Data Mining Tutorial - Session 5: Clustering · 2012. 6. 21. · Data Mining Tutorial E. Schubert,...

Data MiningTutorial

E. Schubert,E. Ntoutsi

Aufgabe 7-1

Aufgabe 7-3ε = 1.1minPts= 2

ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4

DBSCAN andSingle-Link

Data Mining TutorialSession 5: Clustering

Erich Schubert, Eirini Ntoutsi

Ludwig-Maximilians-Universität München

2012-06-21 — KDD class tutorial

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


Convergence of PAM

Let:

I Mi = model (= set of medoids) after the ith iteration.I TD(Mi) = cost of model Mi.

PAM when

There are(n

k

)possible models, but N iterations.

⇒ ∃t1<t2Mt1 = Mt2

⇒ TD(Mt1) = TD(Mt2) contradiction!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


Convergence of PAM

Let:


PAM converges when

TD(Mi) = TD(Mi+1)

There are(n

k


⇒ ∃t1<t2Mt1 = Mt2


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


Convergence of PAM

Let:


PAM does not converge when

∀i ∈ N : TD(Mi) > TD(Mi+1)

There are(n

k


⇒ ∃t1<t2Mt1 = Mt2


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


Convergence of PAM

Let:



∀i ∈ N : TD(Mi) > TD(Mi+1)

There are(n

k

)possible models,

but N iterations.

⇒ ∃t1<t2Mt1 = Mt2


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


Convergence of PAM

Let:



∀i ∈ N : TD(Mi) > TD(Mi+1)

There are(n

k


⇒ ∃t1<t2Mt1 = Mt2


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


Convergence of PAM

Let:



∀i ∈ N : TD(Mi) > TD(Mi+1)

There are(n

k


⇒ ∃t1<t2Mt1 = Mt2

⇒ TD(Mt1) = TD(Mt2)

contradiction!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


Convergence of PAM

Let:



∀i ∈ N : TD(Mi) > TD(Mi+1)

There are(n

k


⇒ ∃t1<t2Mt1 = Mt2


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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123456789

101112

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A B

C

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:BC

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:B

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:BD

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:D

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C D

B

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:D

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C D

B

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:G

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:H

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:IJ

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:I

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:I

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O

ε = 1.1

minPts = 2

Seed list:O

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O P

R

N

ε = 1.1

minPts = 2

Seed list:NPR

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O P

R

N

ε = 1.1

minPts = 2

Seed list:NP

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O PN

R S

T

Q

ε = 1.1

minPts = 2

Seed list:NPQST

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O PN

R S

T

Q

ε = 1.1

minPts = 2

Seed list:NPQS

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

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J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O PN

R SQ

T

ε = 1.1

minPts = 2

Seed list:NPQS

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O PN

R SQ

T

ε = 1.1

minPts = 2

Seed list:NPS

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O PN

R S

T

Q

ε = 1.1

minPts = 2

Seed list:NPS

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

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J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O PN

R S

T

Q

ε = 1.1

minPts = 2

Seed list:PS

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

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F

G H J

I

K

L

K

L

M

N O P

Q R S

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M

O P

R S

T

Q

N

ε = 1.1

minPts = 2

Seed list:PS

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

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J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O P

R S

T

Q

N

ε = 1.1

minPts = 2

Seed list:S

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

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G H

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F

G H J

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K

L

K

L

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N O P

Q R S

T

M

O

R S

T

Q

N P

ε = 1.1

minPts = 2

Seed list:S

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

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EE

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G H

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G H J

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K

L

K

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N O P

Q R S

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M

O

R S

T

Q

N P

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

J

F

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O

R

T

Q

N P

S

ε = 1.1

minPts = 2

Seed list:

