Sequences ii
Download
1 / 16

Sequences II - PowerPoint PPT Presentation


  • 101 Views
  • Uploaded on

Sequences II. Prof. Noah Snavely CS1114 http://cs1114.cs.cornell.edu. Administrivia. Assignments: A5P2 due on Friday Quiz Tuesday, 4/24 Final project proposals due on CMS by this Thursday. Google’s PageRank. H. Start at a random page, take a random walk. Where do we end up?. A. E. I.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Sequences II' - byrd


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Sequences ii

Sequences II

Prof. Noah Snavely

CS1114

http://cs1114.cs.cornell.edu


Administrivia
Administrivia

  • Assignments:

    • A5P2 due on Friday

  • Quiz Tuesday, 4/24

  • Final project proposals due on CMS by this Thursday


Google s pagerank
Google’s PageRank

H

Start at a random page, take a random walk. Where do we end up?

A

E

I

D

B

C

F

J

G


Google s pagerank1
Google’s PageRank

H

Add 15% probability of moving to a random page. Now where do we end up?

A

E

I

D

B

C

F

J

G


Google s pagerank2
Google’s PageRank

H

PageRank(P) = Probability that a long random walk ends at node P

A

E

I

D

B

C

F

J

G


Sequences ii

Example

(The ranks are an eigenvector of the transition matrix)


Modeling texture
Modeling Texture

  • What is texture?

    • An image obeying some statistical properties

    • Similar structures repeated over and over again

    • Often has some degree of randomness


Markov random field

A

D

X

B

C

  • Higher order MRF’s have larger neighborhoods

*

*

*

*

*

*

*

*

X

*

*

*

X

*

*

*

*

*

*

*

*

*

Markov Random Field

  • A Markov random field (MRF)

    • generalization of Markov chains to two or more dimensions.

  • First-order MRF:

    • probability that pixel X takes a certain value given the values of neighbors A, B, C, and D:


Texture synthesis efros leung iccv 99
Texture Synthesis [Efros & Leung, ICCV 99]

  • Can apply 2D version of text synthesis


More synthesis results
More Synthesis Results

  • Increasing window size


More results
More Results

  • aluminum wire

  • reptile skin



Author recognition
Author recognition

  • Simple problem:

    Given two Markov chains, say Austen (A) and Dickens (D), and a string s (with n words), how do we decide whether A or D wrote s?

  • Idea: For both A and D, compute the probability that a random walk of length n generates s


Probability of a sequence
Probability of a sequence

  • What is the probability of a given n-lengthsequence s?

    s = s1 s2 s3 … sn

  • Probability of generating s = the product of transition probabilities:

Probability that a sequence starts with s1

Transition probabilities


Likelihood
Likelihood

  • Compute this probability for A and D

Jane Austen wrote s

“likelihood” of A

Charles Dickens wrote s

“likelihood” of D

???


Problems with likelihood
Problems with likelihood

  • Most strings of text (of significant length) have probability zero

    • Why?

  • Even if it’s not zero, it’s probably extremely small

    • What’s 0.01 * 0.01 * 0.01 * … (x200) … * 0.01?

    • According to Matlab, zero

  • How can we fix these problems?