These attributes are all numerical, but can have widely varying ranges of values, depending on the scale used to measure them. Furthermore, the attributes are not asymmetric and the magnitude of an attribute matters. These latter two facts eliminate the cosine and correlation measure. Eu- clidean distance, applied after standardizing the attributes to have a mean of 0 and a standard deviation of 1, would be appropriate.These attributes are all numerical, but can have widely varying ranges of values, depending on the scale used to measure them. Furthermore, the attributes are not asymmetric and the magnitude of an attribute matters. These latter two facts eliminate the cosine and correlation measure. Eu- clidean distance, applied after standardizing the attributes to have a mean of 0 and a

(a) We randomly select n ? mi/m elements from each group.
(b) We randomly select n elements from the data set, without regard for
the group to which an object belongs.

The first scheme is guaranteed to get the same number of objects from each
group, while for the second scheme, the number of objects from each group
will vary. More specifically, the second scheme only guarantes that,