No borderpoints!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:BC

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:B

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:BD

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:D

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C D

B

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:D

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C D

B

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

J

F

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:H

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:IJ

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:I

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:I

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

P

R

N

ε = 1.1

minPts = 3

Seed list:NPR

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

P

R

N

ε = 1.1

minPts = 3

Seed list:NP

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R S

T

Q

ε = 1.1

minPts = 3

Seed list:NPQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R S

T

Q

ε = 1.1

minPts = 3

Seed list:NPQS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R SQ

T

ε = 1.1

minPts = 3

Seed list:NPQS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R SQ

T

ε = 1.1

minPts = 3

Seed list:NPS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R S

T

Q

ε = 1.1

minPts = 3

Seed list:NPS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R S

T

Q

ε = 1.1

minPts = 3

Seed list:PS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

P

R S

T

Q

N

ε = 1.1

minPts = 3

Seed list:PS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

P

R S

T

Q

N

ε = 1.1

minPts = 3

Seed list:S

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

R S

T

Q

N P

ε = 1.1

minPts = 3

Seed list:S

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

R S

T

Q

N P

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

O

M

R

T

Q

N P

S

ε = 1.1

minPts = 3

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

EE

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

EE

F

G H

I

J

F

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

EE

F

G H

I

J

F

G K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

EE

F

G H

I

J

F

HG

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:IJ

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

EE

F

G H

I

J

F

HG

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:I

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

EE

F

G H

I

J

F

HG

I

J K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

M

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

P

R

N

ε = 1.1

minPts = 4

Seed list:NPR

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

P

R

N

ε = 1.1

minPts = 4

Seed list:NP

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R S

T

Q

ε = 1.1

minPts = 4

Seed list:NPQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R S

T

Q

ε = 1.1

minPts = 4

Seed list:NPQS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R SQ

T

ε = 1.1

minPts = 4

Seed list:NPQS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R SQ

T

ε = 1.1

minPts = 4

Seed list:NPS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R S

T

Q

ε = 1.1

minPts = 4

Seed list:NPS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

PN

R S

T

Q

ε = 1.1

minPts = 4

Seed list:PS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

P

R S

T

Q

N

ε = 1.1

minPts = 4

Seed list:PS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

P

R S

T

Q

N

ε = 1.1

minPts = 4

Seed list:S

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

R S

T

Q

N P

ε = 1.1

minPts = 4

Seed list:S

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

R S

T

Q

N P

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A B

C D

EE

F

G H

I

J

F

HG J

I

K

L

K

L

M

N O P

Q R S

T

O

M

R

T

Q

N P

S

ε = 1.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:BCD

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:BD

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

DC

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:BD

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A B

DC

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:D

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

DC

B

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:D

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

DC

B

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

J

F

K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:HIJ

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:IJ

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

J

I

H K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:IJ

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

J

I

H K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:I

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

I

H J K

L

K

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:IK

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

I

H J K

L

K

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:K

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:K

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

O P

R

N

ε = 2.1

minPts = 4

Seed list:ONPR

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

O P

R

N

ε = 2.1

minPts = 4

Seed list:NPR

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

P

R

N O

S

T

Q

ε = 2.1

minPts = 4

Seed list:NPRQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

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A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

