1 / 24

Version Space using DNA Computing

Version Space using DNA Computing. 2001.10.26 임희웅. Version Space(1). Version Space? Concept Learning Classifying given instance x Maintain a set of hypothesis that is consistent with the training examples Instance X described by the tuple of attributes Attributes Dept, {ee, cs}

storm
Télécharger la présentation

Version Space using DNA Computing

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Version Space using DNA Computing 2001.10.26 임희웅

  2. Version Space(1) • Version Space? • Concept Learning • Classifying given instance x • Maintain a set of hypothesis that is consistent with the training examples • Instance X • described by the tuple of attributes • Attributes • Dept, {ee, cs} • Status,{faculty, staff} • Floor,{four, five}

  3. Version Space(2) • Hypotheses H • Each hypothesis is described by a conjunction of constraints on the attributes • Ex) <cs, faculty> or <cs> • Target concept • X  {0, 1} • Training example D • <cs, faculty, four> + • <cs, faculty, five> + • <ee, faculty, four> - • <cs, staff, five> -

  4. Version Space(3) • Hypothesis that is consistent with training example  all combination of the attributes of the training example i.e. power set • Training example : <cs, faculty, four> • Consistent Hypothesis<cs, faculty, four>,<cs, faculty>, <cs, four>, <faculty, four><cs>, <faculty>, <four>

  5. ∧ cs ee faculty staff four five cs ∧ faculty cs ∧ staff ee ∧ faculty ee ∧ staff faculty ∧ four faculty ∧ five cs ∧ faculty ∧ four cs ∧ faculty ∧ five ee ∧ faculty ∧ four cs ∧ staff ∧ five Version Space(4)

  6. ∧ cs ee faculty staff four five cs ∧ faculty cs ∧ staff ee ∧ faculty ee ∧ staff faculty ∧ four faculty ∧ five cs ∧ faculty ∧ four cs ∧ faculty ∧ five ee ∧ faculty ∧ four cs ∧ staff ∧ five + <cs, faculty, four>,<cs, faculty>, <cs, four>, <faculty, four><cs>, <faculty>, <four><>

  7. ∧ cs ee faculty staff four five cs ∧ faculty cs ∧ staff ee ∧ faculty ee ∧ staff faculty ∧ four faculty ∧ five cs ∧ faculty ∧ four cs ∧ faculty ∧ five ee ∧ faculty ∧ four cs ∧ staff ∧ five + – <cs, faculty, four>,<cs, faculty>, <cs, four>, <faculty, four><faculty>, <four>

  8. ∧ cs ee faculty staff four five cs ∧ faculty cs ∧ staff ee ∧ faculty ee ∧ staff faculty ∧ four faculty ∧ five cs ∧ faculty ∧ four cs ∧ faculty ∧ five ee ∧ faculty ∧ four cs ∧ staff ∧ five + – + <cs, faculty><faculty>

  9. ∧ cs ee faculty staff four five cs ∧ faculty cs ∧ staff ee ∧ faculty ee ∧ staff faculty ∧ four faculty ∧ five cs ∧ faculty ∧ four cs ∧ faculty ∧ five ee ∧ faculty ∧ four cs ∧ staff ∧ five + + – – <cs, faculty>

  10. Version Space using DNA Computing • Problem Definition • Attributes • Dept,{ee, cs} • Status,{faculty, staff} • Floor,{four, five} • Training example D • <cs, faculty, four> + • <cs, faculty, five> + • <ee, faculty, four> - • <cs, staff, five> -

  11. Encoding.1 • Attribute사이에 순서를 고려할 경우 각각의 attribute의 값들을 하나의 기본 DNA sequence로 표현하고 이러한 기본 DNA sequence들을 서로 다른 attribute에 속하는 sequence들 끼리 ligation 될 수 있도록 sticky end조건을 준다. • 이 경우 <cs, faculty>나 <faculty, four>와 같은 것은 생성되지만 <cs, four>는 생성되지 않는다.

  12. Encoding.2(1) • Attribute들 간의 순서를 고려하지 않을 경우 • Adleman 실험의 encoding을 이용 • Attribute value : vertex • Ligation of Attribute value : edge  Complete graph, Overhead

  13. cs ee four faculty staff five Encoding.2(2) Edge • Graph for All Hypothesis Vertex + Dummy strand for blunt end?

  14. cs four faculty Encoding.2(3) • Graph for Hypothesis that is consistent with <cs, faculty, four> Vertex Edge + Dummy strand for blunt end?

  15. Encoding.2(4) • 앞의 과정을 통해서 생성된 double strand를 그대로 사용하지 않고 vertex 부분이 encoding된 single strand만을 추출하여 사용한다. • Single strand를 추출하는 과정은 각각의 attribute value에 해당하는 strand에 complementary 한 strand를 사용해서(bead?) 이루어 질 수 있다. • Why only single strand? •  hybridization을 이용한 교집합 연산을 위해 •  Hypothesis strand에 존재하는 attribute에 대해서 순서를 주었음

  16. Dept Bead Status Floor + 각각의 attribute에 해당하는 dummy sequence Encoding.3(1) • Bead의 이용 • 앞의 Adleman의 encoding방법을 사용하는 것보다 훨씬 적은 수의 sequence가 필요함 • 또한 가능한 모든 hypothesis를 한꺼번에 생성할 수도 있고 특정한 example에 대해서 consistent한 모든 hypothesis를 모두 생성할 수도 있음

  17. Encoding.3(2) • Problem!! • Hypothesis들의 증폭은 어떻게 할 것인가?

  18. Detection(1) – Encoding.2 • 1. Tube1(0) •  first traning example(positive라고 가정)에 대해서 그와 consistent한 모든 hypothesis • 2. 다음 example들에 대해 각각 다음의 작업을 수행한다. • Tube2 •  example과 consistent한 모든 hypothesis • Positive일 경우 • Tube1(n+1) = Tube1(n) ∩ Tube2 • Negative일 경우 • Tube1(n+1) = Tube1(n) - Tube2

  19. Detection(2) – Encoding.2 • Implementation of ‘∩’operation • 최초의 Tube1(0)는 앞서 encoding.2 에서 제안한대로 생성한다.(single strand) • 이후의 example에 대해 생성되는 모든 Tube2는 tube1(0)과 encoding을 complementary하게한다.(single strand) • Tube2를 Tube1에 넣어 hybridization시켜 서로 완전히 결합한 double strand만을 뽑아낸다. • 앞의 결과물을 denature시켜 최초의 Tube1(0)과 같은 방향으로 encoding된 한쪽 single strand만을 다시 추출해낸다.

  20. Detection(3) – Encoding.2 • Implementation of ‘-’operation • How? =_=; • Complement Set과의 ‘∩’ operation? • Another encoding for negative example?

  21. Detection(4) – Encoding.2 • Problem • Strand들의 증폭이 필요하다면?

  22. Detection – Encoding.3 • Bead를 이용한 encoding의 경우 • How? =_=; • ‘∩’, ‘-’ • 증폭

  23. Application • 실제 input이 들어왔을 때 Classification을 어떻게 할 것인가? • Voting?

  24. Reference on Version Space • Machine Learning, T.M. Mitchell, McGraw Hill • Artificial Intelligence-Theory and Practice, Dean, Addison-Wesley

More Related