A data-driven functional projection approach for the selection of feature ranges in spectra with ICA or cluster analysis

Prediction problems from spectra are largely encountered in chemometry. In addition to accurate predictions, it is often needed to extract information about which wavelengths in the spectra contribute in an effective way to the quality of the prediction. This implies to select wavelengths (or wavelength intervals), a problem associated to variable selection. In this paper, it is shown how this problem may be tackled in the specific case of smooth (for example infrared) spectra. The functional character of the spectra (their smoothness) is taken into account through a functional variable projection procedure. Contrarily to standard approaches, the projection is performed on a basis that is driven by the spectra themselves, in order to best fit their characteristics. The methodology is illustrated by two examples of functional projection, using Independent Component Analysis and functional variable clustering, respectively. The performances on two standard infrared spectra benchmarks are illustrated.Comment: A paraitr

The halo masses and galaxy environments of hyperluminous QSOs at z~2.7 in the Keck Baryonic Structure Survey

We present an analysis of the galaxy distribution surrounding 15 of the most luminous (>10^{14} L_sun; M_1450 ~ -30) QSOs in the sky with z~2.7. Our data are drawn from the Keck Baryonic Structure Survey (KBSS). In this work, we use the positions and spectroscopic redshifts of 1558 galaxies that lie within ~3', (4.2 h^{-1} comoving Mpc; cMpc) of the hyperluminous QSO (HLQSO) sightline in one of 15 independent survey fields, together with new measurements of the HLQSO systemic redshifts. We measure the galaxy-HLQSO cross-correlation function, the galaxy-galaxy autocorrelation function, and the characteristic scale of galaxy overdensities surrounding the sites of exceedingly rare, extremely rapid, black hole accretion. On average, the HLQSOs lie within significant galaxy overdensities, characterized by a velocity dispersion sigma_v ~ 200 km s^{-1} and a transverse angular scale of ~25", (~200 physical kpc). We argue that such scales are expected for small groups with log(M_h/M_sun)~13. The galaxy-HLQSO cross-correlation function has a best-fit correlation length r_0_GQ = (7.3 \pm 1.3) h^{-1} cMpc, while the galaxy autocorrelation measured from the spectroscopic galaxy sample in the same fields has r_0_GG = (6.0 \pm 0.5) h^{-1} cMpc. Based on a comparison with simulations evaluated at z ~ 2.6, these values imply that a typical galaxy lives in a host halo with log(M_h/M_sun) = 11.9\pm0.1, while HLQSOs inhabit host halos of log(M_h/M_sun) = 12.3\pm0.5. In spite of the extremely large black hole masses implied by their observed luminosities [log(M_BH/M_sun) > 9.7], it appears that HLQSOs do not require environments very different from their much less luminous QSO counterparts. Evidently, the exceedingly low space density of HLQSOs (< 10^{-9} cMpc^{-3}) results from a one-in-a-million event on scales << 1 Mpc, and not from being hosted by rare dark matter halos.Comment: 15 pages, 6 figures. Accepted for publication in Ap