TACO_ Tunable Approximate Computation of Outliers in Wireless

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					                       TACO:
    Tunable Approximate Computation of Outliers
            in Wireless Sensor Networks


       Nikos Giatrakos*                Yannis Kotidis†       Antonios Deligiannakis#
                         Vasilis Vassalos†           Yannis Theodoridis*
              * Dept.
                    of Informatics,     † Dept.
                                              of Informatics,    # Dept.
                                                                       of Electronic and
              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 Deligiannakis#
                         Vasilis Vassalos†           Yannis Theodoridis*
              * Dept.
                    of Informatics,     † Dept.
                                              of Informatics,    # Dept.
                                                                       of Electronic and
              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
                 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 ‘07)]
                                  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



                                                                                     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
      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
              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
                 0.9                                                          • Intel Lab Data -
                 0.8
                 0.7                                                            Temperature
Avg. Precision




                 0.6
                 0.5
                 0.4
                       1/2 Reduction        1/4 Reduction
                 0.3
                 0.2
                 0.1   1/8 Reduction        1/16 Reduction
                   0
                       10              15             20            25   30
                                                Similarity Angle
                                            TumbleSize=16 support=4


                   1
                 0.9
                 0.8
Avg. Recall




                 0.7
                 0.6
                 0.5
                 0.4
                 0.3   1/2 Reduction          1/4 Reduction
                 0.2
                 0.1   1/8 Reduction          1/16 Reduction
                   0
                       10              15              20           25   30
                                                Similarity Angle                              29
                                            TumbleSize=16 support=4
                                Sensitivity Analysis
                    1
                  0.9
                  0.8                                                    • Boosting
                  0.7
                                                                           Intel Lab Data -
Avg. Precision




                  0.6
                  0.5
                  0.4        1 Boosting Group                              Humidity
                  0.3
                  0.2        4 Boosting Groups
                  0.1        8 Boosting Groups
                    0
                        16       20             24            28    32
                                           TumbleSize
                                Reduction = 1/8, support=4, Φθ=30

                   1
                 0.9
                 0.8
                 0.7
                 0.6
Avg. Recall




                 0.5
                 0.4         1 Boosting Group
                 0.3
                             4 Boosting Groups
                 0.2
                 0.1         8 Boosting Groups
                   0
                        16       20            24            28     32
                                          TumbleSize
                                Reduction=1/8, support=4, Φθ=30                          30
         Performance Evaluation in
                 TOSSIM
• For 1/8reduction                                        9.00E+04
  TACO provides on                                        8.00E+04
                                                                           Min

  average 1/12 less                                                        Average

                      Total Bits Transmitted Per Tumble
                                                          7.00E+04
  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


                                   Epoch
  initialized with 5000 mJ             300

  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                                                                                                1
• Robust [Deligiannakis et                                                                                                                                0.9
                                                                                                                                                          0.8
  al, ICDE ‘09] falls short




                                                                                                                                              F-Measure
                                                                                                                                                          0.7
                                                                                                                                                          0.6
                                                                                                                                                                                                             Robust
  up to 10% in terms of                                                                                                                                   0.5
                                                                                                                                                                                                             TACO 1/4 Reduction
                                                                                                                                                          0.4
  the F-Measure metric                                                                                                                                    0.3                                                TACO 1/8 Reduction
                                                                                                                                                          0.2                                                TACO 1/16 Reduction
                                                                                                                                                          0.1
                                                                                                                                                            0
                                                                                                                                                                                                        1                   2     Support     3                                      4
                          4.00E+04          TACO - Remaining                                                                                                                                                     TumbleSize=16,Corr _Threshold=Cos(30)≈0.87
                                            TACO - Intercluster
Avg. Bits Transmitted Per Tumble




                          3.50E+04
                                            Robust
                          3.00E+04                                                                                                                                                                                                                                     • TACO ensures less
                                                                                                                                                                                                1/16 Reduction
                                                                     1/16 Reduction




