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    salary

    age

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    subspace

    coverage

    selected

    subspaces

    pruned

    subspaces

    average(selected subspaces)

    average(pruned subspaces)

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    density density

    XX

    (a) (b)

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    Y

    X

    y2

    y1

    x2x1

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    0

    1

    2

    3

    4

    5

    0 0.2 0.4 0.6 0.8 1

    Entropy/nats

    Area

    Area vs Entropy

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    {}

    X1X

    2X

    3X

    4

    X1X

    2X

    3X

    1X

    2X

    4X

    2X

    3X

    4X

    1X

    3X

    4

    X1X2 X1X3 X2X3 X1X4 X3X4X2X4

    X2

    X1

    X4

    X3

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    {}

    X1X

    2X

    3X

    4

    X1X

    2X

    3X

    1X

    2X

    4X

    2X

    3X

    4X

    1X

    3X

    4

    X1X

    2X

    1X

    3X

    2X

    3X

    1X

    4X

    3X

    4X

    2X

    4

    X2

    X1

    X4

    X3

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    1500

    2000

    2500

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    3500

    4000

    0 2 4 6 8 10

    Time/secs

    Entropy Threshold (omega)/nats

    ENCLUS_SIG (epsilon = 1.0)ENCLUS_INT

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    0

    500

    1000

    1500

    2000

    2500

    0 0.5 1 1.5 2 2.5 3

    Time/secs

    Interest Threshold (epsilon)/nats

    omega = 8.5

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    0

    10000

    20000

    30000

    40000

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    60000

    70000

    80000

    10 15 20 25 30

    Time/secs

    Dimensionality

    ENCLUS_SIGENCLUS_INT

    0

    200

    400

    600

    800

    1000

    100 150 200 250 300 350 400 450 500

    Time/secs

    Number of Transactions/1000

    ENCLUS_SIG (epsilon = 1.0)ENCLUS_INT

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    0 0.05 0.1 0.15 0.2 0.25 0.3

    Time/secs

    Tau

    CLIQUE

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    Time/secs

    Dimensionality

    ENCLUS_SIGENCLUS_INT

    CLIQUE

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    0

    0.2

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    HS

    BC

    Cheung Kong

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    X

    X

    X

    X X

    X

    1

    2 4

    3 2

    3

    (a) (b) (c)

    Cluster 2

    Cluster 2

    Cluster 1

    Cluster 1Cluster 2

    Cluster 1

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    10 15 20 25 30

    Time/secs

    Dimensionality

    ENCLUS_SIGENCLUS_INT

    ENCLUS_SIG (extra pruning)ENCLUS_INT (extra pruning)

    Y

    X

    Y

    X

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    The clusters fall on different grids. The entropy is

    higher.

    The clusters fall on the same grid. The entropy is

    lower.

    Entropy = 0Entropy = 1.38 nats

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