrary number of geometric tance between points. Using this distance metric, a new dimensions and that it is therefore theoretically possible to generalised interpolation function f that is suitable for an work with any number of dimensions. This is done simply arbitrary 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 multivariate to 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 distance functions do not need to satisfy the formal mathematical B. Scale-based Local Distance Metric requirements for the Euclidean distance definition. The In this section we modify the distance metric defined power of such a generalisation can be seen when we include in Section III-A to include the knowledge given by the the 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 include the size of the support nodes set can be several orders the domain model parameters of arbitrary dimensional of magnitude with increasing problem dimension. The system. Then the dimension-based scaling metric can be increase in the support size can lead to an increase in defined as the 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) i interpolation 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 the interpolation algorithm complexity as well as interpolation IV. Distributed Self-Adaptation in Mapping accuracy. Services We define the term scale for determining the weight A. Benefits of Self-Adaptation of every given dimension with respect to P based on a In this section we extend the capabilities of M-DAD combined Euclidean distance criteria and the information to overcome challenges imposed by the described external already 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 adapt the 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 with is identical for all Si which means that all sets have the contextual information to update the initial application same 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 changes to improve the interpolation results when applied to an significantly over time which necessitate updating the arbitrary number of dimensions. In M-DAD, the support domain model to reflect the changes in the contextual set, Ci , for P is calculated using mP . Symbolically, Ci is knowledge provided by the physical constraints imposed calculated 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 inexpensive local model that selects the support set for calculating P , to deploy and maintain. This adaptation procedure will d is an Euclidean distance function, Ej is an observation recover, over time, the effects of user domain modelling point 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 problem of parameters. These parameters are usually a set of rela- and considerable work is being done by the research tionships between different dimensions or other application community in that area. However, in this work we aim domain characteristics such as obstacles. When predicting to deal with a small set of adaptivity issues that have a the 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 the extended to multi-dimensional distance weighting systems interpolation capability of the network to perform local as 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 own where K (P, Si ) is the distance from the interpolation reading value (y ) using mP (eq. 7). Then, y is compared position 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 nodes modify 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 false tions, nodes will change the weight of each dimension positives. Once a bill is approved by one chamber, it is to 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 chamber initially given in the domain model in order to recover heads must agree to identical version of the bill. When the effect of inaccuracies in the given domain model or to the bill is submitted to the president, the sink node, he adapt 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 Evaluation is calculated using mp . Finally, a prediction accuracy criterion, ∆, 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 the number 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 into dimension 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 the domain model independently from the network, the map- metal body of the ship. The model was restricted to a ping service may become unstable because of the inconsis- small area of the ship deck which has two big doors. The tency in the domain model defined on various nodes. Such chosen part of the ship deck is modelled by a brass sheet inconsistencies may lead to inconsistent system states and which contains a hole segment excavation to model an conflicting differences in calculating mapping values. To opened door. A simple domain model was defined to carry ensure mapping stability we propose a Virtual Congress information about doors that when opened they impact Algorithm 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 the high-level collaboration environment in which the system brass sheet with 10mm width and 2cm length. A FLIR can achieve globally efficient behaviour under dynamic ThermaCAM P65 Infrared (IR) camera [11] was used environmental conditions. The network is viewed as a to take sharp thermal images and produce an accurate virtual congress where nodes are senators who vote for temperature analysis and results. The IR camera delivers legislating changes to the domain model in response to 320 × 240 IR resolution (640 × 480 pixels, full colour) at locally detected environmental conditions. This algorithm 0.08C thermal sensitivity. Finally, a 1371o C blue flame is an attractive solution as senators collaboratively decide was placed on the middle of one edge of the brass sheet upon their local knowledge on the behaviour and correct- as a heat source. Brass (an alloy of copper and zinc) was ness of the system. Logically related nodes, chambers, are chosen for this experiment because it is a good thermal granted 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 sheet A 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 were each senator must monitor the changes over time using recorded in addition to a thermal image taken by the IR equation ?? before putting them into a bill. Senators camera. The mapping services were ran over a subset of send their voting results to the proposing senator. The the data collected from this experiment to observe how proposing 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 on the sheet with the segment hole excavation and sensor thermal measurements as well as a IR camera image were taken after applying heat on the brass sheet. The mapping service were ran using the same size of the thermal data-set used in the previous experiment. Three experimental runs were 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 presence of the obstacle and its characteristics. (2) Run the map- ping service which integrates some of the domain model some interpolation areas contain many sensor readings knowledge. 