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Support Vector Machine basics

  1. Dec 28, 2011 #1
    1. The problem statement, all variables and given/known data

    If I have a 3*3 grid, or 3*3 matrix, which records clicked points.
    I.e.

    Pattern T =

    [1,1] = 1
    [1,2] = 1
    [1,3] = 1
    [2,1] = -1
    [2,2] = 1
    [2,3] = -1
    [3,1] = -1
    [3,2] = 1
    [3,3] = -1

    or

    1 1 1
    -1 1 -1
    -1 1 -1

    What is the best way to statistically match x = 1 vs x = not 1
     
    Last edited by a moderator: Dec 28, 2011
  2. jcsd
  3. Dec 28, 2011 #2

    Mark44

    Staff: Mentor

    What do you mean "statistically match"?
     
    Last edited: Dec 28, 2011
  4. Dec 28, 2011 #3
    I.e.

    A new sequence is entered and we wish to identify group membership to T or C based on sample data for T and C. SInce T and C won't necessarily consist of 2 example database( 1 for each) but rather 1000 for T and 1000 C examples, how does one accurately calculate a match?
     
    Last edited by a moderator: Dec 28, 2011
  5. Dec 28, 2011 #4

    Mark44

    Staff: Mentor

    I still don't have a clue what you're trying to do.
     
    Last edited: Dec 28, 2011
  6. Dec 28, 2011 #5
    My question is related to optical character recognition. So if I draw a T, how do I match it to T that accurately reflects the entire training data?

    I.e. if I have pattern T1, pattern T2, .., are the sequences for n T's.
    C1, C2,..,CN is C training points for n C's.

    If I feed a single C sequence in now, how do I weigh my decision most accurately?
     
    Last edited by a moderator: Dec 28, 2011
  7. Dec 28, 2011 #6

    Mark44

    Staff: Mentor

    OK, now I understand. At the risk of oversimplification, let me define T this way:
    Pattern T =

    1 1 1
    0 1 0
    0 1 0

    To match this pattern, a candidate pattern A should have a distance of 0 from this pattern, with distance calculated as
    [tex]\sqrt{(a_0 - t_0)^2 + (a_1 - t_1)^2 + (a_2 - t_2)^2 + ... + (a_8 - t_8)^2}[/tex]

    In this formula I have flattened out your matrix to a one-dimensional array. The ti values are from pattern T, and the ai values are from the candidate pattern A.

    If you get a "distance" of 0, the two patterns match exactly. If you have several candidate patterns with nonzero distances, pick the one with the smaller "distance."

    That's how I would approach it.
     
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