http:// link.springer.com - PowerPoint Presentation

Slide1

http://

link.springer.com/article/10.1007%2Fs00454-004-1146-y

A

filtered complex is an increasing sequence of simplicial complexes: C0 C1 C2 …

U

U

USlide2

a, b is in

C0

C1 C

2 … C5{a, b, c} is in C4 C5

0

0

0

U

U

U

2

2

U

0

U

http://

link.springer.com

/article/10.1007%2Fs00454-004-1146-y

A

filtered complex

is an increasing sequence of simplicial complexes: C

0

C

1

C

2

…

U

U

USlide3

Filtered complex from data points:Slide4

Filtered 1d-complex from data points:Slide5

Filtered Rips complex from data points:Slide6

A

filtered complex is an increasing sequence of simplicial complexes: C

0 C

1 C2 …U

U

USlide7

Barcode for H

0

H

0 = Z0/B

0 =

cycles

boundariesSlide8

Barcode for

H

1

H1 = Z1

/B1

= cycles

boundariesSlide9

Barcode for

H

2

H2 = Z2

/B2

= cycles

boundariesSlide10

Computing Persistent Homology by

Afra

Zomorodian,

Gunnar Carlssonhttp://link.springer.com/article/10.1007%2Fs00454-004-1146-y

H

k

=

Z

k

/

(

B

k

Z

k

)

i

, p

i+p

i

i

USlide11
Slide12