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 needed integrates 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-DAD length, and strength. mapping framework. M-DAD was given some information about the application domain including the existence of Results and discussion: Figure 2 shows the heat diffu- the obstacle, its location and length. We observe that the sion map generated by the IR camera. Given that the heat map obtained by M-DAD conserves perfectly the global is 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 reduced and right side areas around the heat source, this figure the prediction error and visually it accurately captured the shows that the existence of the obstacle has an effect on effect of the heat obstacle on heat diffusion through the heat diffusion through the brass sheet. It its observed that brass sheet. The M-DAD generated map is smoother than the obstacle strongly reduced the temperature rise in the that rendered with the distributed mapping services, only area on its right side. This map has been randomly down- in some sub-regions containing the obstacle and around sampled to 1000 points, that is 1.5% of the total 455 × 147 the heat source location. to be used by the mapping service to generate the total heat map. Figure 3 shows the map generated by the distributed mapping service described in [1]. Compared with Fig- ure 2, the obtained map conserves perfectly the global appearance and many of the details of the original map with 98.5% less data. However, the area containing the obstacle has not been correctly reconstructed and caused hard edges around the location of heat source. This is due Figure 5. Interpolated heat map generated by M-DAD given to 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 40 more complex domain model than the previous M-DAD 35 version (Figure 4). In this version we give M-DAD the 30 Standard Deviation obstacle width. We notice a better approximation to the 25 real surface near the obstacle. The new details included in 20 the domain model removed two artifacts from both ends 15 of the obstacle. This is due to the inclusion of the obstacle 10 5 Standard Shepard M-DAD width in weighting sensor readings when calculating P 0 which further reduces the effect of geographically nearby 0 2 4 Location 6 8 10 sensors that are disconnected from P by an obstacle. Figure 6. The standard deviation of temperature values at 10 Conclusion: 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, nodes mapping services. that have close humidity reading to that of P . Experiment 2: Mapping from Related Multiple Conclusion: This experiment proves that mapping from Dimensions related multiple dimensions can improve the generated Aim: The aim of this experiment is to study if mapping map quality. This observation is confirmed by the data from related multiple types of the sense data can lead to shown in Figure 6. The results from this experiment and an improved mapping performance by overcoming some Experiment 1 confirms the general theory of M-DAD of 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 Model Cold 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 model temperature 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 in sheet. 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 contains data 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 to the removed temperature reading using the rest of the predict, but can be estimated using published metrics such data set; (3) the standard deviation was calculated for that in [12]. It was assumed that the obstacle is continuous the temperature value resulted from 2 and 3; (4) steps 1 and the existence of this obstacle between two directly to 4 were repeated for each of the 10 sensors temperature communicating nodes will break the wireless links between readings them. The local semantics of the application domain were Results 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 through ature map using the humidity map. Figure 6 shows the an intermediate node(s) as there exists an obstacle between standard deviation of the calculated temperature values the two communicating nodes. by M-DAD and the distributed mapping services. It is Results and discussion: Table I shows three M-DAD observed that M-DAD reduced the standard deviation by mapping runs each with different node distributions. We between 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 the and 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 in described 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 early for 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 Security was 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,” in to the new obstacle length improves the produced map VLDB ’04: Proceedings of the Thirtieth international conference quality. 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 International became 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: Synergies application domain were local to part of the network and of a joint data mining and similarity theory approach,” in SPIE the majority of the clusters did not sense these changes. Aerosense 1999 Conference On Data Mining and Knowledge This 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 und and 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 with tributed 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, http://software.kjinnovation.com/ using the nearest neighbour triangulation RF connectivity InterpMethods.pdf. map as one dimension to predict the heat map. Therefore, [10] M. Burley, K. Bechkoum, and G. Pearce, “A formative survey the 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,” http://www.flir.com.hk/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 different sense modalities. M-DAD spontaneously responses to sys-