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Tunable Approximate Computation of Outliers in Wireless Sensor Networks

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					                       TACO:
    Tunable Approximate Computation of Outliers
            in Wireless Sensor Networks


      Nikos Giatrakos*                 Yannis Kotidis†             Antonios
                        Vasilis Vassalos†                       Deligiannakis#
                                                             Yannis
              * Dept.
                    of Informatics,      † Dept.          Theodoridis Electronic and
                                               of Informatics,  # Dept. of*

              University of Piraeus,      Athens University of   Computer Engineering,
                Piraeus, Greece         Economics and Business, Technical University of
                                            Athens, Greece                Crete,
                                                                     Crete, Greece


8 July 2010                                    HDMS 2010, Ayia Napa, Cyprus
                                              ΠΑΟ:
     Προσεγγιστικός υπολογισμός Ακραίων τιμών σε
     περιβάλλΟντα ασυρμάτων δικτύων αισθητήρων

      Nikos Giatrakos*                 Yannis Kotidis†             Antonios
                        Vasilis Vassalos†                       Deligiannakis#
                                                             Yannis
              * Dept.
                    of Informatics,      † Dept.          Theodoridis Electronic and
                                               of Informatics,  # Dept. of*

              University of Piraeus,      Athens University of   Computer Engineering,
                Piraeus, Greece         Economics and Business, Technical University of
                                            Athens, Greece                Crete,
                                                                     Crete, Greece


8 July 2010                                    HDMS 2010, Ayia Napa, Cyprus
                               PAO:
               Power-friendly Approximate Outliers in
                     Wireless Sensor Networks


      Nikos Giatrakos*                 Yannis Kotidis†             Antonios
                        Vasilis Vassalos†                       Deligiannakis#
                                                             Yannis
              * Dept.
                    of Informatics,      † Dept.          Theodoridis Electronic and
                                               of Informatics,  # Dept. of*

              University of Piraeus,      Athens University of   Computer Engineering,
                Piraeus, Greece         Economics and Business, Technical University of
                                            Athens, Greece                Crete,
                                                                     Crete, Greece


8 July 2010                                    HDMS 2010, Ayia Napa, Cyprus
                            Outline
• Introduction
   – Why outlier detection is important
   – Definition of outlier
• The TACO Framework
   – Compression of measurements at the sensor level (LSH)
   – Outlier detection within and amongst clusters
   – Optimizations: Boosting Accuracy & Load Balancing
• Experimental Evaluation
• Related Work
• Conclusions




                                                             4
                         Introduction
• Wireless Sensor Networks utility
   –   Place inexpensive, tiny motes in areas of interest
   –   Perform continuous querying operations
   –   Periodically obtain reports of quantities under study
   –   Support sampling procedures, monitoring/ surveillance applications etc


• Constraints
   – Limited Power Supply
   – Low Processing Capabilities
   – Constraint Memory Capacity


• Remark - Data communication is the
  main factor of energy drain                                               5
   Why Outlier Detection is Useful
• Outliers may denote malfunctioning sensors
   – sensor measurements are often unreliable
   – dirty readings affect computations/decisions [Deligiannakis ICDE’09]
• Outliers may also represent interesting events detected by
  few sensors
   – fire detected by a sensor

                             16   19   24   30   32   40   39



• Take into consideration
   – the recent history of samples acquired by single motes
   – correlations with measurements of other motes!

