Question

Assuming we have two circles of a radius of 0.5, in which data points in the ground set v are uniformly distributed, we wish to select 2 data points from the ground set that maximize the exemplar clustering function. What is the objective of this clustering function?

a) Minimize the sum of distances between selected data points
b) Maximize the sum of distances between selected data points
c) Maximize the sum of similarities between selected data points
d) Minimize the sum of similarities between selected data points

Answer 1

The exemplar clustering function aims to maximize the sum of distances between selected data points, especially when data points are uniformly distributed across two circles. In such a case, the mean is usually the most appropriate measure of center.

Step-by-step explanation:

The objective of the exemplar clustering function, given that we want to maximize it, would be to maximize the sum of distances between selected data points. Clustering functions typically work to group similar points together, so in a scenario where we want to maximize an exemplar clustering function, it can be understood that we are looking to select points that are as spread out as possible, thus making the sum of distances between them as large as possible.

When examining the shape of the data as per the additional context (i.e., uniformly distributed in two circles of a radius of 0.5), if the data are uniformly distributed then looking at the sum of similarities might not give a meaningful measure as all points would have similar distances to each other. The most appropriate measure of center for uniformly distributed data which don't have skewness or outliers would typically be the mean, as it would provide the central value around which the data is spread.