  Our aim is to evaluate fundamental parameters from the analysis of the
electromagnetic spectra of stars. We may use $10^3$-$10^5$ spectra; each
spectrum being a vector with $10^2$-$10^4$ coordinates. We thus face the
so-called "curse of dimensionality". We look for a method to reduce the size of
this data-space, keeping only the most relevant information.As a reference
method, we use principal component analysis (PCA) to reduce dimensionality.
However, PCA is an unsupervised method, therefore its subspace was not
consistent with the parameter. We thus tested a supervised method based on
Sliced Inverse Regression (SIR), which provides a subspace consistent with the
parameter. It also shares analogies with factorial discriminant analysis: the
method slices the database along the parameter variation, and builds the
subspace which maximizes the inter-slice variance, while standardizing the
total projected variance of the data. Nevertheless the performances of SIR were
not satisfying in standard usage, because of the non-monotonicity of the
unknown function linking the data to the parameter and because of the noise
propagation. We show that better performances can be achieved by selecting the
most relevant directions for parameter inference. Preliminary tests are
performed on synthetic pseudo-line profiles plus noise. Using one direction, we
show that compared to PCA, the error associated with SIR is 50$\%$ smaller on a
non-linear parameter, and 70$\%$ smaler on a linear parameter. Moreover, using
a selected direction, the error is 80$\%$ smaller for a non-linear parameter,
and 95$\%$ smaller for a linear parameter.