                                                                            6
                             Outline
• Introduction
   – Why is Outlier Detection Important and Difficult
• Our Contributions
   – Outlier detection with limited bandwidth
   – Compute measurement similarity over compressed representations of
     measurements (LSH)
• The TACO Framework
   – Compression of measurements at the sensor level
   – Outlier detection within and amongst clusters
• Optimizations: Load Balancing & Comparison Pruning
• Experimental Evaluation
• Related Work
• Conclusions
                                                                         7
       TACO - Our Contributions
• Trade bandwidth for accuracy in a straightforward manner…
   – Encodes sensor measurements using LSH
       • Control over the volume of transmitted data
       • More bits => better accuracy in estimation of whether two vectors are similar
   – Tunes the resulting overhead according to the accuracy levels
     required for outlier detection
   – Supports various popular similarity measures
• Introduction of a novel boosting process that improves
  TACO’s accuracy without increased communication burden
• Proposition of efficient mechanisms for intra-cluster load
  balancing and comparison pruning
• Presentation of a detailed experimental study using a fine-
  grained simulator (TOSSIM), including comparisons with
  directly related work
                                                                                         8
                             Outline
• Introduction
   – Why is Outlier Detection Important and Difficult
• Our Contributions
   – Outlier detection with limited bandwidth
   – Compute measurement similarity over compressed representations of
     measurements (LSH)
• The TACO Framework
   – Compression of measurements at the sensor level
   – Outlier detection within and amongst clusters
• Optimizations: Load Balancing & Comparison Pruning
• Experimental Evaluation
• Related Work
• Conclusions
                                                                         9
                 Outlier Definition
• Let ui denote the latest W measurements obtained by mote Si

• Given a similarity metric sim: RW→[0,1] and a similarity
  threshold Φ, sensors Si, Sj are considered similar if:

                          sim(ui , uj ) > Φ

• Minimum Support Requirement
   – a mote is classified as outlier if its latest W measurements are not
     found to be similar with at least minSup other motes




                                                                            10
  TACO Framework – General Idea
                8.2
Network organization into clusters [(Younis et al, INFOCOM ’04),(Qin et al, J. UCS
                                  0                  Step 1: Data Encoding and Reduction
‘07)]           4.3
                               d 1                   • Motes obtain samples and keep the
                5.1  W            0                  latest W measurements in a tumble
                                 …                • Encode W in a bitmap of d<<W size
                  …




        Clusterhead
        Regular Sensor



                                                                                     11
TACO Framework – General Idea
          If Sim(ui,uj)>Φ {     Step 1: Data Encoding and Reduction
                supportSi++;    • Motes obtain samples and keep the
                supportSj++;}   latest W measurements in a tumble
                                • Encode W in a bitmap of d<<W size

                                Step 2: Intra-cluster Processing
                                • Encodings are transmitted to
                                clusterheads
                                • Clusterheads perform similarity tests
                                based on a given similarity measure and a
                                similarity threshold Φ
                                • … and calculate support values


 Clusterhead
 Regular Sensor



                                                                  12
  TACO Framework – General Idea
                                           Step 1: Data Encoding and Reduction
                                           • Motes obtain samples and keep the
                                           latest W measurements in a tumble
                                           • Encode W in a bitmap of d<<W size

                                           Step 2: Intra-cluster Processing
                                           • Encodings are transmitted to
                                           clusterheads
                                           • Clusterheads perform similarity tests
                                           based on a given similarity measure and a
                                           similarity threshold Φ
                                           • … and calculate support values

                                           Step 3: Inter-cluster Processing
      Clusterhead                          • An approximate TSP problem is solved.
      Regular Sensor                       Lists of potential outliers are exchanged.

Additional load-balancing mechanisms and improvements in accuracy devised
                                                                               13
                 TACO Framework
         8.2
                     0   Step 1: Data Encoding and Reduction
         4.3
                   d 1   • Motes obtain samples and keep the
         5.1 W       0   latest W measurements in a tumble
                     …   • Encode W in a bitmap of d<<W size
          …




Clusterhead
Regular Sensor



                                                         14
      Data Encoding and Reduction
• Desired Properties
   – Dimensionality Reduction
     Reduced bandwidth consumption
   – Similarity Preservation
     Allows us to later derive initial sim(ui , uj ) during vector comparisons



• Locality Sensitive Hashing (LSH)
                         Ph є F [h(ui)=h(uj)]= sim(ui , uj )

• Practically, any similarity measure satisfying a set of criteria
[Charikar, STOC ‘02] may be incorporated in TACO’s framework
                                                                              15
           LSH Example:
    Random Hyperplane Projection
           [(Goemans & Wiliamson, J.ACM ’95),(Charikar, STOC ‘02) ]

•   Family of n d-dimensional
    random vectors (rvi)                                           rv1        Sensor data
                                                                             (2-dimensional)

