  Consider observation data, comprised of n observation vectors with values on
a set of attributes. This gives us n points in attribute space. Having data
structured as a tree, implied by having our observations embedded in an
ultrametric topology, offers great advantage for proximity searching. If we
have preprocessed data through such an embedding, then an observation's nearest
neighbor is found in constant computational time, i.e. O(1) time. A further
powerful approach is discussed in this work: the inducing of a hierarchy, and
hence a tree, in linear computational time, i.e. O(n) time for n observations.
It is with such a basis for proximity search and best match that we can address
the burgeoning problems of processing very large, and possibly also very high
dimensional, data sets.
