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Math Help - Measure "belongingness" to point clouds

  1. #1
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    Smile Measure "belongingness" to point clouds

    I have several "point clouds" in XYZ-space. Each point in these clouds have a certain identity (i.e. these points represent Charlie and those points represent Anna).

    Now a new point appears without its identity known beforhand. I want to know which cloud it "belongs to", for exampel as in which cloud is the closest. How should I do?

    The clouds are not spherical, but often elongated and bent. This means that average distance to the points in each cloud is not a good measure of likely "belonging".

    One idea would be to "encapsulate" each cloud and then measure the distance from the new point to the closest point on the surface of each capsule. I could do it manually/intuitively with fairly good result, but how to do it mathematically in a programmable way? Also, it would be a nice-to-have to consider also the density of different parts of each cloud, and to ignore or down-weight outliers.

    Any ideas are welcome, even name dropping of methods which could be of interest, since I dont even know what to call this problem...
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Optiminimal View Post
    I have several "point clouds" in XYZ-space. Each point in these clouds have a certain identity (i.e. these points represent Charlie and those points represent Anna).

    Now a new point appears without its identity known beforhand. I want to know which cloud it "belongs to", for exampel as in which cloud is the closest. How should I do?

    The clouds are not spherical, but often elongated and bent. This means that average distance to the points in each cloud is not a good measure of likely "belonging".

    One idea would be to "encapsulate" each cloud and then measure the distance from the new point to the closest point on the surface of each capsule. I could do it manually/intuitively with fairly good result, but how to do it mathematically in a programmable way? Also, it would be a nice-to-have to consider also the density of different parts of each cloud, and to ignore or down-weight outliers.

    Any ideas are welcome, even name dropping of methods which could be of interest, since I dont even know what to call this problem...
    This is a classification problem and you should look up the literature on that.

    One method that could possibly work is to use the clouds you have to
    estimate the pdf of C-points and A-points, then use something like the
    likelyhood ratio derived from these pdf's as indicative of which class a
    new point is likely to belong to.

    One way of estimating the pdf could be to use Kernel Density Estimation
    (routines to do this are included with the Matlab distribution I believe
    and if not included are freely available).

    RonL
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