•   Generates for each data vector
    a bitmap of size n as follows:              rv2
    -   Sets biti=1 if dot product of
        data vector with i-th                 rv3
        random vector is positive                                      rv4
    -   Sets biti=0 otherwise
                                          TACO encoding:

                                                       1   0   0   1



                                                                                    16
              Computing Similarity
•      Cosine Similarity: cos(θ(ui,uj))
                                                      ui


    RHP(ui)
                 1 0 1 1 1 1
                    n bits                            θ(ui, ui)        ui

    RHP(uj)      0 0 0 1 1 1
                                          θ(RHP(ui),RHP(uj))=2/6*π=π/3



      Angle                                                 Hamming
    Similarity                                              Distance


                                                                            17
           TACO at the Sensor Level
• Let ui є RW a vector of W quantities sampled by mote Si
• Random Hyperplane Projection LSH Scheme
   – We pick a random hyperplane by producing a spherically symmetric
     random vector r of unit length

   – Define a hash function hr as:

   – Then for any ui,uj є RW :                                          (1)

   – Repeating a stochastic procedure using d random vectors r (RW→[0,1]d) :

                                                                        (2)
         Angle                                             Hamming
       Similarity                                          Distance
                                                                          18
      Supported Similarity Measures
 Cosine       cos(θ(ui , uj))
Similarity


Correlation   corr(ui , uj )=cov(ui , uj) /( σui*σuj ) = Ε[(ui- E[ui])(uj-E[uj])]/ (σui*σuj )
Coefficient   [details in paper]



 Jaccard      Jaccard(A,B) = |A  B|/ |A  B|
Coefficient   see [Gionis et al, SIGMOD ‘01]

Lp-Norms      see [Datar et all, DIMACS SDAM’03]




                                                                                                19
                 TACO Framework
         If Sim(ui,uj)>Φ {     Step 1: Data Encoding and Reduction
               supportSi++;    • Motes obtain samples and keep the
               supportSj++;}   latest W measurements in a tumble
                               • Encode W in a bitmap of d<<W size

                               Step 2: Intra-cluster Processing
                               • Encodings are transmitted to
                               clusterheads
                               • Clusterheads perform similarity tests
                               based on a given similarity measure and a
                               similarity threshold Φ
                               • … and calculate support values


Clusterhead
Regular Sensor



                                                                 20
         Intra-cluster Processing
• Goal: Find potential outliers within the clusters realm
• Back to our running example, sensor vectors are considered
  similar when
                      θ(ui , uj) < Φθ
• Translate user-defined similarity threshold Φθ
                      Φh = Φθ * d/π
• For any received pair of bitmaps Xi, Xj, clusterheads can
  obtain an estimation of the initial similarity based on their
  hamming distance Dh(Xi,Xj) using:
                      Dh(Xi,Xj) < Φh
• At the end of the process <Si, Xi, support> lists are extracted
  for motes that do not satisfy the minSup parameter
                                                                    21
          Intra-cluster Processing
Probability of correctly classifying similar motes as such (W=16, θ=5, Φθ=10):




                                                                           22
                 TACO Framework
                         Step 1: Data Encoding and Reduction
                         • Motes obtain samples and keep the
                         latest W measurements in a tumble
                         • Encode W in a bitmap of d<<W size

                         Step 2: Intra-cluster Processing
                         • Encodings are transmitted to
                         clusterheads
                         • Clusterheads perform similarity tests
                         based on a given similarity measure and a
                         similarity threshold Φ
                         • … and calculate support values

                         Step 3: Inter-cluster Processing
Clusterhead              • An approximate TSP problem is solved.
Regular Sensor           Lists of potential outliers are exchanged.


