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I have a dataset with physiological measures of subjects along time. I would like to create (or select) a mean prototype example in order to be able to identify in new examples how far are they from the mean prototype. A second issue will be to select a threshold to determine what is considered near or far. Each example has 20 numeric features and I have around 300 examples per subject.

First ideas (disregarding outliers):

  • To iterate through all the examples of a subject and find the one who has the minimum mean distance to all the other examples. This will select a specific example from the dataset.
  • To use an evolutionary algorithm to find a prototypical example which has the lowest mean distance to all the other examples. This will create a new example that can be used as prototype.

Now I would like to determine when a new example is close, far or very far from the prototype (mean). A possible approach is to set two thresholds distance to determine to which class or case corresponds the new example (close, far or very far). How could I determine these thresholds? Possibly using number of standard deviations? What other approaches can be followed to perform all this?

Let's assume the distance metric is already selected.

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  • $\begingroup$ When iterating, you can take advantage of symmetry: $d(V_1,V_2)=d(V_2,V_1)$. That results in half the calculations. You calculate $n*(n-1)$ distances, accumulate them in a vector $\endgroup$
    – Juan Leni
    Feb 26 '16 at 16:31
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The object with the lowest mean distance (= the object with the lowest distance sum) is known as the medoid and the basis of k-medoids algorithms such as PAM. Because you must not use k-means with arbitrary distances.

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  • $\begingroup$ Interesting approach, particularly because its fast, however since its dependent on initialization it requires to be ran multiple times. I have found in literature references on Affinity Propagation. Do you know this method? Would you recommend it for this task? vision.jhu.edu/assets/ElhamifarNIPS12.pdf $\endgroup$
    – Javierfdr
    Feb 27 '16 at 17:59
  • $\begingroup$ I tried it (in ELKI, I think I tried all of them multiple times) but it did not work well for me. But every data is different. $\endgroup$ Feb 27 '16 at 19:35
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For your prototype: for each time segment t1-t300, for each feature f1-f20, compute the mean feature value across subjects s1-sn. This is your prototype subject about which you can compute a confindence interval set to your target threshold (e.g, 95%) or set a threshold to +/- Nsd depending upon your definition of an outlier.

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  • $\begingroup$ This is not correct for every possible metric $\endgroup$
    – Juan Leni
    Feb 26 '16 at 20:36

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