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Radial visualization & spring forces

  1. Apr 7, 2008 #1

    jst

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    Hi, I am taking a Data Mining course and have this problem in radial visualization. To complete this problem, we use some physics formulas, which I really do not understand.

    Derive formulas for radial visualization of:

    a. 3-dimensional samples

    b. 8-dimensional samples

    2. Relevant equations

    Here's what our notes have:
    [​IMG]

    3. The attempt at a solution

    I thought it would be very similar to the example in the notes so for part A I did:

    x = (K1 - K3 - K5 - K7)/(K1 + K2 + K3 + K4 + K5 + K6 + K7 + K8)
    y = (K2 - K4 - K6 - K8)/(K1 + K2 + K3 + K4 + K5 + K6 + K7 + K8)

    and part B, I did:

    x = (K1 - K3)/(K1 + K2 + K3)
    y = (K2)/(K1 + K2 + K3)

    I am told: "sqrt (2)/2, or sqrt(3)/2 or 1/2 are in the final expressions because of trig functions: sin and cos for angles of 30, 45 or 60 degrees."

    I'm really lost, our book doesn't have what I need it sort of assumes that this example was enough, but I'm lost. I really don't need the solution, as much as an explanation of how to do it myself.

    Thanks a lot,

    Jason
     
    Last edited: Apr 7, 2008
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