                                                             23
                             Outline
• Introduction
   – Why is Outlier Detection Important and Difficult
• Our Contributions
   – Outlier detection with limited bandwidth
   – Compute measurement similarity over compressed representations of
     measurements (LSH)
• The TACO Framework
   – Compression of measurements at the sensor level
   – Outlier detection within and amongst clusters
• Optimizations: Load Balancing & Comparison Pruning
• Experimental Evaluation
• Related Work
• Conclusions
                                                                     24
              Boosting TACO Encodings
                                          d=n·μ
Xi :       0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0

Xj :       0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0
              1           1           0           1            0        1

                      SimBoosting(Xi,Xj)=1
  Obtain the answer provided by the majority of the μ
    tests
• Check the quality of the boosting estimation(θ(ui,uj)≤ Φθ):
       -   Unpartitioned bitmaps:             Pwrong(d)=1-Psimilar(d)

       -   Boosting:                         , Pwrong(d,μ) ≤
• Decide an appropriate μ:
       -   Restriction on μ : Psimilar(d/μ)>0.5
       -   Comparison of (Pwrong(d,μ) , Pwrong(d))
                                                                            25
                 Comparison Pruning
                    d                     Modified cluster election
                                          process, returns B bucket
0   d/4 d/4   d/2   d/2   3d/4 3d/4   d   nodes

                                          Introducing a 2nd level of
                                          hashing based on the hamming
                                          weight of the bitmaps

                                          Comparison pruning is
         Clusterhead – Bucket Node
         Regular Sensor                   achieved by hashing highly
                                          dissimilar bitmaps to different
                                          buckets                      26
              Load Balancing Among Buckets
SB1 [0-3d/8] SB2 (3d/8-9d/16] SB3 (9d/16-11d/16] SB4 (11d/16-d]
                                                                  Histogram Calculation Phase:
                             [f=(1,0,0), c4=d/12]                 •       Buckets construct equi-width histogram
                                                                          based on the received Xi s hamming
                             [f=(3,3,4,6), c3=d/16]
 [f=(0,0,1), c1=d/12]                                                     weight frequency

    c1=d/12        c2=d/16 c3=d/16                  c4=d/12           Histogram Communication Phase:
       0 0 1       3 3 2 2   3 3 4 6                  1 0 0
                                                                      •    Each bucket communicates to the
   0        d/4 d/4        d/2 d/2 3d/4 3d/4                  d            clusterhead
                                                                            - Estimated frequency counts
                                                                            - Width parameter ci
                                                                      Hash Key Space Reassignment:
                                                                      •    Clusterhead determines a new space
                                  SB3               SB4
        SB1       SB2=SC                                                   partitioning and broadcasts the
                                                                           corresponding information

                                                                                                          27
                             Outline
• Introduction
   – Why is Outlier Detection Important and Difficult
• Our Contributions
   – Outlier detection with limited bandwidth
   – Compute measurement similarity over compressed representations of
     measurements (LSH)
• The TACO Framework
   – Compression of measurements at the sensor level
   – Outlier detection within and amongst clusters
• Optimizations: Load Balancing & Comparison Pruning
• Experimental Evaluation
• Related Work
• Conclusions
                                                                     28
                                     Sensitivity Analysis
                 1
                                                                                 • Intel Lab Data -
                                                                                   Temperature
Avg. Precision




                     1/2 Reduction       1/4 Reduction

                     1/8 Reduction       1/16 Reduction
0.899999998509884
                            10              15             20          25   30
                            Similarity Angle TumbleSize=16 support=4



                 1
Avg. Recall




                      1/2 Reduction        1/4 Reduction

                      1/8 Reduction        1/16 Reduction
0.899999998509884
                            10               15            20          25   30
                            Similarity Angle TumbleSize=16 support=4                             29
                 Sensitivity Analysis
                                   • Boosting
                                     Intel Lab Data -
Avg. Precision




                                     Humidity
Avg. Recall




                                                   30
         Performance Evaluation in
                 TOSSIM
• For 1/8reduction                                        9.00E+04
  TACO provides on                                        8.00E+04
                                                                            Min

  average 1/12 less                                       7.00E+04
                                                                            Average

                      Total Bits Transmitted Per Tumble
  bandwidth                                               6.00E+04
                                                                            Max

  consumption,
                                                          5.00E+04
  which reaches a
                                                          4.00E+04
  maximum value of
                                                          3.00E+04
  1/15
                                                          2.00E+04

                                                          1.00E+04

                                                          0.00E+00
                                                                     TACO 1/16    TACO 1/8    TACO 1/4    NonTACO   SelectStar
                                                                     Reduction    Reduction   Reduction


