directions along which the between variables correlation is maxi-
mal. This implies the projection of the original data set into a
reduced dimensionality space spanned by the major (i.e., having
the higher eigenvalues) components allows us to maximize the
probability of concentrating on the meaningful part of the infor-
mation. In some (very general) sense, a PCA solution corresponds
to an explanatory model of the system at hand [10], but this is only
the beginning of the game, the search for “systems parameter” does
not end with PCA.3 “Subjective” Judgment
PCA, even being the by far more common method to generate a
meaningful synthesis from complex multidimensional data, is not
an obliged way for modeling. The peculiar features of biological
information must be taken into account in order to define a realistic
notion of “systems parameters” (and consequently of what can be
considered a satisfactory explanation of a phenomenon).
Biological data are unescapably discrete: we face a numerable
set of independent vectors, each corresponding to a specific obser-
vation (animal, person, cell sample, etc.) and we are asked to find
some kind of regularities among these discrete events.
This fact both imposes a completely new perspective with
respect to the prevalent style of thought in mathematical modeling
that considers the sketching of a continuous differential equation as
the “paradigmatic form” of a scientific analysis of a phenomenon
and creates a totally new concept of “what is in common” among
different research fields.PjP Pi
4PnP 3P 2
p P^1(^1) p
2
p 3
p 4
pn
Fig. 2The least-square estimation in PCA has as reference point the component (left panel) and the distances
of the observed values from their estimates refer to the bi-dimensional space. In classical regression
procedures (right panel), the neat separation between independent and dependent variables implies the
distances to be minimized refer to theY(dependent variable) axis
Parameters Search 61