P

R

N O

S

T

Q

ε = 2.1

minPts = 4

Seed list:NPQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

PN O

S

T

Q R

ε = 2.1

minPts = 4

Seed list:NPQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

PN O

S

T

Q R

ε = 2.1

minPts = 4

Seed list:NPQS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

PN O

SQ R

T

ε = 2.1

minPts = 4

Seed list:NPQS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

PN O

SQ R

T

ε = 2.1

minPts = 4

Seed list:NPS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

PN O

SR

T

Q

ε = 2.1

minPts = 4

Seed list:NPS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

PN O

SR

T

Q

ε = 2.1

minPts = 4

Seed list:PS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

PO

SR

T

Q

N

ε = 2.1

minPts = 4

Seed list:PS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

PO

SR

T

Q

N

ε = 2.1

minPts = 4

Seed list:S

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

O

SR

T

Q

N P

ε = 2.1

minPts = 4

Seed list:S

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

O

SR

T

Q

N P

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C D

A

C

B

D

EE

F

G H

I

JG

F

H J

I

K

L

K

L

M

N O P

Q R S

T

M

O

R

T

Q

N P

S

ε = 2.1

minPts = 4

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:E

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:GHIJ

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

H J

I

G K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:HIJ

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

H J

I

G K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:HIJK

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

H J

I

G K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:IJK

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

J

I

G H K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:IJK

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

J

I

G H K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:IK

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

I

G H J K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:IK

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

I

G H J K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:K

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:K

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:L

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

O P

R

N

S

T

Q

ε = 4.1

minPts = 5

Seed list:ONPRQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

O P

R

N

S

T

Q

ε = 4.1

minPts = 5

Seed list:NPQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

P

R

N

S

T

Q

O

ε = 4.1

minPts = 5

Seed list:NPQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

PN

S

T

Q

O

R

ε = 4.1

minPts = 5

Seed list:NPQST

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

PN

S

T

Q

O

R

ε = 4.1

minPts = 5

Seed list:NPQS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

PN

SQ

O

R

T

ε = 4.1

minPts = 5

Seed list:NPQS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

PN

SQ

O

R

T

ε = 4.1

minPts = 5

Seed list:NPS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

PN

S

O

R

T

Q

ε = 4.1

minPts = 5

Seed list:NPS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

PN

S

O

R

T

Q

ε = 4.1

minPts = 5

Seed list:PS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

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101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

P

S

O

R

T

Q

N

ε = 4.1

minPts = 5

Seed list:PS

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

P

S

O

R

T

Q

N

ε = 4.1

minPts = 5

Seed list:S

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

S

O

R

T

Q

N P

ε = 4.1

minPts = 5

Seed list:S

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

S

O

R

T

Q

N P

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C DD

A B

C

EE

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

M

L

O

R

T

Q

N P

S

ε = 4.1

minPts = 5

Seed list:

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:

single-linklike effect!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:D


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

E

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:E


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

EE

F

G H

I

J K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

E

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:K


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

E

F

G H

I

J

F

E

G H J

I

K

L

K

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

E

F

G H

I

J

F

E

G H J

I

K

L

K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:L


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

E

F

G H

I

J

F

E

G H J

I

K

L

K

L

M

N O P

Q R S

T

ε = 4.1

minPts = 4

Seed list:


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

E

F

G H

I

J

F

E

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O

ε = 4.1

minPts = 4

Seed list:MO


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN

1 2 3 4 5 6 7 8 9 10 11 12

123456789

101112

A B

C D

A

C

B

D

E

F

G H

I

J

F

E

G H J

I

K

L

K

L

M

N O P

Q R S

T

M

O

R

T

Q

N P

S

ε = 4.1

minPts = 4

Seed list:


Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4


DBSCAN and Single-Linkage Clustering

DBSCAN with minPts = 2⇔ single-linkage dendrogram cut at distance ε.

DBSCAN is O(n2) (with index: O(n log n) only)but this is for a single ε only.

OPTICS (next week) with minPts = 2 is similar to SLINK(efficient algorithm for single-linkage clustering in O(n2))

However, results are generally better with larger minPts!

Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4




DBSCAN is O(n2) (with index: O(n log n) only)

but this is for a single ε only.



Data MiningTutorial


Aufgabe 7-1


ε = 1.1minPts= 3

ε = 1.1minPts= 4

ε = 2.1minPts= 4

ε = 4.1minPts= 5

ε = 4.1minPts= 4




DBSCAN is O(n2) (with index: O(n log n) only)but this is for a single ε only.



Data Mining Tutorial - Session 5: Clustering · 2012. 6. 21. · Data Mining Tutorial E. Schubert,...

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Transcript of Data Mining Tutorial - Session 5: Clustering · 2012. 6. 21. · Data Mining Tutorial E. Schubert,...