                                                                                                                         31
          Performance Evaluation in
                  TOSSIM
• Network Lifetime: the epoch
                                           500
  at which the first mote in the
  network dies.                            400
• Average lifetime for motes
  initialized with 5000 mJ                 300


                                   Epoch
  residual energy
                                           200
• Reduction in power
  consumption reaches a                    100
  ratio of 1/2.7
                                             0
                                                 TACO 1/4    NonTACO   SelectStar
                                                 Reduction

                                                                                32
                                                  TACO vs Hierarchical Outlier
                                                     Detection Techniques
  • Robust [Deligiannakis
    et al, ICDE ‘09] falls
    short up to 10% in
    terms of the F-Measure
    metric
                                   4.00E+04
                                                           TACO - Remaining
                                   3.50E+04                TACO - Intercluster
Avg. Bits Transmitted Per Tumble




                                                                                                                                                                                                                                                   • TACO ensures less
                                                           Robust
                                   3.00E+04


                                                                                                                                                                                            1/16 Reduction
                                                                                                                                                                                                                                                     bandwidth
                                                                                  1/16 Reduction




                                                                                                                                                                                                                                             1/16 Reduction
                                                                                                                                           1/16 Reduction
                                                  1/4 Reduction




                                   2.50E+04
                                                                                                                                                            1/4 Reduction
                                                                                                                                                                            1/8 Reduction
                                                                  1/8 Reduction




                                                                                                                                                                                                             1/4 Reduction
                                                                                                                                                                                                                             1/8 Reduction
                                                                                                           1/4 Reduction
                                                                                                                           1/8 Reduction




                                   2.00E+04
                                                                                                                                                                                                                                                     consumption with a
                                   1.50E+04

                                   1.00E+04
                                                                                                                                                                                                                                                     ratio varying from
                                   5.00E+03
                                                                                                                                                                                                                                                     1/2.6 to 1/7.8
                                   0.00E+00
                                              1   2                3              4                SupportTumbleSize=16, Corr _Threshold=Cos(30)≈0.87
                                                                                                                                                                                                                                                                   33
                             Outline
• Introduction
   – Why is Outlier Detection Important and Difficult
• Our Contributions
   – Outlier detection with limited bandwidth
   – Compute measurement similarity over compressed representations of
     measurements (LSH)
• The TACO Framework
   – Compression of measurements at the sensor level
   – Outlier detection within and amongst clusters
• Optimizations: Load Balancing & Comparison Pruning
• Experimental Evaluation
• Related Work
• Conclusions
                                                                     34
                 Related Work - Ours
•   Outlier reports on par with aggregate query answer [Kotidis et al,
    MobiDE’07]
     – hierarchical organization of motes
     – takes into account temporal & spatial correlations as well
     – reports aggregate, witnesses & outliers
•   Outlier-aware routing [Deligiannakis et al, ICDE ‘09]
     – route outliers towards motes that can potentially witness them
     – validate detection scheme for different similarity metrics (correlation
       coefficient, Jaccard index also supported in TACO)
•   Snapshot Queries [Kotidis, ICDE ’05]
     – motes maintain local regression models for their neighbors
     – models can be used for outlier detection
•   Random Hyperplane Projection using Derived Dimensions [Georgoulas et
    al MobiDE’10]
     – extends LSH scheme for skewed datasets
     – up to 70% improvements in accuracy                                        35
                  Related Work
• Kernel based approach [Subramaniam et al, VLDB ‘06]
• Centralized Approaches [Jeffrey et al, Pervasive ‘06]
• Localized Voting Protocols
   [(Chen et al, DIWANS ’06),(Xiao et al, MobiDE ‘07) ]
• Report of top-K values with the highest deviation
   [Branch et al, ICDCS ‘06]
• Weighted Moving Average techniques [Zhuang et al,
  ICDCS ’07]


