– Why is order important?

(1)

• Exercise 1.1+1.2

– Linearization

– Why is order important?

6. Optimization

1 1 3 6 47

2 2 53

7 8 89

6 4

9 11 11 16 1217

10 12 1313

15 18 1619

14 14

17 5 19 10 25 15 27 20

Jan (1) Feb(2) Feb(3) Feb(4)

D₁ D₂

(2)

• Exercise 2. a

6. Optimization

R1 R3

R5

08 Qtr3 08 Qtr4 09 Qtr1

Time

R

R1 R3

08 Qtr4 R5

09 Qtr1

Time

R

R4

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3

Location

a b c d e f g

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3

a b c d e f g

R41 R42

(3)

• Exercise 2. a

6. Optimization

R1 R3

08 Qtr4 R5

09 Qtr1

Time

R

R1 R3

08 Qtr4 R5

09 Qtr1

Time

R

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3

a b c d e f g

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3

a b c d e f g

R41 R42

(4)

• Exercise 2. a

6. Optimization

R1 R31

08 Qtr4 R5

09 Qtr1

Time

R

R1 R3

08 Qtr4 R5

09 Qtr1

Time

R

R32

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3

a b c d e f g

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3

a b c d e f g

R41 R42 R41 R42

(5)

• Exercise 2. a

6. Optimization

R1 R5

08 Qtr4 09 Qtr1

Time

R

D

C ^R31

R5

08 Qtr3 08 Qtr4 09 Qtr1

Time

R

R32 R12

R11

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3

a b c d e f g

A B

On X, highest minimum rectangles are B and D = ‘b’, and lowest maximum are A and C = ‘a’

On Y, highest minimum rectangle is D = ’09Qtr1’, and lowest maximum is A = ’08Qtr2’

Dx = 1/3; Dy = 3/5; => D and A will create the new split nodes

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3

a b c d e f g

R41

R42

(6)

• Exercise 2. b

6. Optimization

R11 R2

R

R12

R31 R41

R31.1 R31.2 R41.1 R41.2 R5.3 R6.2 R6.3

R32 R42 R5 R6

R5.2

R5.1 R6.1

(7)

• Exercise 2. c

6. Optimization

R31

08 Qtr4 09 Qtr1

Time

R

R32 R12

R11

R5

R6 R2

08 Qtr1 08 Qtr2 08 Qtr3 08 Qtr4

a b c d e f g

R41

R42

(8)

• Exercise 2. c

6. Optimization

R11 R2

R

R12

R31 R41

R31.1 R31.2 R41.1 R41.2 R5.3 R6.2 R6.3

R32 R42 R5 R6

R5.2

R5.1 R6.1

(9)

• Exercise 3.1

– UB-Trees

6. Optimization

Data part

8 17

8 17 3939 5151 28

28

(10)

• Exercise 3.1

– Multidimensional Hierarchical Clustering (MHC)

6. Optimization

Sector Brown Goods White Goods

ALL

0 1

Sector Brown GoodsBrown Goods White GoodsWhite Goods ALL

0 1

...

Product Group

Category Audio Video

Camcorder VCR

...

00 01

0 1

0000 0001 0000 0001 0010

...

Product Group

Category AudioAudio VideoVideo

Camcorder VCR

...

00 01

0 1

0000 0001 0000 0001 0010

(11)

• Exercise 3.2

– Multi-component BI:

• x = 4 *y+z, where 0 ≤ y ≤2, and 0 ≤z ≤3, called <3,4>

basis encoding

6. Optimization

Month Dec Nov Oct Sep Aug Jul Jun Mai Apr Mar Feb Jan

x = 4 *y+z, where 0 ≤ y ≤2, and 0 ≤z ≤3, called <3,4>

basis encoding

• 5 = 4*1+1

M A₁₁ A₁₀ A₉ A₈ A₇ A₆ A₅ A₄ A₃ A₂ A₁ A₀

5 0 0 0 0 0 0 1 0 0 0 0 0

X Y Z

M A_2,1 A_1,1 A_0,1 A_3,0 A_2,0 A_1,0 A_0,0

5 0 1 0 0 0 1 0

(12)

• Exercise 3.2

– Range encoded BI

6. Optimization

M A₁₁ A₁₀ A₉ A₈ A₇ A₆ A₅ A₄ A₃ A₂ A₁ A₀

0 1 1 1 1 1 1 1 1 1 1 1 1

– Persons born in March: ((NOT A

₁

) AND A

₂

)

0 1 1 1 1 1 1 1 1 1 1 1 1

3 1 1 1 1 1 1 1 1 1 0 0 0

5 1 1 1 1 1 1 1 0 0 0 0 0

11 1 0 0 0 0 0 0 0 0 0 0 0