Suitably representing data

Abstract

We may organize the search for the metric d at the basis of the cost functionl ℓ into two main steps: search for a sound representation of the data and use of a metric appropriate to the representation. The term sound stands for a representation allowing to better understanding the data, for instance by decoupling original signals, removing noise, discarding meaningless details, and alike. The result of the splitting could prove less efficient than the direct metric, but more manageable in most cases. Essentially, we are looking for rewriting the metric instances d(yi, yj) as a composition, d′ (g(yi),g (yj) with g optimizing the cost function C, namely: g = arg maxg̃ C[g̃] = arg maxg̃ {∑y∈∑j=ik ℓ [D(g̃)(y)),dj]}. (7.1) © 2008 Springer-Verlag Berlin Heidelberg.