                                                          36
                             Outline
• Introduction
   – Why is Outlier Detection Important and Difficult
• Our Contributions
   – Outlier detection with limited bandwidth
   – Compute measurement similarity over compressed representations of
     measurements (LSH)
• The TACO Framework
   – Compression of measurements at the sensor level
   – Outlier detection within and amongst clusters
• Optimizations: Load Balancing & Comparison Pruning
• Experimental Evaluation
• Related Work
• Conclusions
                                                                     37
                    Συμπεράσματα
• Our Contributions
   – outlier detection with limited bandwidth
• The TACO/ΠΑΟ Framework
   – LSH compression of measurements at the sensor level
   – outlier detection within and amongst clusters
   – optimizations: Boosting Accuracy & Load Balancing
• Experimental Evaluation
   – accuracy exceeding 80% in most of the experiments
   – reduced bandwidth consumption up to a factor of 1/12 for 1/8
     reduced bitmaps
   – prolonged network lifetime up to a factor of 3 for 1/4 reduction
     ratio
                                                                    38
                   TACO:
Tunable Approximate Computation of Outliers
        in Wireless Sensor Networks


               Thank you!
 Nikos Giatrakos   Yannis Kotidis       Antonios
         Vasilis Vassalos             Deligiannakis
                             Yannis Theodoridis
Backup Slides


                40
           TACO Framework
        8.2                 0
                                Step 1: Data Encoding and Reduction
        4.3 W           d   1
                                • Motes obtain samples and keep the
        …                   …
                                latest W measurements in a tumble
                                • Encode W in a bitmap of d<<W size

                                Step 2: Intra-cluster Processing
                                • Encodings are transmitted to
                                clusterheads
                                • Clusterheads perform similarity tests
                                based on a given similarity measure and a
                                similarity threshold Φ
                                • … and calculate support values

Clusterhead                     Step 3: Inter-cluster Processing
Regular Sensor                  • An approximate TSP problem is solved.
                                Lists of potential outliers are exchanged.
  If Sim(ui,uj)>Φ {
        supportSi++;
        supportSj++;}                                               41
      Leveraging Additional Motes for
            d
              Outlier Detection
                                                Introducing a 2nd level of hashing:
                                                •   Besides cluster election, process
                                                    continuous in each cluster so as to
0     d/4 d/4    d/2   d/2   3d/4 3d/4    d
                                                    select B bucket nodes with
                                                •   For                  , 0≤ Wh(Xi)≤ d
                                                    equally distribute the hash key space
                                                    amongst them
                                                •   Hash each bitmap to the
                                                    bucket
                                                •   For bitmaps with Wh(Xi) at the edge of
                                                    a bucket, transmit Xi to the range:
•             Clusterhead is ensured by
    Comparison Pruning – Bucket Node the fact
    that highly dissimilar bitmaps are hashed
              Regular Sensor
    to different buckets, thus never being
    tested for similarity                           which is guaranteed to contain at most
                                                    2 buckets since                   42
    Leveraging Additional Motes for
          d
            Outlier Detection
                                          Intra-cluster Processing:
                                          •   Buckets perform bitmap comparisons
                                              as in common Intra-cluster processing
0   d/4 d/4   d/2   d/2   3d/4 3d/4   d
                                          •   Constraints:

                                              -If                  , similarity test is
                                              performed only in that bucket
                                              - For encodings that were hashed to
                                              the same 2 buckets, similarity is tested
                                              only in the bucket with the lowest SBi
                                          •   PotOut formation:
         Clusterhead – Bucket Node
                                              -Si PotOut if it is not reported by all
         Regular Sensor                       buckets it was hashed to
                                              -Received support values are added
                                              and Si є PotOut iff SupportSi < minSup
                                                                                 43
               Experimental Setup
• Datasets:
   – Intel Lab Data :
      • Temperature and Humidity measurements
      • Network consisting of 48 motes organized into 4 clusters
      • Measurements for a period of 633 and 487 epochs respectively
      • minSup=4
   – Weather Dataset :
      • Temperature, Humidity and Solar Iradiance measurements
      • Network consisting of 100 motes organized into 10 clusters
      • Measurements for a period of 2000 epochs
      • minSup=6




