The general distance function

[andreastausend]

The general distance function consists of two parts. The first part is a list of marginal distance functions that allows to compare different types of findings. The second part is a list of weights for the aggregation of the marginal distances to the general distance function. Consider the following example:

set(user1) =(a1,b1,c1)
et(user2)=(a2,b2,d2)

Each letter a,b,... corresponds to a type of finding. Note that the profile of user1 contains a type of finding that is not featerd by that of user2 and vice versa (c1 and d2). To ease understanding and presentation the following notation seems more adequate

set(user1) =(a1,b1,c1,{})
set(user2)=(a2,b2,{},d2)

Given the marginal distance functions and the weights the general distance is computed as follows

gdist(user1,user2)=(waa mdist(a1,a2)+ wab ndist(a1,b2)+ wa{} +wad mdist(a1,d2)+...+(waa+wab+wa{}+wad+...)

mdist(.,.) represents the marginal distances between two types of findings. waa, wab, etc. denote the positive weights. Note that the marginal distance between any classifies and an empty classifies {} is always one. The apropriate marginal distance for two types of findings is assumed to be selcted by mdist(.,.). The resulting sum is divided by the sum of the weights to ensure that the scale of general distances remains comparable over different subsets of findings. The maximal value for a marginal distance is 1, such that 1 is also the maximal possible general distance between two users.

An important challange to find a distance function that also addresses the time dynamic of the medical consitiutions of users.