[^]L>ON0P-:78;QERSDT,8OK 8;I · 2011-11-22 · e f g 4 [3h,[=[^PGFi

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Number of Tuples, in Millions

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no strongest outliersstrongest outlier(s)Space containsSpace contains

no outliersSpace contains

AB AC BC BE CD CE DE

ABC ABD ABE ACD ACE

ABCDE

D ECA B

ADE BCD CDEBDEBCE

LEMIEUX BRIND’AMOUR

JAGR

ABCE ACDEABDE BCDEABCD

AEAD

LEMIEUX, JAGR LECLAIR

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Legend:

AB AC AD AE BC BD BE CD CE DE

ABC ABD ABE ACD ACE

ABCD ABCE ABDE ACDE BCDE

ABCDE

D ECA B

p Sample OutlieriABCDE Attributes

Common Combo Strongest Combo

ADE BCD CDEBDEBCE

1p p

2 3p

5p pp

p

4p

Non-Strongest Combo

6 7

8

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?ak

0 100 200 300

020

4060

80

NHL 1996: Penalty Minutes

Penalty Minutes

Occ

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nces

0 2 4 6 8 10

020

4060

80

(Penalty Minutes)^0.4

Occ

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nces

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-20 0 20 40 60

020

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014

0

1996 NHL Statistics: Attribute 9

Plus/Minus Rating

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Ï Ý Ï

0 20 40 60 80 1000

1020

3040

NHL 1996: Jersey Number

0 20 40 60 80

020

4060

Games Played

0 20 40 60 80

050

100

150

Assists

-20 0 20 40 60

050

100

150

200

Plus-Minus Statistic

0 5 10 15 20 25 30

010

020

030

040

050

0

Power Play Goals

0 20 40 60 80 100

050

100

150

200

Scoring Percentage

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1996 NHL Stats (original plot):Attribute 10 vs. Attribute 6

Goals

Pen

alty

Min

utes

0 20 40 60

010

020

030

0MATTHEW BARNABY

ENRICO CICCONE BRAD MAY

CHRIS SIMON BOB PROBERT

RICK TOCCHET ERIC LINDROS

KEITH TKACHUK

SHAYNE CORSON

JAROMIR JAGR

MARIO LEMIEUX

ALEXANDER MOGILNY

JOHN LECLAIR

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1996 NHL Stats., Box & Cox Trans. to Normality:Unadjusted Data Points Only: Attribute 10 vs. Attribute 6

Goals

Pen

alty

Min

utes

1.0 1.5 2.0

24

68

10 ENRICO CICCONE TIE DOMI

MATTHEW BARNABY BRAD MAY

CHRIS SIMON BOB PROBERT

SHAYNE CORSON

JAROMIR JAGR

KEITH TKACHUK

MARIO LEMIEUX

ALEXANDER MOGILNY

DAVE REID DOUG BROWN MIKAEL ANDERSSON

JOE MULLEN JOHN LILLEY

DONALD BRASHEAR

DENNIS VIAL

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1996 NHL Stats (using adjusted eigenvalues for neg.sqrt.matrix):Attribute 10 vs. Attribute 6

Goals

Pen

alty

Min

utes

-5 0 5

-20

24

68

MATTHEW BARNABY ENRICO CICCONE

BRAD MAY

SCOTT DANIELS CHRIS SIMON

BOB PROBERT

SHAYNE CORSON RICK TOCCHET

KEITH TKACHUK

THEOREN FLEURY

JAROMIR JAGR

MARIO LEMIEUX

ALEXANDER MOGILNY PAUL KARIYA

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1996 NHL Stats., Box & Cox Trans. to Normality:(neg. sqrt. trans. of robust covar.): Attribute 10 vs. Attr. 6

Goals

Pen

alty

Min

utes

-2 -1 0 1 2

-10

12

DONALD BRASHEAR

DENNIS VIAL ENRICO CICCONE MATTHEW BARNABY

BRAD MAY CHRIS SIMON

BOB PROBERT SHAYNE CORSON

TIE DOMI

KEITH TKACHUK

JAROMIR JAGR

MARIO LEMIEUX

ALEXANDER MOGILNY

DAVE REID MIKAEL ANDERSSON

JOE MULLEN JOHN LILLEY

VIACHESLAV BUTSAYEV

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1996 NHL Stats (Donaho-Stahel transformation):Attribute 10 vs. Attribute 6

Goals

Pen

alty

Min

utes

0 5 10

02

46

8

MATTHEW BARNABY

BRAD MAY

CHRIS SIMON BOB PROBERT

SHAYNE CORSON RICK TOCCHET

KEITH TKACHUK

JAROMIR JAGR

ALEXANDER MOGILNY

MARIO LEMIEUX

ERIC LINDROS

JOHN LECLAIR

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Goals

Pen

alty

Min

utes

-3 -2 -1 0 1 2 3

-2-1

01

23 MATTHEW BARNABY

TIE DOMI BRAD MAY

CHRIS SIMON BOB PROBERT

KEITH TKACHUK

JAROMIR JAGR

MARIO LEMIEUX

ALEXANDER MOGILNY

DAVE REID MIKAEL ANDERSSON

JOE MULLEN JOHN LILLEY

DONALD BRASHEAR DENNIS VIAL

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(Jersey Number)^0.4

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1996 NHL Stats (original plot):Attribute 10 vs. Attribute 6

Goals

Pen

alty

Min

utes

0 20 40 60

010

020

030

0

ROB RAY TIE DOMI BRAD MAY

MATTHEW BARNABY

ENRICO CICCONE

CHRIS SIMON BOB PROBERT

ERIC LINDROS KEITH TKACHUK

JAROMIR JAGR

MARIO LEMIEUX

ALEXANDER MOGILNY

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150Run Time and Recall for the Pure−random Algorithm: 5−D, 100,000 Tuples

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120Run Time and Recall for the Subsampling Algorithm: 5−D, 100,000 Tuples

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200Run Time and Recall for the Hybrid−random Algorithm: 5−D, 100,000 Tuples; delta=0.0800

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AQs�0

0 1000 2000 3000 4000 5000 6000360

380

400

420

440

460Number of Outliers (incl. Recall Rate), Cone Radius, and Percentage of Collisions for 360 Patches

Delta (Cone Radius x 10−4 )

Num

ber

of O

utlie

rs (

targ

et =

493

)

# of Outliers% Collisions

%Collisions

91.1% Recall

76.5%

# of Outliers% Collisions

%Collisions

91.1% Recall

76.5%

0 1000 2000 3000 4000 5000 60000

20

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100

0 1000 2000 3000 4000 5000 60000

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65Scalability of Dimensions for Subsampling and Hybrid−random, for 60,000 Tuples

Number of Dimensions

CP

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Hybrid−random

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x 104

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70Run Time and Dataset Size for Moderate Recall (e.g., 75%+): Subsampling and Hybrid−Random, 5−D

Number of Tuples

CP

U T

ime

in S

econ

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Subsampling

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0 20 40 60 80 100

010

2030

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NHL 1996: Jersey Number

Jersey Number

Occ

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70 80 90 100

01

23

45

Jersey Numbers between 58 and 99

Jersey Number

Occ

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