                                                                       44
                Experimental Setup
• Outlier Injection
   – Intel Lab Data & Weather Temperature, Humidity data :
      • 0.4% probability that a mote obtains a spurious measurement at
        some epoch
      • 6% probability that a mote fails dirty at some epoch
           – Every mote that fails dirty increases its measurements by 1 degree until it
             reaches a MAX_VAL parameter, imposing a 15% noise at the values
           – Intel Lab Data MAX_VAL=100
           – Weather Data MAX_VAL=200
   – Weather Solar Irradiance data :
      • Random injection of values obtained at various time periods to the
        sequence of epoch readings
• Simulators
   – TOSSIM network simulator
   – Custom, lightweight Java simulator
                                                                                           45
                                              Sensitivity Analysis
                                 1                                                               1
                                                                                                                          • Intel Lab Data -
                                                                                                                            Humidity
Avg. Precision




                                                               Avg. Recall
                 0.899999998509884                                               0.899999998509884
                              1/2 Reduction                                                   1/2 Reduction
                              1/4 Reduction                                                   1/4 Reduction
                              1/8 Reduction                                                   1/8 Reduction
                              1/16 Reduction                                                  1/16 Reduction
                 0.799999997019768                                               0.799999997019768
                                         10 15 20 25 30                                                 10 15 20 25 30
                    Similarity Angle TumbleSize=16 support=4                        Similarity Angle TumbleSize=16 support=4

                                 1                                                                  1
                                                                                 0.899999998509884                        • Weather Data -
                                                                                 0.799999997019768
                                                                                 0.699999995529652                          Humidity
Avg. Precision




                                                                   Avg. Recall




                                                                                 0.599999994039536
                           1/2 Reduction                                          0.49999999254942
                                                                                              1/2 Reduction
                           1/4 Reduction                                         0.399999991059304
                                                                                              1/4 Reduction
                           1/8 Reduction                                         0.299999989569188
                                                                                              1/8 Reduction
                             1/16 Reduction                                      0.199999988079072
                                                                                              1/16 Reduction
                 0.899999998509884                                               0.099999986588956
                                        10 15 20 25 30                                                   10 15 20 25 30
                    Similarity Angle TumbleSize=20 support=6                        Smilarity Angle TumbleSize=20 support=6
                                                                                                                                          46
                 Sensitivity Analysis
                                       • Weather Data -
                                         Solar Irradiance
Avg. Precision




                     Avg. Recall




                                       • Boosting
                                         Intel Lab Data -
Avg. Precision




                         Avg. Recall




                                         Humidity



                                                      47
         Performance Evaluation in
                 TOSSIM
                                                        3.50E+04
                                                                                                       TACO 1/16 Reduction
                                                        3.00E+04
                                                                                                       TACO 1/8 Reduction

                     Avg. Bits Transmitted Per Tumble
                                                        2.50E+04                                       TACO 1/4 Reduction
• Transmitted bits                                                                                     NonTACO
  categorization                                        2.00E+04
                                                                                                       SelectStar
  per approach                                          1.50E+04

                                                        1.00E+04

                                                        5.00E+03

                                                        0.00E+00
                                                                   ToClusterhead   Retransmissions   Intercluster            ToBS




                                                                                                                                    48
              Bucket Node Introduction
                                                Φθ
                              10                                        20


Cluster                            #Multihash   #Bitmaps             #Multihash   #Bitmaps
 Size     #Buckets   #Cmps          Messages    PerBucket   #Cmps     Messages    PerBucket
             1          66              0           12         66         0           12
  12         2        38,08           0,90         6,45      40,92      1,36         6,68
             4        24,55           7,71         3,65      30,95      8,88         4,08
             1         276              0           24        276         0           24
  24         2       158,06           1,62        12,81     171,80      2,76        13,38
             4       101,10          14,97         7,27     128,63     17,61         8,15
             1         630              0           36        630         0           36
  36         2       363,64           2,66        19,33     394,97      4,30        20,15
             4       230,73          22,88        10,88     291,14     26,28        12,19
             1        1128              0           48       1128         0           48
  48         2       640,10           3,14        25,57     710,95      5,85        26,93
             4       412,76          30,17        14,49     518,57     34,64        16,21



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