# How to build a mean prototype from data

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.

• 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 Feb 26 '16 at 16:31