                                                                                                                                                                                                                                                      1/16 Reduction
                                                                                                                             1/16 Reduction




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




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




                          2.50E+04
                                                                                                                                                                                                                                                                         bandwidth
                          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        Support       3                                                                                                               4
                                                                                      TumbleSize=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
                    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 Deligiannakis
           Vasilis Vassalos      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 Ï 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
                 0.9
                                                                               1
                                                                             0.9                                      • Intel Lab Data -
                 0.8                                                         0.8
                 0.7                                                         0.7                                        Humidity
Avg. Precision




                                                          Avg. Recall
                 0.6                                                         0.6
                 0.5                                                         0.5
                 0.4        1/2 Reduction                                    0.4        1/2 Reduction
                 0.3        1/4 Reduction                                    0.3        1/4 Reduction
                 0.2        1/8 Reduction                                    0.2        1/8 Reduction
                 0.1        1/16 Reduction                                   0.1        1/16 Reduction
                   0                                                           0
                       10       15      20      25   30                            10       15      20      25   30
                                 Similarity Angle                                            Similarity Angle
                             TumbleSize=16 support=4                                     TumbleSize=16 support=4
                   1
                 0.9
                                                                               1
                                                                             0.9                                      • Weather Data -
                 0.8                                                         0.8
                 0.7                                                         0.7                                        Humidity
Avg. Precision




                                                               Avg. Recall




                 0.6                                                         0.6
                 0.5                                                         0.5
                            1/2 Reduction
                 0.4                                                         0.4        1/2 Reduction
                 0.3        1/4 Reduction                                    0.3        1/4 Reduction
                 0.2        1/8 Reduction                                    0.2        1/8 Reduction
                 0.1        1/16 Reduction                                   0.1        1/16 Reduction
                   0                                                           0
                       10       15      20      25   30                            10       15     20      25    30
                                 Similarity Angle                                            Smilarity Angle
                             TumbleSize=20 support=6                                     TumbleSize=20 support=6                      46
                                                 Sensitivity Analysis
                   1
                 0.9
                                                                           1
                                                                         0.9                                          • Weather Data -
                 0.8                                                     0.8
                 0.7                                                     0.7                                            Solar Irradiance
Avg. Precision




                                                           Avg. Recall
                 0.6                                                     0.6
                 0.5                                                     0.5
                 0.4        1/2 Reduction                                0.4             1/2 Reduction
                 0.3        1/4 Reduction                                0.3             1/4 Reduction
                 0.2        1/8 Reduction                                0.2             1/8 Reduction
                 0.1        1/16 Reduction                               0.1             1/16 Reduction
                   0                                                       0
                       10      15      20      25   30                              10      15      20      25   30
                                Similarity Angle                                             Similarity Angle
                            TumbleSize=32 support=6                                      TumbleSize=32 support=6
                   1
                 0.9
                                                                                1
                                                                              0.9                                     • Boosting
                 0.8                                                          0.8
                 0.7                                                          0.7                                       Intel Lab Data -
Avg. Precision




                                                                Avg. Recall




                 0.6                                                          0.6
                 0.5
                 0.4
                                                                              0.5
                                                                              0.4
                                                                                                                        Humidity
                             1 Boosting Group                                              1 Boosting Group
                 0.3                                                          0.3
                 0.2         4 Boosting Groups                                0.2          4 Boosting Groups
                 0.1         8 Boosting Groups                                0.1          8 Boosting Groups
                   0                                                            0
                       16       20     24      28     32                            16        20   24     28     32
                                  TumbleSize                                                  TumbleSize
                       Reduction = 1/8, support=4, Φθ=30                            Reduction=1/8, support=4, Φθ=30                  47
         Performance Evaluation in
                 TOSSIM
                                                        3.50E+04
                                                                                                      TACO 1/16 Reduction



                     Avg. Bits Transmitted Per Tumble
                                                        3.00E+04
                                                                                                      TACO 1/8 Reduction

                                                        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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posted:3/11/2013
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